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Energy WorkTheorem

  1. Mar 16, 2012 #1
    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!
     
  2. jcsd
  3. Mar 16, 2012 #2
    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.
     
  4. Mar 16, 2012 #3
    Hint for axe problem:

    What energy does the axe use to cleave into the log? Does it do work on the log?
     
  5. Mar 16, 2012 #4
    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?
     
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