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Role of Physics is Critical in Gymnastic

Gymnastic is, undoubtedly, one of the most interesting sports to watch in the Olympics. This support will require an athlete to push the very limits of balance, technique, and strength. Besides, gymnastic, to very extent, hinges upon the laws of physics and a gymnast would require to push the limits of physics as well. The concepts of physics involved in gymnastics are; twisting torque, constant angular momentum, zero angular momentum twist, moment of inertia, and law of gravitation ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"Z2Y8eSrT","properties":{"formattedCitation":"(Sands)","plainCitation":"(Sands)","noteIndex":0},"citationItems":[{"id":1177,"uris":["http://zotero.org/users/local/jsvqEXt1/items/E55JSYJE"],"uri":["http://zotero.org/users/local/jsvqEXt1/items/E55JSYJE"],"itemData":{"id":1177,"type":"article-journal","title":"Why gymnastics","container-title":"Technique","page":"1–11","volume":"19","issue":"3","source":"Google Scholar","author":[{"family":"Sands","given":"William A."}],"issued":{"date-parts":[["1999"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Sands). Moreover, the physics of gymnastics wholly spins around the mass of gymnast in motion. The essay will discuss the applicability of physics in the sport of gymnastics.

Not only the twisting is involved in gymnastic but also the flipping, and the direction of the rotation plays a pivotal role in flipping and twisting coupled with the speed of the rotation. In rotational motion, linear velocity changes into angular velocity and conventionally the angular velocity follows the axis of rotation. Right-hand rule delineates the direction of the vector of angular velocity i.e. when someone curls fingers in the direction of motion the direction of erected thumb will be pointed towards the angular velocity vector ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"m3rTTTcF","properties":{"formattedCitation":"(Yeadon)","plainCitation":"(Yeadon)","noteIndex":0},"citationItems":[{"id":1178,"uris":["http://zotero.org/users/local/jsvqEXt1/items/G6R6XXPB"],"uri":["http://zotero.org/users/local/jsvqEXt1/items/G6R6XXPB"],"itemData":{"id":1178,"type":"article-journal","title":"The physics of twisting somersaults","container-title":"Physics World","page":"33","volume":"13","issue":"9","source":"Google Scholar","author":[{"family":"Yeadon","given":"Fred"}],"issued":{"date-parts":[["2000"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Yeadon). In order to understand twisting in gymnastic there is a little bit more physics. First, the torque is involved which is not only a rotational force but also a vector quantity. The angular momentum that a gymnast gain during twisting and flipping depends on the net value of torque generated during the motion ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"iaXSxBpy","properties":{"formattedCitation":"(Hodgins and Raibert)","plainCitation":"(Hodgins and Raibert)","noteIndex":0},"citationItems":[{"id":1180,"uris":["http://zotero.org/users/local/jsvqEXt1/items/DJB3DDG4"],"uri":["http://zotero.org/users/local/jsvqEXt1/items/DJB3DDG4"],"itemData":{"id":1180,"type":"article-journal","title":"Biped gymnastics","container-title":"Dynamically Stable Legged Locomotion","page":"79","source":"Google Scholar","author":[{"family":"Hodgins","given":"Jessica"},{"family":"Raibert","given":"Marc H."}],"issued":{"date-parts":[["1988"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Hodgins and Raibert). If the second condition of equilibrium satisfies during the motion i.e. net torque = 0 then the motion of the gymnast can be expressed with angular momentum principle.

There is another special case i.e. if a gymnast starts with no rotation at all. In such a case, if there is a change in moment of inertia tensor, will not influence the gymnast’s position. However, this is only a trick that a gymnast uses to get herself to rotate. The key for such a move is to rotate part of the body in one direction and part of the body in opposite direction. Both torques will cancel out each other, and hence no angular momentum.

Works Cited

ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY Hodgins, Jessica, and Marc H. Raibert. “Biped Gymnastics.” Dynamically Stable Legged Locomotion, 1988, p. 79.

Sands, William A. “Why Gymnastics.” Technique, vol. 19, no. 3, 1999, pp. 1–11.

Yeadon, Fred. “The Physics of Twisting Somersaults.” Physics World, vol. 13, no. 9, 2000, p. 33.

Subject: Physics

Pages: 1 Words: 300

Astronomy

1.           Which planet has the highest density?           Which planet has the lowest density?          Which planet gets closest to Earth?           Which planet is furthest from Earth?           Which planet has the highest surface temperature?          Which planet (other than Earth) has had the most number of space-based missions visit it?           Which planet has the largest moon?           Which planet has the highest mass?           Which planet has the lowest mass?           Which planet has the largest radius?           Which planet has the smallest radius?           Which planet has the strongest magnetic field?           Which planet receives the least sunlight?           Which planet has a moon with the thickest atmosphere?           Which planet has a moon with the largest fraction of the planet's mass?           Which planet has a moon with liquid nitrogen geysers?           Which planet has an axial tilt closest to 90 degrees?           Which planet rotates in an orientation that is closest to the opposite direction that it revolves around the Sun? 

2. Recall that speed is v=dtv=dt  where dd  is the distance traveled and tt  is the time it took to make the journey.

The fastest space probe humans have made traveled at 6×1046×104 kilometers per hour.

On average it takes 200 days to reach Mars.

What is the distance in kilometers that such a spacecraft would travel?

 

 

×10×10 

km

What is this same distance in light-minutes?

 light-minutes

Mars is, on average 20 light minutes away. Explain why this number is slightly larger than the number of light-minutes a spacecraft would travel to reach Mars.

LicensePoints possible: 1

3.                  First erupting volcanoes to be discovered outside of Earth were discovered on this moon.                 Largest subsurface ocean known containing more water than all the Earth's oceans.                 Largest moon in the Solar System.                 First moon in the Solar System discovered to have water geysers.                 Moon with the thickest atmosphere.

                 Only moon in the Solar System less dense than water.                 Moon with the greatest hemispheric contrast in albedo.                 Furthest cryogeysers discovered from the Sun were found here.                 Moon that is closest to the size of the main body it is orbiting.

Subject: Physics

Pages: 3 Words: 900

Car Project

Joyci Man

Professor

Course

10 April 2019

Title: Car Research Project

A number of dynamic forces act on the vehicle when it is driven. When the speed or direction of the vehicle is changed, force is first exerted on the car’s tires from where lateral, motive and braking forces are further transmitted to the vehicle’s system, determining the overall dynamic forces acting upon it. The paper will discuss and analyze the maximum torque that a 1997 Automatic transmission Toyota Corolla could exert on standard size tires, along with the forces acting on the road, and the acceleration and RPM of the car.

Maximum Torque

In a car that is running at its peak horsepower RPM, its potential to accelerate would be highest, however, the potential to accelerate is even higher in the first gear. Thus, the maximum torque that a car can produce on its wheel would be a function of its gear ratio and differential ratio which determine the extent to which the engine’s torque gets transferred to the tires. Assuming the car runs under ideal conditions would rule out the possibility of drag, friction, or slips in the clutch or torque converter systems, and thus it is assumed that the differential and the gearbox receive all of the engine's torque without loss. In a 1997 corolla which uses an automatic transmission, a clutch-closed, lock-up torque converter is used. The torque exerted on the gearbox Tg is, therefore, a product of the engine torque Te and the gear ratio at the time ix.

The torque at the gearbox Tg applies to the differential as it is transmitted to the axle by the propeller shaft. The differential Torque Td would be a product of the final drive ration i0 and the gearbox Torque Tg. Furthermore, the differential Torque Td splits between the two front tires, assuming equal RMP under ideal conditions and that the car is not turning. The torque at any wheel, left or right, would thus be half of Td, thus Tw = Td/2. As the various functions defined above are combined, we can get the final form of Tw, which is the maximum torque exerted by the car on the tires or simply wheel torque, as:

Tw = (TE x Ix x Io)/2

The formula requires determining the final drive ratios and gear ratios to obtain the torque on each tire. The given torque Te at 110 ft-lb is likely to be the maximum torque that the engine can generate at peak horsepower RPM. The 7A-FE Engine comes in the automatic variant of the 1997 model, and ideally, the peak engine torque is obtained from a torque-RPM curve where the gradient becomes stable for varying RPM values. Here, Te is taken to be 110 ft-lb or 138 N.m

739775412115000

6178553116580Figure 1 - Torque vs RPM Graph of Toyota's 7A-FE Engine used in 1997 Corolla CITATION toy00 \l 1033 (toyoland)

Figure SEQ Figure \* ARABIC 1 - Torque vs RPM Graph of Toyota's 7A-FE Engine used in 1997 Corolla CITATION toy00 \l 1033 (toyoland)

In the first gear, the car is able to exert maximum torque on its wheels potentially compared to other shifts. Therefore, it is assumed that the car is moving under ideal conditions at 100% engine efficiency, without slippage, and in its first gear. The gear ratio of the 1997 automatic corolla in its first gear can be obtained from the manufacturer’s specifications. According to Corolland, the gear ratio in the 1st shift is i1 = 3.643:1 while the i0 = 2.821:1 for the final drive ratio CITATION Cor00 \l 1033 (Corolland). Therefore,

Tw = (TE x I1 x Io)/2

Tw = (138 x 3.643 x 2.821)/2

= 709.10 Nm

Maximum Force exerted on the road by the wheels

To calculate the force exerted by tires on the road requires the maximum torque on the wheels Tw along with the radius of the tire r. Torque is the product of the force applied on a lever arm, and in this case, Tw, the wheel torque, is assumed to apply on the exact geometric center of the wheel hub. The lever arm can thus be obtained from the radius of the wheel rw upon which the force is being applied as a result of the Torque. This assumption is based on the fact that under ideal conditions, there is no change in the dimensions of the tires as the car is moving and that the radius of both tires is exactly equal. Moreover, since both tires will experience the same Torque, therefore the resulting force Fw will be applied on both wheels equally, as a function of the tire's radius rw and the wheel torque on any given wheel, Tw.

