# Homework Help: Problem (possibly) involving Springs, Free Fall and Air Resistance

1. Sep 3, 2009

### Castiel

1. The problem statement, all variables and given/known data
A mass m is dropped from a height H onto a hard, flat surface. When it collides with the surface, it rebounds with the same speed it had before the collision. However, there is a constant force of air resistance f acting on the mass as it undergoes this motion. Answer the following in terms of f, m, H, and g.

a) How fast is the mass moving just before it hits for the first time?
b) How high does the mass go after the first collision?
c) After how many bounces, the ball comes to rest on the surface. While its overall displacement was -H, it traveled a considerably larger distance. Determine the total distance traveled by the ball.

2. Relevant equations
F=-kx
PEsp=1/2kx^2
KEi+PEi-f(friction)=KEf+PEf+PEsp

3. The attempt at a solution
Should I look at this problem as if the ground were a spring? If so, how do I determine k and x for the equation? It doesn't necessarily travel any distance (for the x variable)

a) Would I simply use PEi=KEf? Should I assume that the mass starts from rest? Or should I put in PEi+KEi=KEf.

b)If I were to assume that it was a spring, how would I translate k and x into other variables to fit with the specifications of the equation (using f, m, H and g) If not, I have no idea where to even begin. Would I simply use the previously found final velocity from a and use that as my new initial, then calculate friction and find the distance?

c) Would I use the final velocity before hitting the ground of the second bounce to calculate the initial velocity for the third bounce, and so on? I have no idea where to even begin to solve this part of the problem. Any hints or suggestions would be greatly appreciated.

2. Sep 3, 2009

### rl.bhat

When mass is moving down, the net acceleration is (g - f/m), where f is the air resistance which opposes the free fall.
While coming down, the net retardation is ( g + f/m)