Physics Momentum HELP!!!!?

Question

A large mass (500kg) moving 10 m/s to the right collides with a smaller mass (5kg) which is initially at rest. The time of contact during the collision is 5 milliseconds. The large mass continues to travel to the right after the collision but at a reduced speed of 8 m/s.

Questions:

1. What is the magnitude of the force which these objects exert on each other?

2. What is the final velocity of the small mass?

Now reverse the situation. The small mass is moving to the right at 10 m/s and collides into the large mass which is at rest. The speed of the large mass after the collision is 1 m/s to the right (Assume that the time of the contact is the same as the previous example)

Questions:

3. What is the magnitude of the force which these objects exerts on each other?

4. What is the final velocity of the small mass?


Please show me how to solve this problem!

Answer 1

Force is found from the impulse equation:

F*∆t = ∆p, where ∆p is the change in momentum. You are given ∆t = 5*10^-3 s. You can find the mometum change of the large mass:

∆p = 500kg*(10m/s - 8m/s) = 1000kg*m/s

F = ∆p/∆t = 1000kg*m/s / 5*10^-3 s =
2*10^5 k*m/s^2 = 2*10^5 N

By conservation of momentum, total momentum before (the small mass has no momentum):

500kg*10m/s

system momentum after

500kg*8m/s + 5kg*V(small)

Equating these gives

500kg*10m/s = 500kg*8m/s + 5kg*V(small)

V(small) = 500*(10-8)/5 = 200m/s

Solve the other part in the same way.

Answer 2

1. You need to find the deceleration of the larger mass.
v = u + at
8 = 10 + a x 0.005
a = - 400m/s^2

F = ma (ignore acceleration is negative)
F = 500 x 400
= 200,000N

2. Momentum must be conserved
m1v1 + m2v2 = m1v3 + m2v4
500 x 10 + 5x0 = 500x8 + 5 x v4
v4 = 200m/s

use same equations for question 3 and 4