# Energy WorkTheorem

1. Mar 16, 2012

I am currently working on a problem that I do not know how to solve. It is on the Work-Energy theorem. I would really appreciate it if you could help. :D

Kinetic Energy = 1/2 mv^2
Potential Energy = mgh
Work = Fd
KE(initial) + PE(initial) = KE(final) + PE(final)

The height above the ground of a child on a swing varies from 50 cm at the lowest point to 200 cm at the highest point. The maximum speed of the child is?

D. dependent on the child's mass

The answer for this question is A, and I do not understand how they got it.

I also have one more question.

The 2.0-kg head of an ax is moving at 60 m/s when it strikes the log. If the blade of the ax penetrates 20 mm into the log, the average force it exerts is

A. 3 kN
B. 90 kN
C. 72 kN
D. 180 kN

I have no idea where to start for these problems. Help would really be appreciated!

2. Mar 16, 2012

### LawrenceC

For the first question:

KE(initial) + PE(initial) = KE(final) + PE(final)

You have the correct equation. You only have to evaluate it. Don't forget about gravity.

3. Mar 16, 2012

### LawrenceC

Hint for axe problem:

What energy does the axe use to cleave into the log? Does it do work on the log?

4. Mar 16, 2012

### tal444

Hint for first question: Think of when the child is at his/her lowest point as 0 cm instead of 50 cm. What does that make his/her highest point equal to?