Therefore Tw = Fw x rw

Or Fw = Tw/ rw

9645652519045Figure 2 - Torque acting on the wheel, gearbox and differential

Figure SEQ Figure \* ARABIC 2 - Torque acting on the wheel, gearbox and differential

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Since Tw was dependent on the final drive and gear ratios, the maximum force exerted by the tires too is a function of these values. According to Toyota’s specifications, the 1997 corolla with a standard tire size uses 175/65R14 81S tire size, which can be used to calculate the radius Rw CITATION Whe19 \l 1033 (Wheel Size). The radius is thus taken to be 0.291m

Fw = Tw/ Rw

= 709.10 x 0.291

= 206 N

Maximum acceleration

Using the value of the maximum force that was being exerted on the road by the tires, fw, the acceleration of the car, aw, can also be determined as the car moves along a straight line in the first gear. Under ideal conditions, it is assumed that other dynamic forces and resistances being exerted on the vehicle such as the friction force, slippage, slope of the road, or the aerodynamic drag, can be ignored. For any given car, the acceleration of the vehicle depends on the total number of resistance forces acting on it that are subtracted by the maximum force it is able to exert Fw. As force is the product of mass and acceleration

∑Fw - ∑FR = m.a

Assuming ideal conditions, we can safely ignore the ∑FR

Fw = m x aw

The mass of the vehicle is again obtained from Toyota's specifications of their model. In this case, the curb weight of the 97 corolla would be used as it represents the weight of the average number of passengers that are usually seated in the vehicle along with the weight of the actual car. The curb weight, m, for the model is 1045 kg CITATION Aut18 \l 1033 (Auto 123).

Therefore,

aw = Fw/m

= 206/1045 = 0.197 m/s2

RPM in 3rd gear, with vehicle speed 70mph

The given values of the vehicle along with the aforementioned manufacturer’s specifications and calculated values are:

ω= 9.5 v/r

v= 70mph = 312.29 m/s

r = 0.291m CITATION Whe19 \l 1033 (Wheel Size)

At 3rd gear at i3 = 1.296 CITATION Cor00 \l 1033 (Corolland)

And Io = 2.821 CITATION Cor00 \l 1033 (Corolland)

To calculate the RPM values from the velocity of the car, it is to be known that the gearbox’s primary function is to use its transmission ratios to modify the engine’s rpm. The power from the engine is transmitted via the output shaft to the drive train, where the final rpms are modified as a result of the final differential ratios i0 following the gear ratios ix. Moreover, every revolution of the tire of the car will move the car to a certain distance as a function of the circumference of the wheel. The final drive ratio i0. The total rpm produced by the engine is ωe will be reduced according to ix and io giving the final rpm at the tire ωt

ωt = ωe / (ix.io).

Since the distance travelled by car for each revolution is determined by the wheel's circumference, therefore the radius of the tire obtained from the manufacturer's specifications can be used to calculate its circumference.

The distance would thus be 2rw x ωt

Combining between the above functions, the final formula will be:

0.00595 x (ω * r) / (i3 * i0) = v (mph)

where 0.000595 serves as the multiplication factor derived for miles per hour)

at v = 70 mph or 31.29 m/s, the third gear i3 is engaged

I3 = 1.296:1

io = 2.821:1

r = 0.291

0.00595 x (ω * 0.291) / 3.656 = 31.29

0.297ω = 70*3.656

ω = 385 rpm

Works Cited

BIBLIOGRAPHY Auto 123. Technical Specifications 1997 Toyota Corolla SD. 2018. 12 March 2019. <https://www.auto123.com/en/new-cars/technical-specs/toyota/corolla/1997/base/sd/>.

Corolland. 1993-1997 Toyota Corolla (US-Spec): transmissions, driveshafts, and axles. 2000. 12 March 2019. <https://www.corolland.com/corolla/1993-1997/transmissions.html>.

toyoland. Toyota 4A-F and 7A-FE engines: details and photos. 2000. 13 March 2019. <https://www.toyoland.com/engines/4A-F.html>.

Wheel Size. Toyota Corolla 1997 Alloy wheel fitment guide US domestic market. 2019. 12 March 2019. <https://www.wheel-size.com/size/toyota/corolla/1997/>.

Subject: Physics

Pages: 4 Words: 1200

Car Research Project

Marty

Professor

Course

12 March 2019

Title: Car Research Project

As a vehicle is being driven, a number of dynamic forces are acting upon it. Any change in the direction or speed of the vehicle exerts forces on the tires first, which transmit braking, motive and lateral forces to the vehicle’s system, and thus determines the dynamic loads acting upon it. In this paper, the maximum torque which could be exerted on the tires by a 1997 Toyota corolla, and the forces that could be exerted by the tires on the road will be analyzed and discussed, along with the RPM and acceleration of the car during the process.

Maximum Torque Exerted by Car on Tires

When a vehicle is being driven, its acceleration reaches its highest potential at peak horsepower RPM. This holds true during all shifts except the first gear, since a higher acceleration is possible through downshifting except for the first gear. The torque being applied on the wheel is a function of the engine’s torque, the differential ratio and the gear ratio. Upon reaching torque peak, the vehicle is able to generate greater acceleration than any other point.

Under ideal conditions, there would be no slip in the torque converter or the clutch, and it is assumed that all of the engine’s torque is transferred to the gear box and the differential without losses, and thus the wheel torque is proportional to the engine torque and the gear ratios. The source of torque is the engine itself, while the torque converter in the 1997 corolla’s automatic transmission connects the engine to the gearbox. The torque converter is lock-up, clutch closed and experiences no slip. In this condition, the torque at the gearbox Tg is a function of the engaged gear ix and the engine torque Te.

The torque is transmitted through the propeller shaft to the axle. The torque at the differential Td, is the gearbox Torque, Tg multiplied by the final drive ratio io. Moreover, the engine power splits between the two front wheels of a front wheel drive car such as the 1997 Corolla. Assuming that the 2 wheels have equal RPM and the driven vehicle is moving in a straight line, the differential torque Td also splits equally into two for each wheel. Therefore, torque at the left wheel Tlw is the same as Torque on the right wheel Trw. It can be further deduced that maximum Torque at any wheel Tw will be half of differential Torque Td due to being further split.

Combining between the different functions of Td, Te, and Tg, the Maximum wheel torque Tw can be written as

Tw = (TE x Ix x Io)/2 (Combining between functions)

Since the given Engine torque of the vehicle Te = 110 ft-lb = 135.58 N.m

Therefore, the values of the gear ratio and final drive ratios must be determined in order to determine the maximum theoretical torque that could be exerted by the engine on the vehicle’s tire. Since the torque Tw is a function of the gear ratio as well as the peak engine torque Te, these values have to be obtained from the manufacturer’s specifications. Generally, manufacturers do not provide customers a complete torque curve, and thus the value of Te = 110 ft-lb is likely to be the maximum torque that the engine can generate at a certain engine speed or RPM. In a torque-RPM curve, this Te generally occurs when the gradient reaches a stable value for subsequent values of RPM.

6178553116580Figure SEQ Figure \* ARABIC 1 - Torque vs RPM Graph of Toyota's 7A-FE Engine used in 1997 Corolla CITATION toy00 \l 1033 (toyoland)

Figure SEQ Figure \* ARABIC 1 - Torque vs RPM Graph of Toyota's 7A-FE Engine used in 1997 Corolla CITATION toy00 \l 1033 (toyoland)

centertop00

Furthermore, the RPM of the car is inversely proportional to the torque of the car CITATION Iqb11 \l 1033 (Husain). Therefore, it follows that the maximum possible torque on the wheels will be exerted by the engine when the car moving along a straight line is in its first gear. Under ideal conditions, engine efficiency and slippage of tires and gears is ignored.

From Toyota’s manufacturer specifications, the gear ratio for the 1st gear in a 1997 automatic-transmission corolla is, i1 = 3.643:1, while the final drive ratio io = 2.821:1 CITATION Cor00 \l 1033 (Corolland).

Therefore,

Tw = (TE x I1 x Io)/2

Tw = (138 x 3.643 x 2.821)/2

= 709.10 Nm

Maximum Force exerted by tires on road

When the maximum wheel torque Tw being exerted by the engine on any given wheel is known, it is possible to calculate the maximum force that the tire is exerting on the road, when the tire radius r is known.

From the principles of mechanics and statics, it is known that the force applied on a lever arm length is the torque. In this case, the wheel torque Tw applies itself on the hub or center of the wheel. Therefore, the radius of the wheel rw will serve as the lever arm upon which the force is applied CITATION RNY14 \l 1033 (Yong, Fattah and Skiadas). It is assumed that in ideal conditions the radius of both wheels are equal and no change occurs in the tire’s dimensions while the vehicle is being driven in a straight line.

8496302676525Figure SEQ Figure \* ARABIC 2 - Torque acting on the wheel, gearbox and differential

Figure SEQ Figure \* ARABIC 2 - Torque acting on the wheel, gearbox and differential

849630343344500

The torque on the left wheel equals the torque on the right wheel Tlw = Trw with the same rw. It follows that the Force on the wheels, Fw will apply equally on both tires and can thus said to be a function of the overall wheel torque Tw and the radius of the wheel rw.

Tw = Fw x rw

The formula for the wheel force Fw can therefore be rewritten as

Fw = Tw / rw

Because Tw is dependent on the gear and final drive ratios, therefore the wheel force function is a function of the final drive ratio, the gearbox ratio, the actual engine Torque Te, and the raidus of the wheel. From the manufacturer’s specifications, the size of a standard tire on the 1997 corolla is 175/65R14 81S CITATION Whe19 \l 1033 (Wheel Size).

Therefore, the overall diameter dw is 22.95 inch = 0.5829m; the tire radius rw = 0.291m

Fw= Tw/ Rw

= 709.10 x 0.291

= 206 N

Maximum acceleration

When the maximum force Fw that the tire can exert on the road is known, the maximum acceleration aw of the car can be determined. However, while moving the car undergoes a number of resistances that exert force on the opposite direction, such as the aerodynamic drag force, friction force, rolling resistance, road’s slope, and slippage. However, it is assumed under ideal conditions that these resistance forces can be ignored.

