15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

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Augustine Byrd
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1 Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a) foce / acceleation is diected towad a fixed point and foce / acceleation is popotional to distance fom that fixed point B ( b ) A ca tavels along a slightly undulating (ising and falling) oad which has a sinusoidal pofile, epeating itself at 80 m intevals with an amplitude of 0.60m. The ca tavels at a steady hoizontal speed of 5 m s -. As a esult, the ca undegoes simple hamonic motion. (i) Calculate the fequency of the simple hamonic motion. ( mak) (b)(i) 80 Peiod of sinusoidal cycle 5 fequency f f 0.88 Hz T 80 5 B (ii) Detemine the maximum vetical acceleation of the ca. ( maks) (ii) maximum acceleation ω A (πf) A (π 0.88) m s - C A (iii) Calculate the maximum vetical velocity and show that this has negligible effect on the esultant speed of the ca. ( maks) (iii) maximum vetical velocity ωa (π 0.88) m s - esultant velocity m s - so negligible M A (c) A sping balance, which ecods weight in N, is suspended fom the oof of a ca as shown in Figue. The sping constant of the sping in the sping balance is. 0 3 N m -. A mass of 5 kg is suspended fom the balance. Figue (i) At what speed would the ca have to tavel fo esonant oscillations to occu? Comment on you answe. ( maks) F6PhysicsEasteHolidaysAssignmentAns-

2 (c)(i) k Natual fequency f of the mass-sping system π m. 0 π 5.4 Hz m 5 o Peiod T π π 0.70 s 3 k. 0 Dis tance 80 so, speed at esonant v O 80.4 Time m s - which is 40 km h - and much faste than a typical ca can tavel o maximum acceleation at esonant a (πf) A (π.4) m s - vetical acceleation >> g so ca leaves oad 3 C Al B B (ii) Sketch a gaph showing how the eading on the balance vaies with time when the ca is tavelling at 5 ms -. Assume that the balance is damped enough to pevent oscillations. Include appopiate values. ( maks) (ii) coect geneal shape: sinusoidal about a positive eading with coect B peiod ( 5.3s) f 0.88 maximum and minimum values coect B max ~ m(g + ω A) 5( ) 63 N, min ~ m(g - ω A) 37 N Balance eading / N Time / s. As an altenative to a petol engine, a pototype ca is fitted with a flywheel. This is spun to a high speed at the stat of a jouney. To stat the ca the flywheel is connected to the dive wheels by a system of geas. The otational enegy stoed in the flywheel is then used to popel the ca. The flywheel has a moment of inetia of 90 kg m Befoe each jouney the flywheel is acceleated until it has an angula speed of 300 ad s -. (a) State the factos, which affect the moment of inetia of the flywheel. ( maks) (a) mass (of the flywheel) distibution of the mass (allow adius of the flywheel) o Σm definition of tems (b) Assuming the angula acceleation to be unifom, detemine the toque equied to acceleate the flywheel to its maximum speed in.5 minutes. F6PhysicsEasteHolidaysAssignmentAns- B B B B

3 (b) ω f ω i Angula acceleation α t toque Iα N m ad s - C C A 3 (c) Calculate the enegy stoed in the flywheel at the stat of a jouney. (c) C l Enegy Iω C J o 4.05 MJ A 3 (d) The aveage esistive foce on the ca duing one jouney is 400N. Calculate the maximum distance the ca can tavel duing this jouney. ( maks) (d) wok done foce distance moved (in diection of foce) Cl Distance moved A m, 0. km 3. (a) Define gavitational field stength at a point in a gavitational field. ( mak) (a) Gavitational foce acting pe unit mass GM O g F/m o g with tems defined B (b) Tides vay in height with the elative positions of the Eath, the Sun and the Moon which change as the Eath and the Moon move in thei obits. Two possible configuations ae shown in Figue. F S F E F M Configuation A F M F S F E Configuation B Figue F6PhysicsEasteHolidaysAssignmentAns-3

