Work, Energy, Power. n (0.S)2 I11gh E [I - (O.Sn e O.S IIIg (1113) NS JlIII2. n kx in the direction OP

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1 TOPC 6 Work, ergy, Power 1 The door of a workig refrigerator is left ope. fter some hours, the temperature of the room i which the refrigerator is placed is uchaged, because the refrigerator absorbs as much heat as it gi ves out. lower, because the refrigerator will extract heat from the room. e uchaged, because the refrigerator is thermostatically cotrolled. higher, because the refrigerator gives out more heat tha it absorbs. lower, because the coolat i the refrigerator will evaporate much more rapidly O brakig, 500 k1 of heat were produced whe a vehicle of total mass 1600 kg was brought to rest o a level road. The speed of the vehicle just before the brakes were applied was m S m S- e 25 m S m S- 625 m S f the ball (of mass ) was dropped from.\11 iitial height h ad made three bouces, the kietic eergy of the ball immediately after the third impact with the surface was (0.S)3 11g 11 [ - (3 x 0.2)] (0.S)2 11gh [ - (O.S e O.S g (1113) NS Jl2 mass is projected vertically upwards with a give velocity. Neglectig air resistace, which oe of the followig statemets is correct? The kietic eergy of the mass is a maximum at the maximum height attaied. accordace with the priciple of coservatio of eergy, the total eergy of the mass is costat throughout the motio. e i accordace with the priciple of coservatio of mometum, the mometum of the mass is costat throughout the motio. The mass travels equal distaces durig equal periods of time durig both ascet ad descet. The potetial eergy icreases uiformly with time durig ascet. S3111; 1S piece of brass udergoes 3 differet processes ivolvig 6 chage of eergy: P : it is lifted vertically 2m Q : it is heated from 15 C to 20 e R: it is accelerated from rest to 10 m 5-1. Give that the specific heat capacity of brass is 3S0 1 K- 1 kg- ad that g = 10 m S-2, the processes, arraged i order of icreasig eergy chage, are PQR QPR 7 e QRP PRQ RQP N ball released from a height "0 above a horizotal surface rebouds to a height " after oe bouce. The graph that relates "0 to " is show below (Fig. ) e ~..c: OL- --'- a 100 holem Fig.! 8 The potetial eergy of a body whe it is at poit P :\ distace x from a referece poit 0 is give by V = kx'. where k is a costat. What is the force actig o till' body whe it is at P? 2kx i the directio OP kx i the directio OP e zero kx i the directio PO 2kx i the directio PO JS41112 car of mass 111 has a egie which ca deliver power P. What is the miimum time i which the car ca be accelerated from rest to a speed v? e V P P V V2 2P 2P V2? v- 4P NS6114 object of mass 111 passes a poit X with a velocity v ad slides up a frictioless iclie to stop at poit Y which is at a height" above X. y _~--JC h 6 Work, ergy, Power 73 ' Physics Topical Paper