Under normal circumstances the acceleration of the vehicle depends on the sum of the total resistance forces ∑FR being subtracted on the force being exerted Fw. Therefore to calculate the force or acceleration

∑Fw - ∑FR = m.a

Under ideal conditions, we remove the ∑FR so that the formula is reduced to:

Fw = m x aw

The mass of the vehicle can be obtained through the manufacturer’s specifications. The curb weight of the 1997 corolla is 1045 kg CITATION Aut18 \l 1033 (Auto 123). The curb weight represents the total weight of the car plus the average weight of an average number of passengers that are expected to be seated within the car.

aw = Fw/m

= 206/1045 = 0.197 m/s2

Since the goal is to determine the maximum acceleration, this can be achieved by either increasing the torque or the force exerted by the transmission and the engine, or decrease the overall weight of the car that has to be moved by the engine. The maximum torque on the wheel is directly proportional to the force being applied, therefore to achieve the highest acceleration would require the vehicle to move in certain RPMs under which a maximum torque is sustained. A car that has a more powerful engine will be able to maintain higher RPMs easily, thus its engine can perform more work at a quicker rate and produce higher torques at a larger range of RPMs (see Fig 1).

To determine, the maximum acceleration of two vehicles that are being compared, it is common to use their power to weight ratio. However, the torque of the car determines the ease at which the car can maintain a certain speed. Despite a higher power to weight ratio, there are certain RPMs at which torque is not at the peak, and thus the vehicle with the lower torque at a certain RPM will accelerate slower.

RPM to run engine at 70mph in 3rd gear

ω= 9.5 v/r

v= 70mph = 312.29 m/s

r = 0.291m CITATION Whe19 \l 1033 (Wheel Size)

For the 1997 corolla, the gear ratio 3rd gear at i3 = 1.296 CITATION Cor00 \l 1033 (Corolland)

and differential ratio is Io = 2.821 CITATION Cor00 \l 1033 (Corolland)

To determine the speed of a vehicle from the RPM or vice versa. It is important to understand that the transmission ratio in the gearbox acts to reduce the engine’s revolution. Similarly, the output shaft from the transmission which carries the engine’s power to the drive train has its revolutions reduced by the final gear ratio at the differential. Furthermore, each revolution that the wheel of the car makes, moves the vehicle at a distance which equals the tire’s circumference.

The transmission gear ration ix will be used to determine the engine revolution in RPM at the gearbox while the io will be used to determine the RPM at the axle. Therefore, the total engine RPM ωe will be reduced by the gear ratio ix and become ωg/ix RPM. While the RPM at the differential ωd will become ωg/io. Therefore, the total RPM of the tire wt will be ωe / (ix.io).

The distance that the car will move forward will be:

2rw x wt where rw is the radius of the car’s tire.

Combining between equations, the formula can be reduced to

0.00595 x (ω * r) / (i3 * i0) = v (mph) (multiplication factor for miles per hour)

Since the 3rd gear is used at v = 70 mph

I3 = 1.296:1

io = 2.821:1

r = 0.291

(ω * 0.000181) / 3.656 = 70

0.291ω = 70*3.656

ω = 879 rpm

Works Cited

BIBLIOGRAPHY Auto 123. Technical Specifications 1997 Toyota Corolla SD. 2018. 12 March 2019. <https://www.auto123.com/en/new-cars/technical-specs/toyota/corolla/1997/base/sd/>.

Corolland. 1993-1997 Toyota Corolla (US-Spec): transmissions, driveshafts, and axles. 2000. 12 March 2019. <https://www.corolland.com/corolla/1993-1997/transmissions.html>.

Husain, Iqbal. Electric and Hybrid Vehicles: Design Fundamentals. 2nd. Boca Raton, FL: CRC Press, 2011.

toyoland. Toyota 4A-F and 7A-FE engines: details and photos. 2000. 13 March 2019. <https://www.toyoland.com/engines/4A-F.html>.

Wheel Size. Toyota Corolla 1997 Alloy wheel fitment guide US domestic market. 2019. 12 March 2019. <https://www.wheel-size.com/size/toyota/corolla/1997/>.

Yong, R N, E A Fattah and N Skiadas. Vehicle Traction Mechanics. Saint Louis, MO: Elsevier Science, 2014.

Subject: Physics

Pages: 6 Words: 1800

Detector Resolution

Defector resolution

Student’s Name

Institution

Course code

Date

Introduction

The radiation is applied in several areas of life for scientific studies, research and to run industries. The production of energy through the nuclear technology and weapons has been closely associated with radioactive activities CITATION Jam14 \l 1033 (Milam, 2014). Recently, it has emerged to be an important aspect for the treatment of cancer patients. However, radiation is regarded has one of the dangerous things and of late it has caused a serious health problem in industries. Exposure to high radiation can result to cancer diseases and radioactivity condition, which can result to death. The common sources of radiation are smoke, nuclear weapon donation, natural radiation and cosmic arrays. And therefore, detectors are the best solutions to the problems caused by radiation. Gamma rays are also one the dangerous electromagnetic radiations which produce high energy and short wavelength and cause a serious damage to the body. The gamma rays are produced by various nuclear interactions which include nuclear reactor or fission. According to Diacon (2017, p. 21), the radioactive exposure can either be internal or external and therefore, necessary actions must be taken to avoid serious tissue damage resulting from such reactions.

The external exposure of radiation is regarded as the emission which comes from the external environment and the internal exposure is termed as the emission from within the body. It is important to point that the exposure from the external factors can be controlled and prevented using different scientific methods. As stated by Cherry & Phelps (2012, p. 25) the contamination, which originates from the external environment can be controlled using different shield methods and through increasing the distance which exist between the radiation sources. The detectors provide assistant in establishing the source of each radiation. And therefore, they offer the best method, which can be applied to control radiation hence limit the effect of the radiation CITATION Ste14 \p 23 \l 1033 (Steinberg & Rasmussen, 2014, p. 23). SCA and other defectors are powerful tools for analysis the radiation and therefore, used to prevent radiation exposure effect. It is therefore, important to study how defectors can applied in detecting and prevention of radiation of causing danger to people. This study therefore, focuses on the comparison of four different types of defectors such as Nai (TI), Ge (Li) and MCA and single channel analyser.

Objectives of the study

The objectives of the study are to ccompare the detector resolution of the NaI (Tl) detector using a Single Channel Analyser (SCA) and a Multi Channel Analyser, and a Germanium Detector. It is also conducted to plot the pulse counts against the radiation and determine how each defector reacts when exposed to amount of radiation. The study was also done to calculate the detection resolution among the detectors, which are used in various fields.

Method and Equipment

In order to complete the experiment several laboratory equipments were used in the lab professionally to achieve the objectives of the experiment. Laboratory equipments used are NIM Bin and power supply, high voltage power supply, Nal (TIL) Crystal and phototube assembly, preamplifier, multi channel analyzer, counter or time, 137 Cs gamma source, and cathode ray. Each of these equipments had specific role to play to ensure that the experiment was complete successful. First, all the equipments were connected with high voltage power supply. For safety precaution the points of connection were checked to confirm the power is off to avoid electrocution. All the connections were done using signal cables which use standard BSN types of connector. The PM- Tube was then connected to Pre-amp using of one the shortest signal cables of about 20-30 cm. The pre-amp was also connected to the Amplifier using any of the length cable, which is very convenient. The other components was the connected using the best and suitable cables to ensure that the connection is perfect for the experiment to occur.

Diagram 1: The layout of Electronic setup for NaI detector (detector lab note, 2019)

In order to achieve accuracy and success of the experiment 137 Cs source was placed in front of the Nal (TI) detector crystal. It was placed in a such a way that the source detector cannot change the measurement between to make sure that it does not interfere with the count rate. The amplifier unipolar output was then observed using the CRO. The observation was made and then the out of pre-amp was sketched. The CRO settings were also recorded for usage in the future.

It is important to point that the fine gain control of the amplifier and the course were adjusted to 662 keV photopeak, which are the most intense pulses. The amplitude (Vp) was also set to be used to lock and gain control. It is essential to ensure that gain setting remain the same during the entire experiment period. And therefore, the setting and the adjustment were made tight to for the accuracy of the experiment. After this had been done, the equipment settings were all recorded. The equipment settings recorded were HV and Amp because the experiment was to be repeated. The changes were also made to the settings of the course to keep the uniformity. However, the width of the channel was then set to 0.2V and the baseline was adjusted below the photopeak amplitude of (egVp-0.1) to ensure that it counts in the photopeak area. The appropriate time was determined to record about 2000 counts, and this time was used for all the measurements which were being done. The baseline was then set to 9.8V to count for the time. The 0.2V was then repeated to the interval down to zero volts, the adjusted was manual to reduce the readings. The background count was also done by removing the source and then the value was divided by 5 (i.e. 1.0 /0.2) and the subtraction made from the counts, which was early obtained. In the final stage, the amplifier and SCA were then disconnected and then the SCA was connected to MCA as indicate in the diagram 2 below. The MCA was then calibrated with the appropriate calibration source and then 137Cs spectrum was then accumulated. And finally the ROI was set for the main photopeak so that the peak report could be generated and then the experiment was saved.

Diagram 2: Electronic setup for NaI detector with Multi-Channel Analyser

Discussion and conclusion

In order to obtain a better result, the number of electric pulses of each experiment was plotted against the number of counts registered. It is essential to point that the pulses indicated the energy established to register counts which is in seconds. Indicated in the figure 1 to 4, the result shows a variation in the number of counts registered in every experiment conducted. Since the purpose of the experiment was to establish the different among the three components detector resolution of Nal (TI), Single Channel Analyzer and Multi channel analysis and Germanium Detector the number of counts registered by each of these components illustrates the different, which exist. The equipments, which were setup, were able to record various numbers of counts per minutes, and the count and the time were used to plot the four graphs. The figures were plotted after the conversion to a kev was done to make it easier to plot and visible as well.

