Practice with SHM & GravityANSWERS ARE AT THE END OF THE WORKSHEET. Note: To simplify calculations, you may use g = 10 m/s2 in all problems

1. A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3.0 kg block is then replaced by a 4.0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4.0 kg block fall before its direction is reversed?a. 9 cm b. 18 cm c. 24 cm d. 32 cm e. 48 cm

2. When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position. Which of the following is true of the values of its speed and the magnitude of the restoring force?

Speed Restoring Force(A) Zero Maximum(B) Zero Zero(C) ½ maximum ½ maximum(D) Maximum ½ maximum(E) Maximum Zero

Questions 3-4: A block oscillates without friction on the end of a spring as shown to the right. The minimum and maximum lengths of the spring as it oscillates are, respectively, xmin and xmax. The graphs below can represent quantities associated with the

oscillation as functions of the length x of the spring.

3. Which graph can represent the total mechanical energy of the block-spring system as a function of x ?(A) A (B) B (C) C (D) D (E) E

4. Which graph can represent the kinetic energy of the block as a function of x ?

(A) A (B) B (C) C (D) D (E) E

5. An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph to the right. The nature of the velocity v

and acceleration a of the object at time is best

represented by which of the following?(A) v > 0, a > 0 (B) v > 0, a < 0 (C) v > 0, a = 0 (D) v = 0, a < 0 (E) v = 0, a = 0

6. If the mass of a simple pendulum is doubled but its length remains constant, its period is multiplied by a factor of

(A) (B) (C) 1 (D) (E) 2

7. When a mass is attached to a spring, the period of oscillation is approximately 2.0 seconds. When the mass attached to the spring is doubled, the period of oscillation is most nearly(A) 0.5 s (B) 1.0 s (C) 1.4 s ( D) 2.0 s ( E) 2.8 s

8. An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?a. 16W b. 4W c. W d. ¼ W e. W

9. What is the kinetic energy of a satellite of mass m that orbits the Earth, of mass M, in a circular orbit of radius R?

a. Zero b. c. d. e.

10. Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the surface of Mars is most nearly (A) 0.25 m/s2 (B) 0.5 m/s2 (C) 2 m/s2 (D) 4 m/s2 (E) 25 m/s2

11. A satellite of mass M moves in a circular orbit of radius R at a constant speed v. Which of the following must be true?

I. The net force on the satellite is equal to and is directed toward the center of the orbit.

II. The net work done on the satellite by gravity in one revolution is zero.III. The angular momentum of the satellite is a constant.(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

12. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each satellite are given below. Which satellite has the greatest speed?

Mass Radius(A) ½m R(B) m ½R(C) m R(D) m 2R(E) 2m` R

13. An asteroid moves in an elliptic orbit with the Sun at one focus as shown to the right. Which of the following quantities increases as the asteroid moves from point P in its orbit to point Q ?

(A) Speed (B) Angular momentum (C) Total energy (D) Kinetic energy (E) Potential energy

14. Two planets have the same size, but different masses, and no atmospheres. Which of the following would be the same for objects with equal mass on the surfaces of the two planets?I. The rate at which each would fall freelyII. The amount of mass each would balance on an equal-arm balanceIII. The amount of momentum each would acquire when given a certain impulse(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

15. A person weighing 800 newtons on Earth travels to another planet with twice the mass and twice the radius of Earth. The person's weight on this other planet is most nearly(A) 400 N (B) 800/ N (C) 800 N (D) 800 N (E) 1,600 N

FREE RESPONSE:1. A body of mass 0.20 kg is attached to a wall by a spring with constant k = 13 N/m. It is initially pulled

a distance of x = 0.20 m from its equilibrium position and released from rest.a. What is the body’s initial potential energy?b. What is the body’s initial kinetic energy?c. What is the body’s total energy?d. What is the body’s speed when it passes through the equilibrium position?e. Amplitudef. Frequencyg. Periodh. the displacement 0.10 s after the mass is releasedi. the velocity 0.10 s after the mass is released.

2. Show that to maintain a circular orbit above a planet, a. The speed has a constant value.

b. The period of the orbit is given by .

An explorer plans a mission to place a 4000 kg satellite into a circular orbit around the planet Jupiter, which has a mass of MJ = 1.9 x 1027 kg and radius RJ = 7.14 x 107 m.

a. If the explorer wants the satellite’s orbit to be synchronized with Jupiter’s rotations that requires an orbit whose period equals Jupiter’s rotation period of 9 hr 51 min = 3.55 x 104s, what would be the orbital radius, RA, in meters?b. What is the velocity, VA, and angular momentum, LA, of the satellite in this position?c. What would the velocity of the satellite have to be in order for it to escape Jupiter’s gravitational pull?d. If 8.66 x 1011 J of work is done on the satellite by rocket thrusters, what is its new velocity?e. At this new velocity, the orbit becomes elliptic. What is the velocity, VB, of the satellite at a position RB = 4.8 x 108 m, as shown in the illustration below.

Answers:Multiple Choice:1- d2- a3- e4- d5- d6- c7- e8- e9- b10- d11- e12- b13- e14- d15- a

Free Response Problem 1

a- 0.26Jb- 0c- 0.26Jd- 1.6m/se- 0.2mf- 1.28 Hzg- 0.78sh- 0.14mi- 1.16m/s

Problem 2:Set the force gravity equal to centripetal force and prove that v must be constant in order for r to be constant.Problem 3:

a- 1.59*108mb- 28142m/sc- 59581m/sd- 35000m/se- 11594m/s