2 secod object of mass 12m passes X with a velocity of 12 v. To what height will it rise? 8 C J electric motor is required to haul a cage of mass 400 kg up a mie shaft through a vertical height of 1200 m i 2.0 miutes. What will be the electrical power required if the overall efficiecy is 80%? [Take g is 10 m S-2] 3.2kW 50kW kw 3000kW C 32kW J8718 *10 The graphs below were obtaied from five differet experimets. ll but oe of the shaded areas o the graphs have uits of eergy. Which shaded area does ot have uits of eergy? experimet power output ofa lamp 8 a ball throw horizotally C chargig a capacitor graph obtaied power ~ O~time forc.e of air ~ resistace o potetial ~ differece o distace charge stretchig a sprig force ~ O~ extesio motio ofa gravitatioal ~ space-craft field away from the arth o time N mass moves o a rough plae iclied at a agle 8 to the horizotal ad, whe movig, experieces a costat frictioal force F. Mass M is attached to it by meas of a light ielastic cord ruig over a smooth pulley. Mass M is allowed to fall a vertical distace x, causig m to move up the plae as show i the diagram below. How much heat is geerated by frictio i this process? F.,. Mgx sio- Fx mgx Mgx si + F... C Mgxsi9 J What is the power required to give a body of mass 111 a forward acceleratio a whe it is movig with velocity v up a frictioaless track iclied at a agle 9 to the horizotal? mavg si 9 (G!' + gv) si 9 B lav si 9 + mgv may + mgv C may + mgv si 9 si 9 N The mutual potetial eergy V of two molecules separated by distace x is show i the diagram. v o--+--~ X Which of the followig correctly describes the force betwee the molecules? attractive for repulsive for x<rl x>rl B X>" x<r. C x< rl x>r2 x< "2.t>r2 x> "2 x<r2 J costat force is applied to a body which is iitially statioary but free to move i the directio of the force. ssumig that the effects of frictio are egligible, which of the followmg graphs best represets the variatio of P, the power supplied, with time t? Pl= BC PLP~ o tot 0 t M PlL P~ 1 r' x o tot L..J N Work, ergy, Power 74. ' Physics Topical Paper

3 15 The diagram shows two bodies X ad Y coected by a light cord passig over a light, free-ruig pulley, X starts from rest ad moves o a. smooth plae iclied at 30 to the horizotal. motor i,._l_., t J What will be the lotal kietic eergy of the system whe X has travelled 2.0 m alog the plae? (g = 9.8 ms-2). 20J 132J B 59J 137 J C 64J J90 16 crate is pushed 10 m alog a horizotal surface by a force of 80 N. The frictioal force opposig the motio is 60 N. What are the correct values for the icrease i iteral eergy of the system ad the additioal kietic eergy of the crate? icrease i iteral eergyj additioal kietic eergyj B C J901l; J9~16 17 The graph shows how F, the attractive force betwee two atoms, varies with d, their separatio. F Or-~~~----~ ~~--~d Which area represets the eergy required to separate the atoms to ifiity assumig that they are origially at their equilibrium spacig? 2 2+)- B 3 2 +) C N The diagram shows a arragemet used to fid the output power of a electric motor. The wheel attached to the motor's axle has a circumferece of 0.5 m ad the belt which passes over it is statioary whe the weights have the values show. 50N f the wheel makes 20 revolutios per secod, what is the output power? 300W C 600W B 500W 700 W J911115; J9616 *19 mass ll, attached to the ed of a ustretched sprig, is iitially supported by a platform as show i Fig. 2. This platform is the removed ad the mass falls, evetuall y comig to rest at the positio show i Fig. 3. ustretched sprig platform 1ZZ:z:iZ:z:~Z:Z:12 Fig. 2 Fig. 3 Which of the followig correctly relates the chages i potetial eergy ad heat dissipatio which may occur durig this process? decrease of gravitatioal = icrease of strai eergy potetial eergy decrease of gravitatioal = icrease of strai eergy + potetial eergy eergy dissipated as heat C decrease of gravitatioal = decrease of strai eergy + potetial eergy eergy dissipated as heat decrease of gravitatioal potetial = icrease of eergy+ eergy dissipated as heat strai eergy decrease of gravitatioal potetial = eergy dissipated eergy+ decrease of strai eergy as heat N9JJ 20 body of mass 111 moves at costat speed v for a distace 3 agaist a costat force F. What is the power required to sustai this motio'! V Fs Fv N Work, ergy, Power 75 ' Physics Topical Papel