The experiment indicates that there are general differences among the defectors and in Nal (TI) as indicated in figure 1, the array are long in the Y-axis. This could be as result of semiconductor detector, which permits the separation of the Y rays with the energy. In figure 1, the number of counts of Nal (TI) moves upward straight few minutes after the experiment started, and that is when Nal (TI) receives a lot of heat. It projected straight and then lowers but the arrays are up at on the Y-axis compared to other defectors. It is possible that there is utilization of high energy resolution during the experiment process, which is a very critical factor in a small size of the semi conductor and this could be the result of the long arrays on the y-axis registered with Nal (TI).

Figure 1: Nal Single CA experiment

Figure 1, shows an experiment result of Nal single CA. the experiment indicates that single channel analyzer registers high photopeak compare to the rest of the defectors. The photopeak of the single channel analyser is 750 and the pulses are 49. However, it is noticed that the pulse count of the single channel analyzer falls on the same condition as its peak amplitude and its falls height. It has also a window, which is established with similar threshold. It is therefore, important to note that there are two SCA, which can be applied, the SCA with and without timing. According to Markson (2014, p. 21, timing SCA usually produce logic output signals, which are associated to the time of the occurrence and therefore the SCA used in this experiment was non timing because the time does not exist at the end of the experiment. In this experiment, can be stated that the pulse counts of the defectors change when the heat or the amount of radiation changes. The pulses and the photopeak depends on the radiation, it is likely that after the nine pulse count a lot of heat or radiation was received by Nai and this prompted a sudden change of photopeak. It has several counts of 1025 and the mean of the entire count is 56.36, which can mean that it registered several value counts throughout. The mode is and therefore, many of the pulse counts made by the Nai MCA are zero. Though the counts were made by the zero but zero value was registered in major counts throughout the experiment.

Figure 3: Multi Channel Advisor experiment result

The MCA registered dwindle and pulse counts and this means it has few pulses cunts compared to the rest of the defectors.

Figure 4: Germanium Experiment of radiation counts

However, it is noted that the four spectrum registered different photopeak heights and the registered by each spectrum could be based on the radiation intensity applied in each case. In figure 1 to 4 the number of counts registered in each case is directly proportional to the quantity of the radiation, which was used to accomplish the experiment. Based on the four experiments, it is evident that Nal (TI) recorded the highest radiation. Nal (TI) has the photopeak with the longest height of approximately 7500 counts compared with the rest which registered less than 5000 counts. In this case, Nal (TI) utilizes a lot of energy of radiation. However, the experiment established that Ge (Li) detectors register several counts compared to Nal (TI) and the rest of the defectors. The experiment shows that Ge (Li) registered an estimated 5410 counts; Nal (TI) registered 49, MCA registered barely 1000 counts. It is therefore, evident that Ge (Li) has many counts compare to the rest of the defectors. It is therefore, can be concluded that Ge (Li) has a high resolution compared to the rest of the defectors. This experiment therefore, agreed with the hypothesis, which have been made by several scientists regarded the resolution of defectors. According to Cherry & Phelps (2012, p. 31), Ge (Li) has superior resolutions and because of the resolution, it registers several counts compared to other defectors with less resolution. This therefore, means that in terms of resolution Ge (Li) has a higher resolutions among the four defectors. The result of high resolution could be as the result of the application of different component during the reaction with heat. Cherry and Phelps (2012, p. 32) pointed that the Ge (Li) defectors deploys themigration of the electrons. It also utilizing the holes which exist between the valence and condcution bands during the radiaton detection and Nai (TI) uses the scintillation. This is the reason the two defectors registers different counts and arrays. Though Nai (TI) has the longest photopeak height, it registers few electron pulse counts estimate to be 49 compared to Ge (Li), which registers almost 5241 counts.

The experiment also shows that that a Ge(Li) registered a long straight photopeak and several of them throughout the recording. It also registered several pulse counts compared to Multi channel analyser and single channel analyser. The fact that the experiment registered a several pulses indicates its resolution and therefore, it is evident that Ge (Li) has a high resolution compared to Single Channel Analyser and Multi Channel Analyser. The pulse height of Ge (Li) is higher than the MCA and SCA and therefore, it means that it requires a lot of radiation. The voltage of the MCA and SCA is also less, which means that less radiation was used during the experiment process.

Conclusion

The experiment shows that there is a clear variation among the four defectors in terms of radiation utilization, and how each defector react when exposure to radiation. It is noted that the high resolution registered by Ge detector was as a result of detection techniques, which were used to conduct the experiment. But the studies have established that Ge detector has the high resolution compared to NaI (TI) and other defectors. In the comparison between Multi channel Analyser and Single channel Analyser, the MCA has proven to be clearer and accurate compared to SCA. It is therefore, worth noting that MCA produce more accurate result than SCA and therefore, it is advisable to use MCA for radiation detection. MCA should also be deployed rather than SCA because of its techniques to resolve complex conditions using multiple emission and several radionuclides as indicated in figure 2 above. It is also established that NaI (TI) has a higher photospeak and small background window and therefore, it can be used to high energy. It is therefore, important to point that the experiment was done in the laboratory, to to ccompare the detector resolution of the NaI (Tl) detector using a Single Channel Analyser (SCA) and a Multi Channel Analyser, and a Germanium Detector and experiment discovered that there is a clear distinction among the four defectors and how they are applicable. Their differences are based on resolution, wavelengths, photopeak and radiation required for each defector reaction.

Subject: Physics

Pages: 8 Words: 2400

Discussions

Name of Student

Name of Professor

Name of Class

Day Month Year

Discussions

1.

The Sun and all the planets have high internal temperatures as compared to temperatures on their surfaces as the surface temperature is linked with the energy that they receive from the Sun and radiates the energy back to space. Different sources of energy are responsible for internal heat such as the mass of the planet, the presence of different gasses; carbon dioxide and other greenhouse gases.

2.

When Moon was seen through first telescopes in the early 1600s, it changed people’s perception. Previously, it was believed that the Sun and other planets were orbiting around the Earth but after that people believe the Earth and other planets are moving around the Sun.

Subject: Physics

Pages: 1 Words: 300

Dr. Yahia Hamada

Dr. Yahia Hamada

[Student Name]

[Institutional Affiliation(s)]

Author Note

Profile of Dr. Hamada

Dr. Yahia Hamada

Dr. Yahia Hamada received his undergraduate degree from Alexandria University, Egypt, under a group of esteemed scholars, known for their great contributions to natural science, especially the science of chemistry. Most of these teachers were taught at the best institutions of the world in Germany, England, France, Russia, Japan, and the US.

During his second and third year at his university, Professor Housin Sadek introduced the disciplines of thermodynamics and physical chemistry to him. Professor Sadek was regarded as the best teacher at the campus since he got his education from the legendary Albert Einstein himself at Princeton, US. Inorganic Chemistry was imparted to him by Dr. Tahani M. Salem, who was the mentor of the famous Ahmed H. Zawail. Finally, he learned Advanced Inorganic Chemistry from

Professor Mohammad El-Sayed.

Dr. Hamada is currently a professor of biochemistry at the Lemoyne-Owen College in Memphis, Tennessee. His contributions including research in the newly-emerging field of Bio-inorganic Chemistry, which is the interdisciplinary study that includes the field of physics, chemistry, biology, and medicine. He also studied macromolecules and model systems of metal-containing natural systems.

His current interests in the field of Bio-inorganic chemistry include the study of Aqueous Solution. This study includes a detailed analysis of macromolecules, such as proteins. Also, this study includes the study of complex but important molecules and model systems. These include Potentiometry, metal ion speculation and the multinuclear system as tools to study different ions of varying low molecular weight ligands. Most of his work is inspired by the great chemists such as Richard Feynman (1919- 1988). Most of his articles are published in the Journal of Coordination Chemistry (by Taylor and Francis) and the Journal of Solution Chemistry (by Springer).

References

BIBLIOGRAPHY There are no sources in the current document.

Subject: Physics

Pages: 1 Words: 300

Earth Field NMR/MRI Experiment

Introduction/Background

NMR alludes to the conduct of atomic nucleus in the presence of a magnetic field. The main rule required to comprehend MRI is the way that atomic nucleus have minimal atomic magnets. These nucleus have a characteristic "precise force" called spin. While the first of this spin is quantum mechanical, the experiment can start to comprehend it in similarity with established spinning objects.

Atomic spins

The hydrogen nucleus is the most regularly utilized for MRI experiments. The 1H nucleus is a spin-1/2 nucleus and has two conceivable quantum states in the presence of a magnetic field that focuses, for instance, along the positive z axis: the low energy state is classified "spin up", and the high energy state "spin down".

In the presence of a fixed outside field, the spinning top will experience a torque. At the point when the axis of the precise force is even (for example opposite to the gravitational field), the impact of this torque is anything but difficult to watch, the impact of the torque is to influence the axis to precess about the outside field. At the point when the course of the precise force vector from the gravitational field heading, there is no recognizable precession. So as to watch this precession, the experiment should apply a mechanical torque that is symmetrical to the axis so as to turn the axis of the precise force.

The NMR marvel which shapes the premise of MRI was first detailed in 1945 (Gao et al. 2005). They were granted the Nobel Prize in 1953 for their revelations. Following the presentation of MRI imaging, there has been a fast expansion of MRI methods in indicative drug. At the point when utilized clinically these methods are known as MRI and MRS. Notwithstanding, there are numerous different applications outside the medicinal field including for instance, human studies, fossil science, development, material examination and sustenance quality investigation.

NMR and subsequently MRI, rely on the capacity to identify and quantify signals that emerge because of two key properties of issue. These are that atoms, among other key properties, exhibit nuclear magnetism and nuclear spin. For spin half isotopes, 1H is the best nucleus over numerous other dynamic nuclei, for example, C, N and P for three significant reasons. To start with, the bounty of 1H is 100% (Iwasa, 2006).

