Solve Work-Energy Theorem Problems with Expert Help

[NguyenAdam]

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?

A. about 5.4 m/s
B. about 7.7 m/s
C. about 29 m/s
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

The answer is 180 kN.

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

 

[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.

 

[LawrenceC]

Hint for axe problem:

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

 

[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?