4 21 small metal sphere of mass is movig through a viscous liquid. Whe it reaches a costat dowward velocity v, which of the followig describes the chages with time i the kietic eergy ad gravitatioal potetial eergy of the sphere? kietic eergy gravitatioal potetial eergy costat ad equal to V 2 mv 2 decreases at a rate of mgv B costat ad equal to V 2 mv 2 decreases at a rate of (mgv- ~ mv 2) C c~stat ad equal to ~2 mv 2 decreases at a rate of (~2 mv 2- myv) icreases al a rate of mgv decreases at a rate of mgv icreases at a rate of mgv decreases at arate of (12 mv 2- my\') J bicycle dyamo is started at time zero. The total eergy trasformed by the dyamo durig the first 5 secods icreases as show i the graph. eergyj V o o times What is the maximum power geerated at ay istat durig these first 5 secods? O.OW C 0.30W 0.13W 0.50W J94116 The heat-shield of the vehicle dissipates heat at a rate P, so that the mea temperature of the vehicle remais costat. Takig g as the relcv.mt value of the acceleratio of free fall, which expressio is equal to P? C lgv lgv si e v2 1211lV2 si2e N boat movig at costat speed v through still water experieces a total frictioal drag F. What is the power developed by the boat? J force of 1000 N is eeded to lift the hook of a crae at a steady velocity. The crae is the used to lift a load of mass 1000 kg at a velocity of 0.50 m S-. How much of the power developed by the motor of the crae is used i liftig the hook ad the load? [Take gas 10 m S-2.] 5.0kW 5.5 kw C 20kW 22kW N The egie of a iter-city trai, travellig at 50 m S-, delivers a power of 2 MW. What is the tractive force exerted by the egie? 4xlO"N xlo5 N The diagram shows a wheel which is drive by a electric motor. rope is fasteed at oe ed to a sprig balace. The rope passes over the wheel ad supports a freely hagig load. Whe the wheel is turig at a steady speed. the balace readig is costat. circumferece of. 50 rev 5-1 wheel = O.30m 23 power statio has a efticiecy of 40% ad geerates 1000 MW of electrical power. What is the iput power ad the wasted power? iput powerlmw wasted powerlmw C N sprig balace load = loon 24 space vehicle of mass re-eters the arth's atmosphere at a agle eto the horizotal. Because of air resistace, the vehicle travels at a costat speed v. What is the output power of the motor? 0.3 kw C 1.5 kw 1.2 kw 1.8 kw N Work, ergy, Power 76 ' Physics Topical Paper

5 29 small electric motor is used to raise a weight of 2.0 N through a vertical height of 80 em i 4.0 s. motor 33 (b) The strai eergy stored i the bow just before release of the arrow is 95 J. Whe the arrow of mass 170 g is fired, 90% of the strai eergy is trasferred to the arrow. Show that the speed of the arrow as it leaves the bow is 32 ms-. [3] N (part) Log Questios The efficiecy of the motor is 20%. What is the electrical power supplied to the motor? O.OSOW C 2.0W B 0.80 W 200 W N The maufacturer claims that the maximum power delivered by the egie of a car of mass 1200 kg is 90 kw. Fid the miimum time i which the car could accelerate from rest to 30 m S- (67 m.p.h.). idepedet test quotes a rest to 30 m 8-1 time of 13.4 s. Suggest a reaso for the differece from the time you have calculated. J (a) efie power. *(b) Why is it that, i the S system of uits, power caot be detied usig the equatio power = potetial differece x curret? [2] NS (a) what way is the mometum of a body affected by the resultat force actig o it? [2] (b) (c) coveyor belt travellig at a speed of3.0 m S- ad at a agle of 20 to the horizotal has t8 kg ofsugar dropped o to it each secod as show i Fig. 4. ssumig that the sugar has egligible speed before reachig the belt, calculate (i) the mometum gaied i each secod by the sugar, the force which the belt must exert o the sugar to ~lccelerate it to the speed of the belt, (iii) the work doe per secod by the belt o the sugar i exertig this force. (iv) the potetial eergy gaied i each secod by all the 36 kg of the sugar which is o the belt. [7] From your aswers to (b) tid the extra power required by the drivig motor whe the belt is loaded rather tha uloaded. [2] N (c) (i) perpefllal motio machie would be able to produce a cotiuous output of work with o eergy iput. State the physical priciple which makes this impossible. [2] Fig. 5 shows oe suggestio put forward as a perpetual motio machie. The ball i positio would fall off the top of the water doig work o the pulley belt. t B it would move sideways doig o work ad eter the bottom of the tak by a valve system which would prevet water from escapig. t would the float to the top ready to start agai o --- Fig.S xplai why this system will ot behave as a perpetual motio machie. [5] J (part) 35 (a) (i) xplai what is meat by the cocept of work. Hece derive the equatio p = gh, for the potetial eergy chage of a mass 111 moved through a vertical distace " ear the arth's surface. [4] J98J 15 (part) 36 (c) The miimum flyig speed for a bird called a housemarti is 9.0 m S-. t reaches this speed by fallig from its est before swoopig away. Calculate the miimum distace its est must be above the groud. [2] (d) house-marti has a mass of 120 g. Whe it returs to its est, it is travellig horizotally at P with a speed of 13.0 m S- ad at a distace 7.5 m below its est. t the glides upwards to the est, as show i Fig. 6. Neglectig ay air resistace, calculate (i) the kietic eergy of the house-marti at P, the total gai i potetial eergy as it glides upwards to its est, 6 Work, ergy, Power 77 ' Physics Topical Paper