Second, it has a high gyromagnetic proportion which makes it the simplest nu-clear spin to be watched and third the centralization of atoms containing 1H is high in natural tissue. The reason these three elements are significant is on the grounds that NMR flag force is straightforwardly corresponding to them. Other nuclei of lower wealth, lower gyromagnetic proportion and conceivably lower focus produce littler flags and are thusly difficult to watch even with flag averaging to maximize the resultant flag to commotion proportion (Carretta & Lascialfari, 2007).

Generally, MRI depends on the location and examination of a flag that is generated from nuclear spin precise force in a magnetic field at warm harmony. Accordingly, there is a further factor that additionally decides the extent of the watched NMR flag. This is the conveyance of the spin between these alleged spin states. Spin half nuclei are appropriated between spin up and spin down introductions and that can be envisioned as a mass property of the example.

Since the NMR flag is identified with the extent of the mass magnetisation related with the populace contrast between these two expresses, a basic issue is the characteristic low affectability related with their discovery.

This is on the grounds that at body temperature and in a clinical magnet, nearly the same number of nuclei are in the spin up state as in the spin down state.

For the MRI experiments, the experiment need:

a homogeneous, static magnetic field

an example with bunches of 1H nuclei, which in the presence of a have net harmony magnetization

a test which creates a transverse magnetic field whose field sways in resonance with the Larmor precession recurrence of the nuclei.

In EF/NMR, the experiment utilize the EMF as the homogeneous, static field. Be that as it may, the magnitude of the EMF is little, and as a result, the net magnetization is likewise little. This net magnetization can be expanded by setting up the framework in a bigger magnetic field, and after that turning the magnetization into the EMF course before the NMR experiment.

References

Gao, S., House, W., & Chapman, W. G. (2005). NMR/MRI study of clathrate hydrate mechanisms. The Journal of Physical Chemistry B, 109(41), 19090-19093.

Iwasa, Y. (2006). HTS and NMR/MRI magnets: Unique features, opportunities, and challenges. Physica C: Superconductivity and its applications, 445, 1088-1094.

Carretta, P., & Lascialfari, A. (Eds.). (2007). NMR-MRI, μSR and Mössbauer Spectroscopies in Molecular Magnets. Springer Science & Business Media.

Subject: Physics

Pages: 3 Words: 900

Electricity

Your Name

Instructor Name

Course Number

Date

Title: Electricity

Electric engineering is the newest branch of engineering and is introduced around the end of the 19th century. It is about electrical technologies and its main focus on electricity, electrons, and electromagnetism. Electric engineering also covers concepts like control system, power, signal processing, and telecommunications.

An electrical engineer is the one who uses the concept of mathematics and physics of electricity, and electromagnetism and develops new equipment of electricity. The introduction of electricity to our lives has been done by electric engineering who analyses the concept of physic to make the basic elements that are necessary for the generation of electricity.

The topic of electricity in physics is helpful for electrical engineering to evaluate the product, components and the general mechanism of the electric system. These topics will clear the concepts of electrical engineering in conducting research on developing electrical products.

The concept of electricity in physics guides electric engineer to understand the entire electric system which is the base of electric engineering. Electronic circuits, inductors, resistors, diodes, and transistors are the topics that are used in physics to explain electricity and these topics are the base of electric and electronic engineering.

The electric charge has been explained in physics as a subatomic particle that can generate magnetic and electric power and after bringing the electric changes near to each other the can exert force. In Physics, this concept of electric force is explained with the help of Coulomb’s law. This law explains that on what the electric force depend and by using such concept the electric engineers can increase or decrease the intensity of electric force.

Physics says that electric current is the flow of charged particles and resistance oppose the flow of current. Information like this will help the students of electric engineers to design electric circuits which is the importance of electric engineer course.

Ohm’s law explains that the flow of charges in the shape of voltages is the same as the flow of water through a pipe. It says that current which is passing through a conductor must be equal to the voltage given to it and divide by the resistance of the medium through which it is flowing. The concept of ohm’s will help the students of electric engineering to fit series and parallel connection of voltages and will help to identify ways to minimize resistance. Thus the general public will get more current with less voltage.

The electric field indicates the ways a positive charge could move and this is a concept give in physics. This concept is important for power system engineers which are the sub-field of electric engineering. Power Engineers study the transmission of electric power. Without understanding the concept of the electric field the ways of transmission of electric power would not be possible to analyze.

However, the skills required for electric engineering includes the understanding of complex electric designs and the ability to build them up from scratch. The complex electric designs contain insulators and conductors and the understanding of these concepts is necessary to read the complex electric designs and to build them again.

In a nutshell, the concept of electricity in physics helps the student of electrical engineering to understand the core mechanism of an electric system. Electric engineering revolves around the concept of electric system and physics guides the students of Electric engineering to get the understanding of the electric world and helps to do new discoveries in this field. Thus without the knowledge of electricity, Electric Engineers are unable to use the concept of electromagnetics, electricity, and electronics to generate new electric devices. It is, therefore understanding of electricity is necessary for electric engineers.

Subject: Physics

Pages: 2 Words: 600

How Noise Canceling Headphones Work

RUNNING HEAD: ASSIGNMENT

How Noise Canceling Headphones Work?

Name of Student

[Name of the Institution]

How Noise Canceling Headphones Work?

Introduction

If you are a music lover or prefer to listen to it more in open spaces, then there is no possible reason why you will want to try voice canceling headphones. Teenagers, even adults, nowadays, are compelled to try new products that provide better quality, due to the ever changing technological innovations. Sound canceling headphones serve by blocking the outside noise while solely allowing the music from internal sources to reach your ears ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"RprbTWHT","properties":{"formattedCitation":"(Williamson, 2007)","plainCitation":"(Williamson, 2007)","noteIndex":0},"citationItems":[{"id":8,"uris":["http://zotero.org/users/local/Fw9DaQie/items/9ACQAMP5"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/9ACQAMP5"],"itemData":{"id":8,"type":"patent","authority":"United States","call-number":"US11/344,272","number":"US20070177741A1","title":"Batteryless noise canceling headphones, audio device and methods for use therewith","URL":"https://patents.google.com/patent/US20070177741A1/en","author":[{"family":"Williamson","given":"Matthew"}],"accessed":{"date-parts":[["2019",12,10]]},"issued":{"date-parts":[["2007",8,2]]},"submitted":{"date-parts":[["2006",1,31]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Williamson, 2007). This is quite a fascinating phenomenon that uses the application of physics. Now the question is, “How do these noise-canceling headphones work?” The essay will give a possible answer to the question in the light of physics.

Discussion

It is essential to first know what sound is, in order to learn how to cancel the noise. You possibly perceive it in the shape of a wave if you try to visualize it. Although this two-dimensional visualization may certainly prove useful later, but it is not the right representation of what sound is. The phenomenon cannot be understood unless you thoroughly understand that concept. This is where physics comes in. Sound, as you perceive it, is just the compression and decompression of air molecules ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"jil1IJXQ","properties":{"formattedCitation":"(Sapiejewski and Monahan, 2003)","plainCitation":"(Sapiejewski and Monahan, 2003)","noteIndex":0},"citationItems":[{"id":13,"uris":["http://zotero.org/users/local/Fw9DaQie/items/E7KBKH9H"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/E7KBKH9H"],"itemData":{"id":13,"type":"patent","title":"Headset noise reducing","author":[{"family":"Sapiejewski","given":"Roman"},{"family":"Monahan","given":"Michael J."}],"issued":{"date-parts":[["2003",7]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Sapiejewski and Monahan, 2003). Picturing noise as a three-dimensional pulse across air can be rather simpler. Such molecules in motion result in very minor air pressure fluctuations. These changes in pressure are termed as “amplitude” ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"zvKaLhM2","properties":{"formattedCitation":"(Kimura, 2010)","plainCitation":"(Kimura, 2010)","noteIndex":0},"citationItems":[{"id":11,"uris":["http://zotero.org/users/local/Fw9DaQie/items/CWKQ8IJF"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/CWKQ8IJF"],"itemData":{"id":11,"type":"patent","title":"Noise canceling headphone","author":[{"family":"Kimura","given":"Tominori"}],"issued":{"date-parts":[["2010",9]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Kimura, 2010). Our ears and brain detect these changes in air pressure as “sound”. Both the amplitude and magnitude of sound depend on each other. The higher the amplitude, the louder will be the sound produced ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"eImsWW1p","properties":{"formattedCitation":"(Bergeron et al., 2012)","plainCitation":"(Bergeron et al., 2012)","noteIndex":0},"citationItems":[{"id":9,"uris":["http://zotero.org/users/local/Fw9DaQie/items/4VRKFYES"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/4VRKFYES"],"itemData":{"id":9,"type":"patent","title":"Noise reduction headset","author":[{"family":"Bergeron","given":"Mark"},{"family":"Crump","given":"Stephen"},{"family":"Gauger Jr","given":"Daniel M."}],"issued":{"date-parts":[["2012",5]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Bergeron et al., 2012).

Noise-canceling headphones form a barrier suppressing sound waves of higher frequency ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"rg9uZd1d","properties":{"formattedCitation":"(Bergeron et al., 2012)","plainCitation":"(Bergeron et al., 2012)","noteIndex":0},"citationItems":[{"id":9,"uris":["http://zotero.org/users/local/Fw9DaQie/items/4VRKFYES"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/4VRKFYES"],"itemData":{"id":9,"type":"patent","title":"Noise reduction headset","author":[{"family":"Bergeron","given":"Mark"},{"family":"Crump","given":"Stephen"},{"family":"Gauger Jr","given":"Daniel M."}],"issued":{"date-parts":[["2012",5]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Bergeron et al., 2012). While deliberately eliminating low-frequency sound waves, they add an additional level of noise reduction. How does this happen to noise-canceling headphones? The answer is that they generate their specific sound waves, which in all respects, emulate the input noise with the exception of one: there is a phase shift of 180 degrees between the input waves and the waves of a headphone ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"IPcZEMz4","properties":{"formattedCitation":"(Trajkovic et al., 2002)","plainCitation":"(Trajkovic et al., 2002)","noteIndex":0},"citationItems":[{"id":15,"uris":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"itemData":{"id":15,"type":"patent","title":"Active noise canceling headset and devices with selective noise suppression","author":[{"family":"Trajkovic","given":"Miroslav"},{"family":"Gutta","given":"Srinivas"},{"family":"Cohen-Solal","given":"Eric"}],"issued":{"date-parts":[["2002",10]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Trajkovic et al., 2002).

