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Ball attached to String (Potential Energy)

  1. May 14, 2011 #1
    1. The problem statement, all variables and given/known data

    A 2.40 kg ball is attached to a ceiling by a 2.00 m long string. The height of the room is 3 m. What is the gravitational potential energy of the ball relative to:

    a) the ceiling?

    b) the floor?

    c) a point at the same elevation as the ball?

    P for potential energy
    m for mass in kg
    g for gravity
    h for height

    2. Relevant equations

    3. The attempt at a solution
    For b), I found the answer which was 23.52.

    For a), though, I got 70.56 because P=(2.4)(9.8)(3)=70.56. The 3 is from the fact that the ceiling is 3m off the ground and a) is asking about the ceiling. It says that I'm wrong

    For c), I don't have any idea of what they're talking about. Is it the same thing as b)?
  2. jcsd
  3. May 14, 2011 #2
    Energy is always relative. Potential energy is defined as the potential energy of one point, vs. the potential energy at another point. The equation, more precisely, should be written [tex]U = mg \Delta h[/tex] for some different in height [tex]\Delta h \equiv h - h_0[/tex].

    Usually the 'reference' point ([tex]h_0[/tex]) is taken to be "zero height" ([tex]h_0 = 0[/tex]), and that is often either sea-level, or ground-level, or floor-level, etc.

    While the ceiling is 3m off the ground ([tex]h_0 = 3[/tex]), it is only 1m away from the ball (the ball is what you're finding the potential energy of). h = 3m - 2m = 1m

    If they're asking for the potential of the ball with respect to something at the same height, what is the difference in height [tex] \Delta h[/tex]?
  4. May 14, 2011 #3
    ok, so I did 2.4(9.8)(1)=23.52 for a). i still get it wrong....

    and for c), do i just do 2.4(9.8)(2) because it's the inverse?
  5. May 14, 2011 #4
    Sorry, forgot to highlight a key point. In this case, the ball is lower than the reference point. I.e. [tex]\Delta h = h - h_0 = 2m - 3m[/tex]

    Its not the inverse problem. Its asking what is the potential difference between something at h = 2m, and a reference point at [tex]h_0[/tex] = 2m
  6. May 14, 2011 #5
    How far is it between ball and ceiling? Ball and floor?
  7. May 14, 2011 #6
    so will a) be negative because 2-3=-1? therefore, will the answer be -23.52?

    and will c) be zero because 2-2=0 and 2.4(9.8)(0)=0?
  8. May 14, 2011 #7

    the problem said the ceiling to the floor was 3m
  9. May 14, 2011 #8
    a) will be negative becaus there's a 2!! meter negative drop from the ball to the ceiling. c) is zero as there's no drop. Well done.
  10. May 14, 2011 #9
    :smile:I recommend to make a simple drawing to visualize the problem. Best of luck
  11. May 14, 2011 #10
    well ok, i did 2.4(9.8)(-1). that gives me -23.52. it still tells me i'm wrong :confused:
  12. May 14, 2011 #11
    oh and thanks for c). i got it right.
  13. May 14, 2011 #12
    If you have a -2m drop from ball to ceiling, and a 1m drop from ball to floor, and a 0m drop from ball to somthing on the same level, I think it will solve.
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