Honors Assignment - Momentum
Reading Chapter 7
Objectives/HW
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The student will be able to: |
HW: |
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1 |
Define and calculate momentum using appropriate SI units. |
1 |
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2 |
Define and calculate impulse and solve problems relating impulse, momentum, and force. |
2 – 6 |
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3 |
State and apply the law of conservation of momentum with proper consideration to internal and external forces. |
7 – 9 |
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4 |
Use conservation of momentum to solve related problems. |
10 – 19 |
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5 |
Define elastic and inelastic collisions and use the definitions to solve related problems. |
20 – 26 |
Homework Problems
1. Can a bullet have the same momentum as a truck? Explain.
2. An object with initial momentum 5.00 kg m/s, 0.0° experiences a net force of 20.0 N, 180° for a duration of 1.50 seconds. (a) Determine the net impulse. (b) Determine the object’s momentum at the end of the 1.50 seconds.
3. A rubber ball of mass 50.0 grams bounces off the floor. Its velocity just before the bounce is 5.00 m/s, 270° and just after the bounce 4.50 m/s, 90°. (a) Determine the change in momentum of the ball. (b) Determine the net impulse acting on the ball. (c) Determine the average force of the ball acting on the floor if the bounce lasts just 0.010 seconds.
4. The momentum of a certain car changes by 500 kg m/s in 2.00 seconds. (a) Determine the amount of net force on the car. (b) If the car has mass 1500 kg, by how much does its velocity change?
5. The main engines of the space shuttle each burn fuel at a rate of 492 kg/s. The exhaust gases have a velocity of 3390 m/s, 270.0°. (a) What is the thrust developed by each of the main engines? (b) The solid boosters produce a thrust of 11.8 MN. Assuming the exhaust velocity is the same as the main engines what is the mass burn rate?
6. I used to own an old
house with a chimney that was falling apart as the old mortar between the
bricks dried out. I used to worry the wind would blow it over. Suppose the
wind reaches 75 mph and blows directly against the side of the chimney, which
has dimensions 3.0 m ´ 0.90 m. The density of
air is 1.2 kg/m3. Find the force on the chimney due to the wind
(a) assuming the air is brought to a stop by the impact, and (b) assuming the
air rebounds in the opposite direction at 75 mph.
7. If only an external force can change the momentum of a system or object, how can the internal force of a car’s brake pads and rotors bring the car to a stop?
8. NASA scientists often face a common problem when sending a spacecraft to another world. The spacecraft will be moving at tremendous speed to get to the world, but then it must be slowed down in order to be put into orbit. In light of the law of conservation of momentum, how is it possible to slow down a spacecraft in the void and vacuum of space?
9. Two bullets of equal mass are shot at equal speeds at blocks of wood on a smooth ice surface. One bullet, made of rubber, bounces off the wood. The other bullet, made of aluminum, burrows into the wood. Which bullet makes the wood move faster? Why?
10. A 95 kg fullback, running at 8.2 m/s, 0.0°, collides in midair with a 128 kg defensive tackle moving in the opposite direction. Both players end up with zero speed. (a) What was the fullback’s momentum before the collision? (b) What was the change in the fullback’s momentum? (c) What was the change in the tackle’s momentum? (d) What was the tackle’s original momentum? (e) What was the tackle’s speed originally?
11. Ball A, mass 5.0 g, moves at a velocity of 20.0 cm/s, 180.0°. It collides with Ball B, mass 10.0 g, moving with velocity 10.0 cm/s, 180.0°. After the collision, ball A is still moving but with a velocity of 8.0 cm/s, 180.0°. (a) Find the momentum of ball B after the collision. (b) Find the resulting velocity of ball B. (c) By how much did each ball’s momentum change?
12. A 2575 kg van runs into the back of an 825 kg compact car at rest. They move off together at 8.5 m/s. Ignoring friction, find the initial speed of the van.
13. A 15 g bullet is shot into a 5085 g wooden block standing on a frictionless surface. The block, with the bullet in it, acquires a speed of 1.2 m/s. Calculate the speed of the bullet.
14. A hockey puck, mass 0.115 kg, moving at 35.0 m/s, strikes an octopus thrown on the ice by a fan. The octopus has a mass of 265 g. The puck and octopus slide off together. Find the speed. (Yes, there truly are hockey fans that throw octopuses on the ice. Isn’t life strange?)
15. A 50 kg woman, riding on a 10 kg cart, is moving east at 5.0 m/s. The woman jumps off the cart and hits the ground running at 7.0 m/s, eastward, relative to the ground. Calculate the velocity of the cart after she jumps off.