The figure below represents the mechanism of how these noise-canceling headphones work. Consider the two waves: one is generated by the noise-canceling headset and the other one is generated by the ambient noise. Both of them seem to have the same amplitude and frequency which shows that their crests and troughs are configured so that crests of one wave align with the troughs of the other wave and the trough of the first wave aligns with the crest of another ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"K93FQobo","properties":{"formattedCitation":"(Trajkovic et al., 2002)","plainCitation":"(Trajkovic et al., 2002)","noteIndex":0},"citationItems":[{"id":15,"uris":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"itemData":{"id":15,"type":"patent","title":"Active noise canceling headset and devices with selective noise suppression","author":[{"family":"Trajkovic","given":"Miroslav"},{"family":"Gutta","given":"Srinivas"},{"family":"Cohen-Solal","given":"Eric"}],"issued":{"date-parts":[["2002",10]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Trajkovic et al., 2002). The phenomenon of destructive interference is observed as the two waves completely cancel the effect of each other. As a result, the listener is able to pay attention to the sound that he desires ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"FJb5XozF","properties":{"formattedCitation":"(Trajkovic et al., 2002)","plainCitation":"(Trajkovic et al., 2002)","noteIndex":0},"citationItems":[{"id":15,"uris":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/GLHIQWCQ"],"itemData":{"id":15,"type":"patent","title":"Active noise canceling headset and devices with selective noise suppression","author":[{"family":"Trajkovic","given":"Miroslav"},{"family":"Gutta","given":"Srinivas"},{"family":"Cohen-Solal","given":"Eric"}],"issued":{"date-parts":[["2002",10]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Trajkovic et al., 2002).

255270028829000

Moreover, the additional structure present in headphones contributes to producing the noise canceling effect ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"Qx9u4czc","properties":{"formattedCitation":"(Sapiejewski and Monahan, 2003)","plainCitation":"(Sapiejewski and Monahan, 2003)","noteIndex":0},"citationItems":[{"id":13,"uris":["http://zotero.org/users/local/Fw9DaQie/items/E7KBKH9H"],"uri":["http://zotero.org/users/local/Fw9DaQie/items/E7KBKH9H"],"itemData":{"id":13,"type":"patent","title":"Headset noise reducing","author":[{"family":"Sapiejewski","given":"Roman"},{"family":"Monahan","given":"Michael J."}],"issued":{"date-parts":[["2003",7]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Sapiejewski and Monahan, 2003). This includes a microphone that is mounted inside the ear cushions and receives external stimuli that cannot be actively silenced. Signal-canceling circuitry, which includes electronics mounted in the ear cushions. It detects the microphone signal and produces a sound "fingerprint," which records the received wave's intensity and magnitude. At last, the speaker, which detects the "anti-sound" produced by the signal-canceling electronics along with the regular sound. The anti-sound eliminates the noise by the phenomenon of destructive interference, however, it does not alter the intended sound waves in the regular sound.

Conclusion

Noise-canceling headphones provide an extra compression of twenty decibels with the utilization of the above features. This implies that approximately 70% of background noise is successfully blocked, rendering noise-canceling headphones perfect for airplane and bus travel, open floor atmospheres or other destinations with elevated ambient noise thresholds.

Bibliography

ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY Bergeron, M., Crump, S., Gauger Jr, D.M., 2012. Noise reduction headset.

Kimura, T., 2010. Noise canceling headphone.

Sapiejewski, R., Monahan, M.J., 2003. Headset noise reducing.

Trajkovic, M., Gutta, S., Cohen-Solal, E., 2002. Active noise canceling headset and devices with selective noise suppression.

Williamson, M., 2007. Batteryless noise canceling headphones, audio device and methods for use therewith. US20070177741A1.

Subject: Physics

Pages: 2 Words: 600

K-space

Student’s name

Course id

Submitted to

Date

K-Space

Today, medicine is no longer imaginable without diagnostic imaging. With the discovery of x-rays in 1895, an important milestone in medicine was already set but the more significant invention of the last century was magnetic resonance imaging (MRI), enabling non-invasive 3-dimensional anatomical data of the human body to be generated without ionising radiation1.

Looking back in time, the basis of MRI was nuclear magnetic resonance (NMR) in chemistry and X-rays. In 1970 the first pictures of the brain were taken. In 1973, Paul Lauterbur presented a two-dimensional NMR image of a water-filled object. In 1977, a thorax image was taken on MRI for the first time. With the findings of the projection reconstruction techniques from the computer tomography at that time, Lauterbur was able to reconstruct the two-dimensional images from the one-dimensional NMR measurement. NMR and X-rays have together led to rapid development and technological advances in medicine.

The scientific basis for MRI imaging was described in about 1800 by Jean Baptiste Fourier (1768-1830). Without this transformation, the calculation of MRI images would not be possible today. The unit for the magnetic field strength was named after the inventor Nikola Tesla (1856-1943). Nikola Tesla described the formation and effect of magnetic fields. Erwin L. Hahn discovered in 1950 the "spin echoes", which is one of the most basic methods of signal generation in magnetic resonance imaging.

The first clinical MR systems were installed in 1983. The field strengths were 0.2 - 0.5T, this was followed by 1T and 1.5T systems, which have been critical to medical imaging for the last 25 years. About ten years ago, 3T systems were introduced. The intention was to increase the field strength further to invest the obtained signal-to-noise ratio in better spatial resolution or shorter examination time. There are now more than 10 Tesla for research purposes. The technical development is so rapid that, compared to earlier, the MRI is primarily adapted to patient needs2.

MRI produces images of the human body. During scanning or sampling, the patient is placed under the effect of a constant magnetic field with controllable field gradients at all coordinates; these fields allow spatial coding and the selection of a “slice”, which is the two-dimensional element on which you want to obtain the image. The excitation is carried out with the application of a radio frequency (RF) signal, which produces the phenomenon of resonance on the selected spins, achieving the accumulation of energy, which is delivered as an NMR signal.

It is called k-space because the signals received from the NMR process are in frequency and phase. Therefore, all of these NMR data correspond to the Fourier transform of the image of the section along the path; in this way, and the reconstruction of the image is done with the application of the Fourier Inverse Transform, IFFT, on these data. To reduce the acquisition time, various alternatives have been proposed, and within these, the sampling of the k-space on trajectories that do not allow acquisition on a Cartesian grid, however, as a consequence, the complexity of the reconstruction is increased. The methods most used in the reconstruction of images acquired on non-Cartesian trajectories in k-space are the Gridding algorithms and the direct Fourier transform (DFT).

The signal recorded during an MRI sequence is stored in the space K. The space K corresponds exactly to a Fourier plane. It is therefore sufficient to apply an inverse 2D Fourier transform on the k-space to obtain an image of the section of the human body. It is the spatial coding, which makes it possible to acquire the data of the image in frequential form, adapted to the K-space3. When the system retrieves the signal, it fills a mathematical space which is called quarter space or K-space. This space K will contain all the information necessary for the formation of the image. We go from the k-space to the image by a double Fourier transform, and from the image to the Fourier space thanks to a double inverse Fourier transform. The filling of this space Fourier is an invisible step for us users, but it is essential for any formation of the image.

Reference list

Bashir U. K space | Radiology Reference Article | Radiopaedia.org. Radiopaedia.org. https://radiopaedia.org/articles/k-space. Published 2019. Accessed May 15, 2019.

Soll E. The History of Medical Imaging | Doctors Imaging | MRI, Ultrasound, CT Scan, X-Ray, Mammograms in Metairie. Doctorsimaging.com. http://www.doctorsimaging.com/the-history-of-medical-imaging/. Published 2019. Accessed May 15, 2019.

Qureshi M, Kaleem M, Omer H. Journey through k-space: an interactive educational tool. Alliedacademies.org. http://www.alliedacademies.org/articles/journey-through-kspace-an-interactive-educational-tool.html. Published 2019. Accessed May 15, 2019.

Subject: Physics

Pages: 2 Words: 600

Lab Report

Name

4 March 2018

Title: Lab Report

Purpose

The purpose of the experiment is to determine the horizontal component of the magnetic field of the earth, and to determine the magnetic fields caused by a current carrying solenoid through tracing its path. Thirdly, the purpose was to determine the direction of the magnetic field which surrounds a long straight wire using a pair of compasses.

Procedure

The magnetic fielded of the earth emerges from its inner core and becomes horizontal near the earth’s magnetic equator. The earth’s magnetic field can be studied using a Helmholtz coil. In one part of the experiment, a Helmholtz coil was used, which consisted of two similar coils that were separated at the same distance as their radius, and carry the same current. The magnetic field was measured by positioning small compasses between the two coils. It was noticed that the compasses pointed towards our right side, which pointed towards the north-west area, as we passed a current through the coil.

In the wire experiment, a current I was passed along a straight wire generating a magnetic field around it. In theory, the field lines produced by the current form concentric circles that surround the straight wire. The distance away from the wire R, and the current I, determine the magnetic field’s magnitude (B). The direction of the field can be determined through the right-hand rule. The direction in our experiment was measured by placing two compasses in the vicinity of the wire while a current of 12 A was passed through it. We observed the right compass to have the opposite direction of the one we placed at the left, which faced south against the right one, which was pointing North. The value of R was measured to determine the experimental value of earth’s horizontal component.

In the solenoid experiment, the magnetic field should ideally be constant along its length and remain inside the solenoid. It is parallel to the axis of the solenoid. However, in our experiment with a real solenoid, the magnetic field was not observed to be constant at its ends, and some portion of the field was observed outside the solenoid. Compasses were used to determine the direction of the magnetic field that began to curve slightly as they were placed in series.

Results

Horizontal Component BE of the Earth’s magnetic field

BE = BW (neutral point)

BW = 0I /(2r) = BE ; Where 0 = 4.0 x 10-7 H/m

r measured at 9.2 cm = 9.2 x 10-2 and I = 12A

BE = 0I /(2r)

= (4.0 x 10-7 x 12) / ( 2 x 9.2 x 10-2)

= 0.0000150792 / 0.57805

= 2.61 x 10-5 T

= 0.26 T

BE (Horizontal component) = 0I /(2 rcos) where = 550

= 4.5 x 10-5 T or 0.45 T

BE (theoretical) = 44,100 nT

BE (experimental) = 45,000 nT

Discrepancy = (45000-44,100 / 44,100) x 100%

= 2.041%

Errors

In our experiment results, a discrepancy of 2.04% was observed compared to the theoretical value of the magnitude of the earth’s magnetic field. These errors could result from a number of factors, for instance the presence of magnetic fields being produced by other nearby electronic appliances or devices that possibly interfered with the measurement of the magnetic field and affected the value of R on the paper. Moreover, the accuracy and precision of the measurements from the instrument which we used to measure the magnetic field and distance away from the wire, possibly due to random or parallax errors arising from the compass readings while trying to obtain the magnetic field’s direction. Moreover, since the horizontal component was being measured, therefore rounding off could affect the precision of the results. Another possible source of error could be the nature of the wire itself that did not produce a uniform field, along with that the presence of other metal objects may have affected the compasses readings.

Conclusion

To conclude, the experiment we performed in the lab to determine the magnitude and direction of the magnetic fields in the case of the long straight wire, and the directions of the field in the case of the solenoid and Helmholtz coil was successful as we were able to understand and observe how the magnetic field of the earth is affected by passing a current. Although the experimental results slightly deviated from the theoretical values, there were various sources of errors that affected our measurements to cause the deviation. However, the experiment was still completed successfully, as we were able to successfully measure and calculate the magnitude and direction of the horizontal component of the magnetic field of the earth.

Subject: Physics

Pages: 3 Words: 900

Lab Report

Student’s Name:

Instructor’s Name:

Class Name:

Date when Due:

Works Cited

Lab Report

The Potentiometer

Purpose

To assemble the precision null reading instrument for measuring the voltage

Part A: Usage of the slide bridge as the variable-voltage source

Theory

The potentiometer is three terminal resistors with rotating or sliding contact which creates the adjustable voltage divider. When just two terminals have utilized the wiper one end, it will be a rheostat or variable resistor. It is essentially a voltage divider that is used in measuring the voltage. They are mostly used as the control devices like volume controls on the audio equipment.

A metal with cross-sectional area A and length x has a resistance of:

Rx=ρI/A

Whereby the ρ= resistivity of the metal in Ω.m

Assuming that the voltmeter is ideal the internal resistance Rv=∞s so that Iv=0 through the voltmeter, hence the voltage reading shall be given as Vx=I Rx=ρIAx…1

Where I=VaRt=voltage of the power supplytotal R of the I-m wire=const.

Hence we see that Rx∝x…(2)

Material

1-m Bridge, power supply, voltmeter and cables

Method

DC circuit is set up as shown in the diagram below to prove the voltage versus position on the bridge

Circuit Diagram

Procedure

The circuit is set up as shown above. The DC voltage Vo was set at 2V. Vo=Vx when X=1m

The slide is then moved and touch the wire at the positions provided in the table. Every time measure Vx and it is filled in the table.

X

cm

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100

Vx

V

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Graph of Vx vs X is drawn on the full page with X along the x-axis. Best-fitting straight line is drawn. The graph is drawn to verify the validity of the equation 2

Discussion

.

From the graph, it is evident that Vx is proportional to X hence the equation 2 R_x∝x has been proved. Resistance in a wire is affected by the material of the wire, the thickness of the wire and the length of the wire. In a wire, the resistance increases when the length of the wire increases and as the thickness of the wire decreases. The resistance of an electrical component is defined as the ratio of the voltage to the current that flows through it

When the resistance in a wire is constant is a considerable range, Ohm’s law could be applied for predicting the behavior of the material.

Conclusion

In conclusion, assemble of the precision null reading instrument for measuring the voltage was done. The experiment also proved that that Vx is proportional to X hence the equation 2 R_x∝x was proved. Resistance in a wire is affected by the material of the wire, the thickness of the wire and the length of the wire.

Part B: Usage of the bridge as the potentiometer

Purpose

To use the bridge as the potentiometer

Theory

In the circuit diagram below, the slide position x is adjusted till the galvanometer G reading is recorded as zero. A galvanometer is a sensitive ammeter. It reads zero when the voltage V in across the power cell is equal to the Vx and by using the two different cells, one that is known voltage Vk and the other as the unknown voltage Vu. Using equation 1, the slide position of the cells with the Vo=0

Vk=(ρIA)xa

By combining the two we attain Vu=(xuxk)Vk

Circuit diagram

Procedure

1. The circuit is set up as shown in the diagram above and replacing the Dc voltmeter with the power cell, and galvanometer is done in series. By using the voltmeter, Vo is verified to be 2 V at the power supply.

2. The first’s cell is the black student cell with Vk of 1.02V. The slide position that produces the null reading on the galvanometer is done xk=45.5 cm

3. The student cell is replaced with the dead dry cell. The new slide position is measured, and it gives the null reading Xu 72 cm

4. By using equation 3, the unknown voltage established Vu=1.6v

5. The circuit is then connected with the voltmeter, and the cell is parallel to measure the voltage of the cell V’u=1.5V

Results and Discussions

Discrepancy

%D=(Vu-V’u/V’u)*100

Vu=1.6v

V’u=1.5V

(1.6-1.5/1.5)*100

D=6.67%

Sources of errors

Parallax error while reading the distance and voltage

Resistance present in the circuit

Inherent error resulting from malfunctioning of the equipment of measurement like the voltmeter

Conclusion

In conclusion, the bridge was used as the potentiometer. The discrepancy of 6.67% was found in the values of V’u and Vu. The sources of error causing the discrepancy compromise of parallax error while reading the distance x and voltage V, resistance present in the circuit and inherent error resulting from malfunctioning of the equipment’s of measurement like the voltmeter

Subject: Physics

Pages: 2 Words: 600

Lab Report #3

Student’s Name:

Instructor’s Name:

Class Name:

Date when Due:

Works Cited

Lab Report #3

Aim

To use electric meters to establish the relationship between resistance, current, and voltage

Part A: Verification of the validity of Ohm’s Law

Introduction

According to the Ohms Law V=IR (1)

I=Current measured by Ammeter A= [I] =Amps

V=Voltage as measured by Voltmeter V= [V] =Volts

R= Resistance of the decade-resistance box Ω=[R] = Ohms

Method

Dc circuit is set up as shown in the figure below, and the current and voltage are measured using voltmeter and ammeter

Circuit Diagram

Procedure

The circuit is set up as shown above. By using the cables required, connection to the power supply using the DC range B is made. The connection is made to the convenient range while maximizing needle deflection in the needle in both the ammeter and voltmeter

Resistance is kept constant at 100Ω while voltage is varied as shown in the table and each time measurement of the current is filled in the table.

R constant =100Ω

V

V

1.0

2.0

3.0

4.0

5.0

I

mA

0.01

0.02

0.03

0.04

0.05

Graph of V versus I is drawn with V along the y-axis. The best fitting line is drawn, and the slope is established

Step 2 is repeated while keeping the current constant at 10mA. Resistance is changed and adjust the voltage and the current by turning the black knob of the power supply

Current constant 10 mA

R

100

200

300

400

500

V

V

1.0

2.0

3.0

4.0

5.0

Draw a graph of V against R with R along the x-axis. The best fitting line is drawn and find the slope

Results

The gradient is Resistance ΔV/ΔA=R =100Ω

Gradient of the graph is Current ΔV/ΔR=I= 0.01A= 10mA

Part B: Measurement of the resistance of the two resistors that are connected in series n and also parallel.

Introduction

When the two resistors are R2, and R1 are connected in series, the equivalent resistance is given by:

Rs=R1+R2 (2)

When the resistors are connected in parallels, the equivalent resistance is provided by

1Rp=1R1+1R2 (3)

Procedure

Connect two resistors of 100Ω in series as shown in the diagram. Voltage is set at 1.0v. The current is then measured I=0.005mA

Using equation 1 find the equivalent resistance

Rs=V/I 200Ω

Using equation 2 found the theoretical value of Rs and compute the percent disparency D

Theoretical value of Rs=100+100 =200Ω

{(200-200)/200}*100=0% disparency

Connect the two 100Ω resistors in parallel as illustrated in the diagram. Voltage is set at 1.0V. The parallel current is measured Ip=0.02mA

Using the equation 1 establish the equivalent resistance

R=V/I=50Ω

Using the equation 3 find the theoretical value for Rp and compute the disparency D

Theoretical value of Rp=50

{(50-50)/50}*100= 0% disparency

Errors

There were no sources of errors since there were 0% disparency

Conclusion

In conclusion electric meters were used to establish the relationship between resistance, current, and voltage.

Subject: Physics

Pages: 2 Words: 600

Lab-Practical 7

Finding the EMF and Internal Resistance of a Cell

Name

[Name of the Institution]

Abstract

This report aims at describing the experiment conducted to find and calculate the EMF and internal resistance of a battery or a cell. Initially, the important concepts related to this topic are discussed. A general overview of current, voltage, internal resistance and EMF is provided. Then the details of the experiment are discussed. The equipment used to conduct the experiment is also listed. The whole procedure of finding the EMF and the internal resistance of a battery or a cell has been explained in a detailed manner. Finally, a graph is also plotted from the experimental data.

Aim

The aim of the experiment and this report is to determine the EMF (electromotive force) of a cell or a battery and calculate its internal resistance.

