1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gravitational Potential energy problem

  1. Oct 14, 2011 #1
    1. The problem statement, all variables and given/known data
    A 400-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy of the child–Earth system relative to the child’s lowest position when (a) the ropes are horizontal, (b) the ropes make a 30.0° angle with the vertical, and (c) the child is at the bottom of the circular arc.


    2. Relevant equations

    Ug = mgy

    3. The attempt at a solution

    For a) there was no problem.

    For b) I thought it was as simple as applying Ug = mgy cos 30° = (400 N)(2.0 m) cos 30°

    But the book says its Ug = mgy (1-cos 30°)

    That's my confusion... why 1 - cos 30° and not cos 30° by itself??

    any help? Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Oct 14, 2011 #2

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The problem is asking for the GPE relative to the lowest position. For part (b), the figure shows that 2 cos 30 is the vertical distance from the swing to its ropes attachment point. You want the vertical distance from the swing to the low point.
     
  4. Oct 15, 2011 #3

    Ok but why substract 1 - cos 30°? :(

    thanks for the help!
     
  5. Oct 15, 2011 #4

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the 30 degree position, the vert distance from the swing to the top is 2cos30 m. The vert distance from the low point of the swing to the top is 2. Thus, the distance from the swing in its 30 degree position to the low point is (2) - (2cos30) = 2(1-cos30) m.
     
  6. Oct 15, 2011 #5
    lolll it's only factored out right??

    Thanks a lot!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook