Study Guide for Gravitation, Centripetal Motion, and Momentum Exam

Part I consists of 20 multiple choice questions and Part II consists of several free response questions. Part I questions relate to the topics listed below. The free response questions are based on topics of momentum.

1. Momentuma) Be able to calculate the momentum of an object using p =mvb) Be able to use the impulse momentum theorem to solve problems, using J=FΔt=Δpc) Be able to apply conservation of momentum pbefore=pafter to inelastic collisions, elastic

collisions, and explosions

2. Newton’s Universal Gravitationa) Be able to calculate the gravitational force of attraction between two objects using

Fg=Gm1m2/r2

b) Be able to state how the gravitational force varies with distance or changes in massc) Be able to calculate gravitational field strength using g= Fg/md) Be able to draw the gravitational field around a mass such as earth. Be able to draw a

uniform gravitational field such as the gravitational field that exists on earth.

3. Centripetal Forcea) Be able to calculate centripetal acceleration and centripetal force using ac=v2/r and Fc=mac

b) Be able to identify the direction of velocity, centripetal acceleration, and centripetal forcec) Be able to calculate the speed of an object that is moving in a uniform circle when given the

time it takes for the object to complete one lap using v = d/t where d is the circumference of the circle

Sample Multiple Choice Questions

1. An object travels in a circular path of radius 5.0 meters at uniform speed of 10 m/s2. What is the magnitude of the object’s centripetal acceleration?a) 10m/s2 b) 2 m/s2 c) 5 m/s2 d) 20 m/s2

Base your answers to questions 2-6 on the diagram below which represents a ball of mass M attached to a string. The ball moves at a constant speed around a flat horizontal circle of radius R.

2. When the ball is in the position shown, the direction of the centripetal force is toward pointa) A b) B c) C d) D

3. The centripetal acceleration of the ball isa) Zero d) Constant in direction, but changing in magnitudeb) Constant in magnitude, but changing in directionc) Changing in both magnitude and direction

4. If the string is shortened while the speed of the ball remains the same, the centripetal acceleration willa) Decrease b) increase c) remain the same

5. If the mass of the ball is decreased, the centripetal force required to keep it moving in the same circle at the same speed willa) Decrease b) Increase c) remain the same

6. The instantaneous velocity of the mass at the position shown is directed toward positiona) A b) B c) C d) D

Base your answers to questions 7-10 on the diagram below which represents a 2 kg mass moving a circle at the end of a 0.5 m string. The mass moves at a constant speed of 4 m/s.

7. The force exerted on the mass by the string isa) 8 N b) 16 N c) 32 N d) 64 N

8. If the string is cut at the position shown, the mass will move toward which point?a) A b) B c) C d) D

9. At the position shown, the mass is accelerating toward pointa) A b) B c) d) D

10. The speed of the mass is changed to 2 m/s. Compared to the centripetal acceleration of the mass when moving at 4 m/s, its acceleration when moving at 2 m/s would bea) Half as great b) twice as great c) one fourth as great d) 4 times as great

11. Two masses of 10 kg and 1 kg, respectively, are located 1.0 meter apart. The gravitational force that each mass exerts on the other isa) 6.7 x 10-9 N b) 6.7 x 10-10 N c) 6.7 x 10-11 N d) 6.7 x 10-12 N

12. Gravitational force of attraction F exists between two point masses, A and B, when they are separated by a fixed distance. After mass A is tripled and mass B is halved, the gravitational attraction between the two masses isa) 1/6 F b) 2/3 F c) 3/2 F d) 6F

13. Two objects of fixed mass are moved apart so that they are separated by 3 times their original distance. Compared to the original gravitational force between them, the new gravitational force isa) 1/3 as great b) 1/9 as great c) 3 times greater d) 9 times greater

14. Which diagram best represents the gravitational force, Fg, between a satellite, S, and Earth?

15. Which diagram best represents the gravitational field lines surrounding Earth?

16. What is the gravitational field strength on a planet where a 2 kg mass has a weight of 16 Newtons on the planet’s surface?a) 1/8 N/kg b) 8 N/kg c) 10 N/kg d) 32 N/kg

17. A 2 kg object weighs 19.6 N on Earth. If the acceleration due to gravity on Mars is 3.71 m/s2, what is the object’s mass on Mars?a) 2.64 kg b) 2 kg c) 19.6 N d) 7.42 N

Multiple Choice Problems on Momentum

18. If a 3 kg object moves 10 meters in 2 seconds, its average momentum isa) 60 kg m/s b) 30 kg m/s c) 15 kg m/s d) 10 kg m/s

19. A 15 N force acts on an object in a direction due east for 3.0 seconds. What will be the change in momentum of the object?a) 45 kg m/s (E) b) 45 kg m/s (W) c) 5 kg m/s (E) d) 0.2 kg m/s (W)

20. A 2 N force acts on a mass. If the momentum of the mass changes by 120 kg m/s, the force ats for a time ofa) 8s b) 30 s c) 60 s d) 120 s

More Momentum Questions on Next Page

Free Response Midterm Review Questions on Momentum

Example 1 (Gravitation):

a) Calculate the gravitational force between the Earth and the Sun. The Sun has a mass of 2 x 1030 kg and is a distance of 1.5 x 1011 m from Earth. (Show all work including the equation and substitutions with units).

b) Find the acceleration of the earth due to this force. (Show all work including the equation and substitution with units).

Example 2 (Centripetal Motion): If the moon moves in a circular orbit around the Earth and has a speed of 3,683,000 m/s, what is the centripetal force on the moon? (Show all equations including equation and substitution with units).

Example 3: Explosion

A cannon with a mass of 500 kg initially at rest fires a clown of 100 kg to the right at a velocity of 15 m/s.

What is the recoil velocity of the cannon? (Show all work)