Conservation of Momentum and Collision Review

1. A car crashes into a wall at 25 m/s and is brought to the rest in 0.1 s. Calculate the average force exerted on a 75-kg test dummy by the seat belt.

2. A railroad diesel engine weighs four times as much as a freight-car. If the diesel engine coasts at 5 km/h into a freight-car that is initially at rest, how fast do the two coast after they couple together?

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3. A 2-kg ball of putty moving to the right has a head-on inelastic collision with a 1-kg putty ball moving to the left. If the combined blob does not move just after the collision, what can you conclude about the relative speeds of the balls before they collided?

4. A stationary body of mass m^2 = 5 kg is struck by another body of mass m1= 1 kg traveling at vx = 8 m/s. After the collision the first body is moving at a right angle to the original velocity at a speed of vy = 4 m/s.
a) Determine the direction and magnitude of the recoil velocity of the second (5 kg) body.
b) Determine if the collision was elastic.
c) Determine the magnitude of the force if the collision lasted 0.2 ms.

5. A student standing on a frictionless rotating platform holds two dumbbells with outstretched arms. Each dumbbell, which has a mass of 2.4 kg, is held away from the students body by arms which are both 0.75 m in length. The rotational inertia of the platform and student’s body is 2.0 kgm2 as they both rotate at 45 revs/min. The student then pulls the dumbbells close to his chest.
a) Determine the new angular velocity
b) By pulling the dumbbells close to his chest how much work did the student do?

6. A 5kg fish swimming 1m/s swallows an absent minded 1kg fish swimming towards it at velocity that brings both fish to a halt immediately after lunch. What is the velocity v of the smaller fish before lunch?

7. Imagine light as a particle reflected by a mirror purely elastically. Prove that incident angle is equal to the angle of reflection.

Solution Preview
1. A car crashes into a wall at 25 m/s and is brought to the rest in 0.1 s. Calculate the average force exerted on a 75-kg test dummy by the seat belt.

First calculate the acceleration:
a = 25(m/s) / 0.1s = 250 m/s^2
Then calculate the force using Newton’s second law:
F = ma = 75kg x 250(m/s^2) = 18750N

2. A railroad diesel engine weights four times as much as a freight-car. If the diesel engine coasts at 5 km/h into a freight-car that is initially at rest, how fast do the two coast after they couple together?

Initial and final momentum must be conserved. We can assume that the mass of the diesel car is m and the freight car is 4m.
pi = mv0 = m(5)
pf = (m + 4m) vf = 5m vf

Therefore:
5m = 5mvf
vf = 1km/h

3. A 2-kg ball of putty moving to the right has a head-on inelastic collision with a 1-kg putty ball moving to the left. If the combined blob does not move just after the collision, what can you conclude about the relative speeds of the balls before they collided?

Momentum must be equal in magnitude and opposite in direction.
First ball: p = …

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