Download Ch. 8 Note Sheet

AP PHYSICS C
NAME___________________________
CH. 8 MOMENTUM AND ITS CONSERVATION
DATE_____________PERIOD_________
NOTESHEET
1.
Define the following terms:
a. Center of mass
b. Impulse
c. Momentum
d. Conservation of momentum
2. The concept of the center of mass allows us to describe the movement of a system of particles
by ____________________________________________________.
3. Equations for the center of mass:
4. Sample Problem 1: Calculate the center of mass of the following system: A mass of 5 kg lies at x
= 1, a mass of 3 kg lies at x = 4 and a mass of 2 kg lies at x = 0.
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5. Sample Problem 2: Calculate the center of mass of the following system: A mass of 10 kg lies at
the point (1,0), a mass of 2 kg lies at the point (2,1) and a mass of 5 kg lies at the point (0,1).
6. Center of Mass Equations:
a. Velocity of the center of mass:
b. Acceleration of the center of mass:
c. External Net Force
7. Sample Problem 3: Consider the system from problem 2, but now with forces acting upon the
system. On the 10 kg mass, there is a force of 10 N in the positive x direction. On the 2 kg mass,
there is a force of 5 N inclined 45o above horizontal. Finally, on the 5 kg mass, there is a force of
2 N in the negative y direction. Find the resultant acceleration of the system.
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8. Two masses, m1 and m2, m1 being larger, are connected by a spring. They are placed on a
frictionless surface and separated so as to stretch the spring. They are then released from rest.
In what direction does the system travel?
9. Sample Problem 5: A 50 kg man stands at the edge of a raft of mass 10 kg that is 10 meters
long. The edge of the raft is against the shore of the lake. The man walks toward the shore, the
entire length of the raft. How far from the shore does the raft move?
10. Impulse can be defined mathematically, and is denoted by J: __________________
11. More on Impulse:
12. Sample Problem 6:
a. What is the impulse of a force of 10 N acting on a ball for 2 seconds?
b. The ball has a mass of 2 kg and is initially at rest. What is the velocity of the ball after the
force has acted on it?
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13. From our equation relating impulse and velocity, it is logical to define the momentum of a single
particle, denoted by the vector p, as such: __________________________
14. Sample Problem 7: A particle has linear momentum of 10 kg-m/s, and a kinetic energy of 25 J.
What is the mass of the particle?
15. Relation between force and acceleration: If we take a time derivative of our momentum
expression we get the following equation:
16. Sample Problem 8: A 2 kg bouncy ball is dropped from a height of 10 meters, hits the floor and
returns to its original height. What was the change in momentum of the ball upon impact with
the floor? What was the impulse provided by the floor?
17. Sample Problem 9: A ball of 2 kg is thrown straight up into the air with an initial velocity of 10
m/s. Use the impulse-momentum theorem, calculate the time of flight of the ball.
18. Momentum and Kinetic Energy:
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19. Total momentum of a system: Suppose we have a system of N particles, with masses m1, m2,…,
mn. Assuming no mass enters or leaves the system, we define the total momentum of the
system as the vector sum of the individual momentum of the particles.
20. Sample Problem 10: A 60 kg man standing on a stationary 40 kg boat throws a .2 kg baseball
with a velocity of 50 m/s. With what speed does the boat move after the man throws the ball?
21. Sample Problem 11: A .05 kg bullet is fired at a velocity of 500 m/s, and embeds itself in a block
of mass 4 kg, initially at rest and on a frictionless surface. What is the final velocity of the block?
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22. Sample Problem 12: An object at rest explodes into three pieces. Two, each of the same mass,
fly off in different directions with velocity 50 m/s and 100 m/s, respectively. A third piece goes
off in the negative y-direction is also formed in the explosion, and has twice the mass of the first
two pieces. Determine the direction of the second particle and the speed of the third particle.
Let θ1 = 65o.
Θ2
θ1 = 65o
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23. Sample Problem 13: A spaceship moving at 1000 m/s fires a missile of mass 1000 kg at a speed
of 10000 m/s. What is the mass of the spaceship it slows down to a velocity of 910 m/s?
24. Define the following terms:
a. Collisions:
b. Elastic Collision:
c. Inelastic Collision:
d. Totally Inelastic Collision:
25. Elastic Collisions: Why are these collisions special?
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26. Sample Problem 14: Two balls, each with mass 2 kg, and velocities of 2 m/s and 3 m/s collide
head on. Their final velocities are 2 m/s and 1 m/s, respectively. Is this collision elastic or
inelastic?
27. Sample Problem 15: Two balls of mass m1 and m2, with velocities v1 and v2 collide head on. Is
there any way for both balls to have zero velocity after the collision? If so, find the conditions
under which this can occur.
28. Sample Problem 16: Two balls with equal masses, m, and equal speed, v, engage in a head on
elastic collision. What is the final velocity of each ball, in terms of m and v?
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29. Sample Problem 17: One pool ball traveling with a velocity of 5 m/s hits another ball of the
same mass, which is stationary. The collision is head on and elastic. Find the final velocities of
both balls.
30. Inelastic Collisions: So what if kinetic energy is not conserved?
31. Sample Problem 18: A car of 500 kg, traveling at 30 m/s rear ends another car of 600 kg,
traveling at 20 m/s. in the same direction The collision is great enough that the two cars stick
together after they collide. How fast will both cars be going after the collision?
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32. 2-D Collisions: Two balls of equal masses move toward each other on the x-axis. When they
collide, each ball ricochets 90 degrees, such that both balls are moving away from each other on
the y-axis. What can be said about the final velocity of each ball?
33. Sample Problem 19: Two pool balls traveling in opposite directions collide. One ball travels off
at an angle θ to its original velocity, as shown below. Is there any possible way for the second
ball to be completely stopped by this collision? If so state the conditions under which this could
occur.
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34. Sample Problem 20: Two objects are traveling perpendicular to each other, one moving at 2
m/s with a mass of 5 kg, and one moving at 3 m/s with a mass of 10 kg, as shown below. They
collide and stick together. What is the magnitude and direction of the velocity of both objects?
35. Sample Problem 21: A common pool shot involves hitting a ball into a pocket from an angle.
Shown below, the cue ball hits a stationary ball at an angle of 45o, such that it goes into the
corner pocket with a speed of 2 m/s. Both balls have a mass of .5 kg, and the cue ball is traveling
at 4 m/s before the collision. Calculate the angle with which the cue is deflected by the collision.
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