Unit 6 Test Review Gravitation & Oscillation Chapters 13 & 15

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1 A.P. Physics C Unit 6 Test Review Gavitation & Oscillation Chaptes 13 & 15 * In studying fo you test, make sue to study this eview sheet along with you quizzes and homewok assignments. Multiple Choice Review: On this potion of the test, you will not be allowed to use you calculato o AP fomula sheet. (You may, howeve, use you AP table of infomation.) Appoximate g=10m/s fo simplicity of calculations. No patial cedit will be given. 1. A new planet is discoveed that has twice the Eath s mass and twice the Eath s adius. On the suface of this new planet, a peson who weighs 500N on Eath would expeience a gavitational foce of... a. 15N b. 50N c. 500N d. 1000N e. 000N. What is the obital speed of a satellite of mass m obiting the eath at a distance fom the cente of the Eath? (Assume that G stands fo the gavitational constant and M stands fo the Eath s mass.) a. b. c. Gm d. Gm 3. Which one of the following would be the coect value fo the escape speed fo a kg object fom a 0,000kg asteoid of adius 100m? (All answes ae in metes pe second.) a. 0G b. 400G c. G d. 0 G e. 50 G e. 4. A ock of mass m is a distance R above the suface of a planet. If the planet has a mass of M and adius also equal to R, what is the value of g at the location of the ock? a. R Gm b. R c. R Gm d. R e. 4R 5. Two 1kg masses ae in distant oute space at a distance of 1m apat fom each othe. How much wok must you do to move them to a distance of m apat? G G a. G b. c. d. G e. 4G 4

2 6. A 10kg mass is attached to a sting of length 40m, and hung down fom a ooftop to make a long pendulum. If the pendulum is set into simple hamonic motion, what is its peiod of vibation? a. π / seconds b. π seconds c. π seconds d. 4 π seconds e. 8 π seconds 7. A block attached to the lowe end of a vetical sping oscillates up and down. If the sping obeys Hooke s law, the peiod of oscillation depends on which of the following? I. Mass of the block II. Amplitude of the vibation III. Foce constant of the sping a. I only b. II only c. III only d. I and II e. I and III 8. A simple pendulum and a mass hanging on a sping both have a peiod of 1s when set into small oscillatoy motion on Eath. They ae taken to Planet X, which has the same diamete as Eath but twice the mass. Which of the following statements is tue about the peiods of the two objects on Planet X compaed to thei peiods on Eath? a. Both ae shote. b. Both ae the same. c. Both ae longe. d. The mass-sping s peiod is shote; the pendulum s peiod is the same. e. The pendulum s peiod is shote; the mass-sping s is the same. 9. A mass is attached to a sping and set into simple hamonic motion. Which one of the following statements is tue about the mass? a. The mass has minimum kinetic enegy when it is at equilibium. b. The mass has maximum velocity when it is at its amplitude. c. The total mechanical enegy of the mass is geate when it is at equilibium than at its amplitude. d. The mass expeiences the maximum estoing foce at equilibium. e. The mass has maximum acceleation when it is at its amplitude.

3 10. A student is asked to detemine the mass of Jupite. Knowing which of the following about Jupite and one of its moons will allow the detemination to be made? I. The time it takes fo Jupite to obit the Sun. II. The time it takes fo the moon to obit Jupite. III. The aveage distance between the moon and Jupite. a. I only b. II only c. III only d. I and II e. II and III 11. A mass attached to a sping is vibating with simple hamonic motion accoding to the following equation: x = (0.4)cos(8πt) Assuming all quantities ae measued in S.I. units, what is the peiod of vibation of the mass? a. 0.5s b. 0.4s c. s d. 4s e. 8s Poblem Review: On this potion of the test, you may use you calculato, AP fomula sheet, and AP table of infomation. Patial cedit will be given on these poblems. 1. A 5kg od is hung fom a 10cm-long vetically-oiented sping, and stetches the sping an additional 3cm fom equilibium. a. Calculate the k-value of the sping. b. Now an additional identical sping is connected, so that the od is suppoted by a sping at both ends. If it is set into oscillation, what is the peiod of its motion? 13. Calculate the fequency of motion fo a 10kg simple pendulum with a length of 75cm.

4 14. A simple hamonic oscillato is moving with an amplitude of 8cm and fequency of 9.Hz. Calculate the maximum velocity and acceleation of the oscillato. 15. A kg sphee with a adius of 1cm is suspended fom one end of a long thin od that is fee to pivot about an axis though its cente. Calculate the peiod of its motion, if the od has a mass of 800g and a length of 90cm. Body Mass (kg) Mean Radius (m) Distance fom Sun (m) Eath 5.98x x x10 11 Sun 1.991x x Moon 7.36x x * Distance fom the Eath s suface to the Moon s suface = 384,000 km 16. Use the given infomation in the table to detemine a. the gavitational foce between the Moon and Eath. b. the obital speed of the Moon aound the Eath. c. the peiod of obit of the Moon.

5 17. A 5kg ock is eleased fom est at a distance of 0m above the suface of a cetain spheical asteoid. If the asteoid s mass is 7,500,000kg and its adius is 5.8m, how fast is the ock moving when it stikes the asteoid s suface? 18. Fo the same asteoid as discussed in #17, calculate its escape speed. 19. A sping (k=19.6n/m) is connected to a 3kg mass, making a hoizontal mass-sping system. If the system is compessed 5cm and eleased fom est, find the following: a. The maximum speed of the mass. b. The x-location (distance fom equilibium) whee the speed of the mass is 1/3 its maximum speed. 0. A cetain planet has two moons obiting aound it, with the second moon s obit having a adius that is.4 times as lage as the adius of the fist moon s obit. If the fist moon completes a full obit once evey 1.5 hous (measued in Eath time), what is the peiod of obit of the second moon?

6 1. Actual A.P. Physics C Fee-Response Question, sot of (008): In an expeiment to detemine the sping constant of an elastic cod of length 0.60 m, a student hangs the cod fom a od as epesented above and then attaches a vaiety of weights to the cod. Fo each weight, the student allows the weight to hang in equilibium and then measues the entie length of the cod. The data ae ecoded in the table below: (a) Use the data to plot a gaph of weight vesus length on the axes below. Sketch a best-fit staight line though the data. (b) Use the best-fit line you sketched in pat (a) to detemine an expeimental value fo the sping constant k of the cod.

7 . Actual A.P. Physics C Fee-Response Question, sot of (007): In Mach 1999, the Mas Global Suveyo (GS) enteed its final obit about Mas, sending data back to Eath. Assume a cicula obit with a peiod of 118 minutes and obital speed of 3400 m/s. The mass of the GS is 930kg and the adius of Mas is 3.43x10 6 metes. a. Calculate the adius of the GS obit. b. Calculate the mass of Mas. c. Calculate the total mechanical enegy of the GS in this obit. d. If the GS was to be placed in a lowe cicula obit (close to the suface of Mas), would the new obital peiod of the GS be geate than o less than the given peiod? Justify you answe.

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,