Work energy theorem for falling object

[cdotter]

Homework Statement

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?

Homework Equations

Total work = $\Delta K$

The Attempt at a Solution

I have no idea how to do this problem.

 

[ideasrule]

How much work does gravity do?

 

[cdotter]

How much work does gravity do?

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

 

[cdotter]

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

 

[PhanthomJay]

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

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

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

follow ideasrule's hint

 

[cdotter]

Force is not mass times acceleration. Net force is mass times acceleration.follow ideasrule's hint

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 (V_f²=V_i²+2ax in this case), but the problem says not to use the kinematics equations.

 

[PhanthomJay]

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 (V_f²=V_i²+2ax in this case), but the problem says not to use the kinematics equations.

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.

 

[cdotter]

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

 

[l'Hôpital]

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

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.

 

[cdotter]

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.

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