# Work energy theorem for falling object

1. Feb 22, 2010

### cdotter

1. The problem statement, all variables and given/known data
A branch falls from the top of a 95.0 m tall redwood tree, starting from rest. How fast is it moving when it reaches the ground?

2. Relevant equations
Total work = $\Delta K$

3. The attempt at a solution
I have no idea how to do this problem.

2. Feb 22, 2010

### ideasrule

How much work does gravity do?

3. Feb 22, 2010

### cdotter

Work is force times distance. Force is mass times acceleration. I need a mass to determine that.

4. Feb 22, 2010

### cdotter

How would I solve this problem when I'm only given a height?

5. Feb 22, 2010

### PhanthomJay

Force is not mass times acceleration. Net force is mass times acceleration.

6. Feb 22, 2010

### cdotter

I must be brain dead because I don't get the hint. Gravity does work, yes. But how do I calculate the work to, in turn, find the final velocity? My book says the final velocity is 43.2 m/s. How do I calculate that when I'm given one variable (the height)? It doesn't make any sense.

edit: I know I can get the answer using the kinematics equations (Vf2=Vi2+2ax in this case), but the problem says not to use the kinematics equations.

7. Feb 22, 2010

### PhanthomJay

Check out your own relevant equations. Work is force times distance (that will give you the work done by gravity once you figure out the force of gravity), and net work is delta KE (that will give you its speed). It must of course yield the same result as the kinematic equations.

8. Feb 22, 2010

### cdotter

Isn't work done by gravity m*g*h? Where do I get the mass from?

9. Feb 22, 2010

### l'Hôpital

Don't worry so much about the mass. Let it be m. Just work with the constants and who knows? It might just cancel out.

10. Feb 22, 2010

### cdotter

I always overlook something like that. Thank you for the help, everyone.