6 (iii) its kietic eergy as it reaches its est, (iv) its speed as it reaches its est. path of bird's llight est 38 (a) (b) t is ofte stated that may fos of trasport trasform chemical eergy ito kietic eergy. xplai why a cyclist travellig at costat speed is ot makig this trasformatio. xplai what trasformatios of eergy are takig place. [5] N efie i) work, power. [3] By referece to equatios of motio, derive a expressio for the kietic eergy k of a object of mass movig at speed v. [4] ,-:-.... Fig. 6 iscuss qualitatively how air resistace affects, if at all, each of your aswers i (d). [4] N (part) 37 (a) Startig with the defiitio of work, deduce the chage i the gravitatioal potetial eergy of a mass m, whe moved a dist&ce " upwards agaist a gravitatioal field of field stregth g. [3] (b) By usig the equatios of motio, show that the kietic eergy K of a object of mass travellig with speed v is give by K =} lv 2 [3] cyclist, together with his bicycle, has a total mass of 90 kg ad is travellig with a costat speed of 15 m S- o a at road at, as illustrated i Fig. 7. He the goes dow a small slope to B so descedig 4.0 m. Calculate Fig. 7 (i) the kietic eergy at, the loss of potetial eergy betwee ad B, (iii) the speed at B, assumig that all the lost potetial eergy is trasformed ito kietic eergy of the cyclist ad bicycle. [5] B (d) car is travellig alog a horizotal road with speed v, measured i metres per secod. The power p, measured i watts, required to overcome exteral forces opposig the motio is give by the expressio P= cv +kv3, where e ad k are costats. (i) Use base uits to obtai a S uit for the costat k. For oe particular car, the umerical values. i S uits, of c ad of k are 240 ad 0;98 respectively. Calculate the power required to eable the car to travel alog a horizotal road at 31 m s-. [6] The car i has mass 720 kg. Usig your aswer to where appropriate, calculate, for the car travellig at 31 m s-', (i) its kietic eergy, the magitude of the exteral force opposig the motio of the car, (iii) the work doe i overcomig the force i Oi) durig a time of 5.0 miutes. [5] By referece to your aswers to (d), suggest. with a reaso, whether it would be worthwhile to develop a system whereby, whe the car slows dow, its kietic eergy would be stored for re-use whe the car speeds up agai. [2] J2000l12 (d) (i) cyclist travellig at a costat speed of 15 ms- o a level road provides a power of 240 W. Calculate the total resistive force. The cyclist ow travels at a higher costat speed. xplai why the cyclist eeds to provide a greater power. [4] 6 Work, ergy, Power 78 'N Physics Topical Paper

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions )

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions ) 04 - LAWS OF MOTION Page ) A smooth block is released at rest o a 45 iclie ad the slides a distace d. The time take to slide is times as much to slide o rough iclie tha o a smooth iclie. The coefficiet