Investigation 5
Impulse and Momentum
The Impulse-Momentum relationship says: Impulse = Force x time of impact = change in momentum
1. An unfortunate bug splatters on the windshield of a car traveling at 60 mi/hr on the freeway.
a. Compare the force of the car on the bug to the force of the bug on the car. Which one is greater?
Both have the same value – Newton’s Third Law.
b. The time of impact is the same for both the bug and the car. Compare the impulse on the bug to the impulse on the car. Which one is greater?
Impulse = force x time. Since the forces are the same and the times are the same the impulses must be the same.
c. Compare the change in momentum of the bug to the change in momentum of the car. Which one is greater?
Impulse equals the change in momentum. Since the impulses are the same, the changes in momentum must be the same.
d. Does the bug or the car undergo the greater acceleration? Explain briefly.
Because the bug’s mass is less than the car’s mass, the bug will undergo the greater acceleration – Newton’s Second Law.
2. A block with a mass of 8 kg slides on a horizontal, frictionless surface at 4 m/s. It collides with and sticks to a 2 kg block that is at rest.
a. What is the value of the momentum of the 8 kg block before the collision occurs?
Momentum = mass x velocity = (8 kg) x (4 m/s) = 32 kg m/s.
b. What is the value of the momentum of the 2 kg block before the collision occurs?
Momentum = mass x velocity = (2 kg) x (0, at rest) = 0.
c. What is the value of the total momentum of the system before the collision occurs?
Total momentum = (momentum of 8 kg block) + (momentum of 2 kg block) = 32 kg m/s + 0 = 32 kg m/s.
d. What should the value of the total momentum of the system be after the collision occurs?
Momentum is conserved in the collision, so the total momentum after the collision must be the same as the total momentum before the collision = 32 kg m/s.
e. How fast are the blocks traveling after the collision occurs?
Momentum before = momentum after; 32 kg m/s = (8 kg + 2 kg) x (velocity after);
32 = 10 x (velocity after); so velocity after = 32/10 = 3.2 m/s
Impulse and Momentum
A 50 kg bungee jumper jumps off a bridge. She is in free fall for 3 sec. At 3 sec the bungee cord begins to stretch, slows her down, and brings her to a stop 2 sec later (a total of 5 seconds). Take the acceleration due to gravity to be 10 m/s2.
Fill in the blanks in the following table.
type of motion / time (sec) / velocity (m/s) / momentum(kg m/s)
free
fall / 0 / 0 / (50) x (0) = 0
1 / 10 / (50) x (10) = 500
2 / 20 / (50) x (20) = 1000
3 / 30 / (50) x (30) = 1500
slowed by bungee / 4
5 / 0 / (50) x (0) = 0
By how much did her momentum change from time t = 3 sec to time t = 5 sec?
Momentum at 5 sec – momentum at 3 sec = 0 – 1500 = __-1500______kg m/s
What is the value of the impulse on her from 3 sec to 5 sec??
Impulse = change in momentum = -1500 ______-1500______Newton sec
What is the average force that acted on her by the bungee cord from 3 sec to 5 sec?
Force = impulse/time = (-1500)/(2) = ______-750______Newtons
Would there be a problem if the bungee cord stopped her in 1/10 sec instead of 2 sec? Explain.
For a shorter tie the force stopping her would be greater. The denominator (time) would be smaller making the quotient a lot, lot, lot larger.
Momentum – Recoil
A steel ball (A = 4 kg) and a wooden ball (B = 1 kg) are at rest and separated by a compressed spring.
1. What is the value of the total momentum of the system before the spring is released?
No motion, so no momentum. Zero.
The spring is now released causing the balls to recoil in opposite directions. In this case,
2. what is the value of the total momentum of the system?
Momentum is conserved, so the total momentum remains zero.
3. does the spring exert a greater force on ball A or ball B?
The forces are the same – Newton’s Third Law.
4. which ball has a higher recoil speed? Why? Explain.
Wooden ball – it has less mass. For the same force, the smaller the mass the greater the acceleration – Newton’s Second Law.
5. If you were to jump straight upward from the earth’s surface, will the earth recoil? Explain.
Yes! But because the mass of the earth is so large, the amount it recoils is tiny.
Two-dimensional Elastic Collision
3. The diagram shows the top view of the corner of a pool table with the cue ball and the eight ball. Carefully draw the position of the cue ball when it makes contact with the eight ball so that it causes the eight ball rolls into the corner pocket. Show also the path of the cue ball takes after the collision.