16. A 92 kg fullback, running at 5.0 m/s, attempts to dive across the goal line for a touchdown. Just as he reaches the goal line, he is met head-on in midair by two 75 kg linebackers, one moving at 2.0 m/s and the other at 4.0 m/s. If they all become entangled as one mass, with what velocity do they travel? Does the fullback score?
17. A 10.0 g bullet leaves a rifle with a speed of 800.0 m/s. What should be the minimum mass of the rifle in order that its recoil speed cannot possibly exceed 1.50 m/s?
18. A robotic space probe of mass 7600 kg is traveling through space at 120 m/s. Mission control determines that a change in course of 30.0° is necessary and instructs the probe to fire rockets perpendicular to its direction of motion. If the escaping gas leaves the craft’s rockets at an average speed of 3200 m/s, what mass of gas should be expelled?
19. You are investigating a
car wreck. Mr. Q was traveling east in an 1800 lb car and collided with Ms. X
who was traveling south in a 2200 lb car. The cars stuck together and the skid
marks indicate that they moved in a direction of 325° after the collision. Both drivers claim
to have been driving the speed limit of 45 mph. (a) Show mathematically that
one of them has to be lying. (b) Assuming Ms. X is telling the truth, how fast
was Mr. Q driving?
(c) Assuming Mr. Q is telling the truth, how fast was Ms. X driving? (Now, who
do you think was really lying?)
20. When two automobiles collide it will always be an inelastic collision. And if there is friction the total momentum of the two cars will be reduced in the collision. (a) Is this type of collision a violation of the law of conservation of energy? Explain. (b) Is this type of collision a violation of the law of conservation of momentum? Explain.
21. A railroad car with mass of 5.0 ´ 105 kg collides with a stationary railroad car of equal mass. After the collision, the two cars lock together and move off at 4.0 m/s. (a) Determine the initial speed of the first car. (b) Determine the amount of momentum before and after the collision. (c) Determine the total amount of kinetic energy before and after the collision. (d) Explain what becomes of the “missing” kinetic energy.
22. A golf ball, mass 0.046 kg, rests on a tee. It is struck by a golf club with an effective mass of 0.220 kg and a speed of 44 m/s. Assuming the collision is perfectly elastic, find the speed of the ball when it leaves the tee.
23. A steel glider with a mass of 5.00 kg moves along an air track 15.0 m/s, 0° It overtakes and collides with a second glider of mass 10.0 kg moving in the same direction at 7.50 m/s. After the collision the first glider continues in the same direction at 7.00 m/s. (a) With what velocity did the second glider leave the collision? (b) What was the change in momentum of the first glider? (c) What was the change in momentum of the second glider? (d) Was the collision elastic? (prove your answer numerically)
24. A proton (mass = 1.67 x 10-27 kg) moves with a speed of 6.00 Mm/s. Upon colliding elastically with a stationary particle of unknown mass, the proton rebounds on its own path with a speed of 3.60 Mm/s. Find the mass of the unknown particle.
25. Ball A of mass 5.00 kg
moves at a velocity of 4.00 m/s, 0°
to collide with a stationary, identical ball, B. After the collision ball A
moves in a direction of 30.0°;
ball B moves toward 300.0°. (a) Determine the
momentum of ball A and of ball B after the collision.
(b) Find the velocity of each ball after the collision. (c) Show numerically
that the collision is elastic.
26. Choose and solve one of the following problems from your book, pp. 202 – 208: 12, 61, 68, 69, 71, 76, 77
Selected Answers
6.67 ´ 10-27 kg
5.33 kg
160 kg
3480 kg/s
angle would be 309°, not 325°
0.041 m/s forward,TD!
16 cm/s, 180°
0.333 m/s
3.46 m/s, 30.0°; 2.00 m/s, 300.0°
5.0 m/s, west
6.1 m/s
8.0 m/s
10.6 m/s
11 m/s
11.5 m/s, 0°
26 mph
79 mph
73 m/s
410 m/s
48.0 N, 270.0°
250 N
3600 N in the dir. of the wind
7300 N in the dir. of the wind
1.67 MN
40.0 J before and after
844 J before; 784 J after
( not elastic)
16 MJ; 8.0 MJ
60 g cm/s
160 g cm/s, 180°
0.475 kg m/s, 90.0°
17.3 kg m/s, 30.0°; 10.0 kg m/s, 300.0°
25.0 kg m/s, 180°
40.0 kg m/s, 180°
40.0 kg m/s, 0°
780 kg m/s, 0°
780 kg m/s, 180°
780 kg m/s, 0°
780 kg m/s, 180°
4.0 ´ 106 kg m/s
0.475 N s, 90.0°
30.0 N s, 180°