4 Conside a kg mass of sea wate at position P. This mass expeiences foces F E, F M and F S due to its position in the gavitational fields of the Eath, the Moon and the Sun espectively. (i) Daw labelled aows on both diagams in Figue to indicate the thee foces expeienced by the mass of sea wate at P. (b)(i)diection of F E coect in each diagam diection of F M coect in each diagam diection of F S coect in each diagam F S must be distinguished fom F M penalty of mak fo any missing labelling B B B 3 (ii) State and explain which configuation, A o B, of the Sun, the Moon and the Eath will poduce the highe tide at position P. ( maks) (ii) Because sun and moon pulling in same diection M O esultant of F M and F S is geatest. O clea esponse including summation of F M and F S. Configuation A will poduce the highe tide at position P. Al (c) (c) Calculate the magnitude of the gavitational foce expeienced by kg of sea wate on the Eath s suface at P, due to the Sun s gavitational field. adius of the Eath s obit.5 0 m mass of the Sun kg univesal gavitational constant, G N m kg - GMm F C 30 C (.5 0 ) N kg - ( N kg - ) Al 3 4. (a) How much wok is done in moving an electon fom point X to point Y? [The pemittivity of fee space 0 ε C m - N - ] Wok done on the electon change in potential enegy of the electon W E p Qq W 4πε 0 Qq 4πε 0 Qq 4πε 0 ( )( ) W 4π W J (b) What is the potential diffeence between point X and point Y? ( maks) W V q V V Note: Both positive and negative answes will be accepted. F6PhysicsEasteHolidaysAssignmentAns-4

5 5. (a) Figue 3 Thee identical esistos, each with esistance, and a capacito of F ae connected to a 30 V battey with negligible intenal esistance, as shown in Figue 3. Switches S and S ae initially closed, and switch S 3 is initially open. A voltmete is connected as shown in Figue 3. (i) Detemine the eading on the voltmete. (4 maks) (a)(i) The net esistance of the two paallel esistos + // // The total esistance of the cicuit T + Using Ohm s law: I V I T 3 I 0 V Voltage acoss voltmete V V I V V 0 0 V 4 Since all thee esistos have equal values, it is possible to compae the esist ance of the paallel combinat ion to the tot al esistance and then split the voltage coectly with a minimum of witten calculation. Full cedit could be eaned fo this appoach. (ii) Switches S and S ae now opened, and then switch S 3 is closed. Detemine the chage Q on the capacito afte S 3 has been closed fo a vey long time. ( maks) F6PhysicsEasteHolidaysAssignmentAns-5

6 (ii) Q CV Q ( )(30) C (b) Afte the capacito is fully chaged, switches S and S emain open, switch S 3 emains closed, the plates ae held fixed, and a conducting coppe block is inseted midway between the plates, as shown in Figue 4. The plates of the capacito ae sepaated by a distance of.0 mm, and the coppe block has a thickness of 0.5 mm. Figue 4 (i) What is the potential diffeence between the plates? ( mak) (b)(i) The 30 V battey is still connected acoss the capacito and thee is no cuent, so the potential diffeence emains the same. The potential between the plates is 30 V (ii) What is the electic field inside the coppe block? ( mak) (ii) At equilibium, the field inside any conducto is zeo. The electic field inside the coppe block is zeo. (iii) On the diagam above, daw aows to clealy indicate the diection of the electic field between the plates. ( maks) (iii) Fo aows diected down between the top plate and the coppe block. Fo having no aows inside the coppe block. ½ Fo aows diected down between the coppe block and the lowe plate. No cedit was awaded if them was nothing dawn between the plates. ½ (iv) (iv) E d V Detemine the magnitude of the electic field in each of the spaces between the plates and the coppe block E o V m Sola stoms consist of potons and helium nuclei emitted fom the sun. A paticula sola stom hits the Eath s atmosphee at a speed of. 0 6 m s -. The paticles pass above the Noth magnetic pole moving paallel to the Eath s suface. In this egion the Eath s magnetic field is diected vetically downwads and has a flux density of T. (a) Calculate the adius of the path of a poton fom the stom as it passes diectly above the Eath's Noth magnetic pole. F6PhysicsEasteHolidaysAssignmentAns-6

7 mass of a poton kg chage on a poton C (a) The magnetic foce acting on the poton povides the necessay centipetal foce fo the poton. mv Bev mv Be m C C A 3 (b) Figue 5 shows the initial velocity of a poton and the diection of the Eath s magnetic field. Daw and label, on Figue 5, the path of the poton and that of a helium nucleus which has the same initial velocity as the poton. State on the diagam the adius of the path of each paticle. mass of a helium nucleus 6.8 x 0-7 kg chage on a helium nucleus 3. x 0-9 C helium nucleus path poton path Figue 5 (b) labelled poton path, cuved in coect diection helium adius of 440 m / x distinguishable and unambiguous both in same diection B B B 3 F6PhysicsEasteHolidaysAssignmentAns-7

ev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e

ev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e . A paallel-plate capacito has sepaation d. The potential diffeence between the plates is V. If an electon with chage e and mass m e is eleased fom est fom the negative plate, its speed when it eaches