Introduction

Every cell and every battery consists of some medium through which current flows. This medium offers some resistance to the current flowing through it. This resistance inside the cell or the battery is known as internal resistance. When current flows through the battery, as a result of this resistance, some heat is lost within the cell. It warms up the cell. Moreover, all the voltage provided by the cell does not reach the load. Some of it is dropped across the internal resistance as well. This report explains the difference between terminal voltage and EMF and provides the whole procedure for finding the internal resistance in a cell through an experiment in the laboratory.

Finding the EMF and Internal Resistance in a Cell

Before explaining the details of the experiment, some of the fundamentals associated with the experiment will be discussed below.

Voltage (V)

Voltage is the potential difference across a conductor. It is the potential difference between two points CITATION All18 \l 1033 (All About Circuits, 2018). The unit of voltage is volt (V).

Electric Current (I)

Electric current can be defined as the rate of flow of charged particles (or electricity) through a medium CITATION All18 \l 1033 (All About Circuits, 2018). The medium is called a conductor. It can be a copper or a silver wire.

The unit of current is ampere (A).

1 ampere = 1 coulomb per second

Resistor (R)

A resistor can be defined as an electrical component that limits the flow of current that flows across its terminals CITATION All18 \l 1033 (All About Circuits, 2018). All the conducting mediums offer resistance to the current flowing through them. The measure of hindrance offered by the resistor is called resistance.

The unit of resistance is ohm (Ω)

Cell

A cell is a device that stores and converts chemical energy into electrical energy CITATION Nus18 \l 1033 (Nustem, 2018). It is also known as an electrochemical cell. A cell is used to provide power to electric appliances.

Battery

A battery is a group of cells. A cell is a single unit and battery is a grouping of a number of cells.

REF _Ref8121016 \h Figure 1 represents a cell and a battery symbolically.

Figure SEQ Figure \* ARABIC 1: Battery and Cell

Ohm’s Law

Ohm’s law relates current with voltage is a circuit. It can be defined as a law according to which the voltage across the two ends of a conductor is always proportional to the current that flows through it. Mathematically, it can be expressed as follows.

V=IR

Where V denotes voltage across the conductor, I represents current and R represents the resistance offered by the conductor to the flowing current. Resistance (R) is the constant of proportionality in the above equation.

The EMF (Electromotive Force)

EMF or electromotive force is the quantity of chemical energy that is converted into electrical energy by the source such as a cell or a battery when a unit charge flows through it. The unit of EMF is volt.

EMF = energy / charge

EMF gives us a measure of the energy within a battery that forces the current to flow in the circuit. Since the current always flow as a result of potential difference, EMF itself is a potential difference. The units of potential difference and EMF are the same.

Figure SEQ Figure \* ARABIC 2: EMF

In REF _Ref8131251 \h Figure 3, the voltage across the terminal will be the EMF because no current is flowing through the circuit.

Internal Resistance

It has been explained earlier that each cell in a battery has an internal resistance (r). The unit of internal resistance is ohm ().

When an external load is added to the terminals of a battery, some voltage is dropped across the internal resistance of the cell or battery. This results in the dissipation of energy in the form of heat within the cell. That is the reason why a cell or a battery warms up when it is supplying current.

Figure SEQ Figure \* ARABIC 3: EMF

Therefore

E = voltage across R + lost volts

In order to also measure the current as well, we need to add an ammeter in series with the battery.

Figure SEQ Figure \* ARABIC 4: EMF and Internal Resistance

When current flows through a circuit, it is resisted by the internal resistor of the cell. As a result, some thermal or heat energy is dissipated in the cell. It causes warming up of the cell. REF _Ref8131957 \h Figure 4 shows that the cell is in series with its own internal resistance and also with the resistor (R) which has been connected externally. The same current flows throughout the circuit i.e. across the load, the internal resistance and the cell.

As per the Ohm’s law:

V = IR

Hence from REF _Ref8131957 \h Figure 4:

E = I (R+r)

Or E = IR + Ir

As IR=V

So E = V + Ir

We can see from the above equation that EMF (E) is the sum of terminal voltage and voltage dropped across the internal resistance. It clearly shows that the EMF is greater than the terminal voltage. When I=0, then E=V.

Equipment Used (Apparatus)

The following equipment and electronics tools are required in the experiment to find the internal resistance.

Battery or Cell

Resistors box including 2k, 4k, 6k, 8k, 10k resistor

Voltmeter

Ammeter

Connecting wires

A push button will be required to reduce risks. It allows connecting circuit only momentarily.

The procedure of Finding Internal Resistance and EMF (Electromotive Force)

In order to find the Electromotive force of the battery, the voltmeter should be connected across the terminals of the battery. When no current flows through the circuit, the voltage at the terminal is equal to the EMF of the battery or the cell.

Then the circuit should be set up as shown in REF _Ref8131957 \h Figure 4. The battery should be connected in series with the resistor and an ammeter. A voltmeter should be connected across the resistor or the terminals of the battery.

First, the values of the current (I) and terminal voltage (V) should be measured using a 1K resistor. The values are recorded in tables. Then the same procedure is repeated for resistance 2K and then 4 and so on. The experiment is repeated for accuracy.

Tabulated Results

We already know that E = I(R+r)

The value of internal resistance of r can be found by rearranging this equation.

r = (E –IR)/I

For R=1K => r=41.67 Ω

Resistance / Ω

Terminal P.D. / V

Current / A

Internal res / r

1 K Ω

4.8 V

0.0048 A

41.67 Ω

2 k Ω

4.898 V

2.449x10-3 A

41.65 Ω

4 k Ω

4.948 V

1.23x10-3 A

42.27 Ω

6 k Ω

4.965 V

8.274 x10-4 A

42.3 Ω

8 k Ω

4.9736 V

6.217 x10-4 A

42.46 Ω

10 k Ω

4.979 V

4.979x 10-4 A

42.17 Ω

Plotting the Graph

The graph can be plotted by plotting the current (I) along the x-axis and the terminal voltage (V) across the y-axis.

Calculating the value of r from the graph

The graph shows a straight line. If we take two points on the graph and find the slope, we will have the value of the internal resistance. The following points on the graph have been chosen at random

Y1 = 4.965

Y2= 4.898

X1= 0.0008275

X2= 0.002449

R = slope = [y2 – y1] / [x2 –x1]

= 41.31 Ω

Discussion

By connecting a resistance (R) of low value to a cell, very little resistance is offered and hence, the current (I) flowing through the circuit has a higher value. By increasing the resistance, the current flowing through the circuit is decreased. On the other hand, by increasing the resistance, the terminal voltage (V) is increased.

We also observed that when the external resistance (R) was not connected yet, the terminal voltage was the highest. This is the EMF of the battery. The Y-intercept of the Voltage-Current Graph should give the value of EMF, because Y-Intercept, the current value is zero. Moreover, the internal resistance can be found by finding the slope of the Voltage-Current graph.

Risk Assessment

It is important to connect the resistors with the battery with due care. If a very low-value resistance is used, a very high current will flow through the circuit. It will damage the circuit. Therefore only high-value resistance should be connected. In addition to this, another precautionary measure is to use a push button in the circuit. It allows connecting the battery with the rest of the circuit only momentarily.

Conclusion

Our experiment shows that every battery or cell consists of an internal resistance which hinders the flow of current through the battery. As current flows through it, the battery warms up and some energy is dissipated in the form of heat. Consequently, the voltage that the battery supplies to the external load are less than the EMF of the battery. The value of internal resistance is as low as 40-50 ohms. By plotting the current-voltage graph, the value of this internal resistance can be found from calculating the slope of the graph.

References

BIBLIOGRAPHY All About Circuits, 2018. Ohm’s Law - How Voltage, Current, and Resistance. [Online] Available at: https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-current-resistance-relate/

Circuit Globe, 2018. Cell and Battery. [Online] Available at: https://circuitglobe.com/difference-between-cell-and-battery.html

Nustem, 2018. MEASURING THE EMF AND INTERNAL RESISTANCE OF A CELL. [Online] Available at: https://nustem.uk/activity/emf-and-internal-resistance/[Accessed 2019].

Subject: Physics

Pages: 4 Words: 1200

No NEED

Title

Name

Institution

Solution of the Numerical

η = k U Z ………………………… (1)

Whereas, k = 1.1 × 10-9 V-1

U = 100 k V

Z = 74

Putting values in the equation (1)

η = 1.1× 10-9 V-1 × 100 × 103 V × 74

η = 74 ×1.1 × 100 × 10-9+3

η = 8.14 × 10-3

Why many features of X-ray tubes are designed for dissipation of heat?

At the anode target, approximately 99% kinetic energy undergoes dissipation in form of heat. As a result of this continuous X-ray emission activity from cathode to anode, X-ray tube is having destructive consequences in terms of malfunctioning of temperature-specific X-ray tube. Hence, it is quite essential to dissipate heat from X-Ray tube. Cooling, if, accomplished in inadequate manner, is potent enough to disrupt the working X-ray tube in two possible ways. First one is; vacuum required for the appropriate working of X-rays is affected when sublimation of anode target material takes place under high temperature. Cathode—the tungsten filament, attracts the damaging ions from the target material under surpassing vapor pressure.

So it is important to ensure that X-ray tube is not allowed to become overheated. With the association of fault protection, careful monitoring of cooling process must be done in order to let the X-Ray tube function properly. For undertaking cooling process, a water or air cooling device is attached with the tube. In this way, extra heat energy is absorbed by water or air and X-ray tube continues to function properly.

Describe some of the features of a typical rotating anode X-ray tube.

Rotating X-ray tube is called so because it is having a rotating anode. The fundamental rationale behind the introduction of rotating anode is the dissipation of exceeding heat energy. If X-ray beam keeps penetrating same spot on anode interminably, the chances of overheating become irrefutable. Hence, its distinctive feature is “rotating anode” for mitigating the consequences of overheating.

Subject: Physics

Pages: 1 Words: 300

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