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Mechanical Energy problem

  1. Mar 29, 2013 #1
    1. The problem statement, all variables and given/known data
    A 1.2 kg dynamics cart is rolling to the right along a horizontal lab desk at 3.6 m/s, when it collides head on with a spring bumper that has a spring constant of 2.00 * 10^2 N/m.

    a) Determine the maximum compression of the spring
    b) Determine the speed of the cart at the moment that the spring was compressed by 0.10 m.


    2. Relevant equations
    E mechanical = E potential + E kinetic
    E kinetic = 1/2 m v^2
    E elastic = 1/2 k x^2
    E gravitational = mgh


    3. The attempt at a solution

    a) I got 0.28 m, and the book agrees.

    b) The answer should be 1.3 m/s. Here's what I get:

    Eg is constant, because the height doesn't change. Equal is:

    Et = Ee + Ek

    In the previous solution, i set Ee2 + 0 = Ek1 + 0 since before there is no elastic energy and afterwards there is no kinetic energy

    So Et = 1/2 * 2 * 10 ^2 N/m * 0.28 ^ 2 m ^2 = 7.84 joules

    Et - Ee = Ek

    7.84 J - 1/2 * 2 * 10^2 N/m * 0.10^2 m^2 = Ek = 6.84 J

    1/2 * 1.2 kg * v^2 = 6.84 J

    sqrt(6.84 / 1.2 kg / 0.5) = v^2 = 11.4 m^2 / s^2

    Square rooted I get 3.4 m/s

    The book says I'm doing b wrong, but I don't understand what I did wrong, or if the book is wrong.
     
  2. jcsd
  3. Mar 29, 2013 #2
    I'm getting the same answer as you.
     
  4. Mar 29, 2013 #3
    Hello !!!

    Do not worry. You are correct and if book does not concur with you, its wrong.

    I get 3.36 m/s which is approximately same as your answer.
     
  5. Mar 29, 2013 #4

    haruspex

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    Fwiw, you can get the book answer by making the mistake of setting the KE equal to the PE when the spring is compressed .1 m.
     
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