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Math Help - (M2) Mechanics collision question

  1. #1
    Lauwra
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    (M2) Mechanics collision question

    A small smooth ball strikes a smooth vertical wall at right angles.

    Its kinetic energy after impact is one-half of its initial kinetic energy.

    Find the coefficient of restitution between the ball and the wall.


    This is what I have got so far:
    Let speed of approach be u and speed of separation be v

    KE = 1/2 mv^2

    so therefore

    1/2 m (2)^2 = 1/2 * 1/2 m (v) ^2

    Then I just do not have a clue what to do from there.
    If it helps the textbook tells me the answer is e = 1/√2, I just don't know how to get there...
    Any help will be appreciated
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Lauwra View Post
    A small smooth ball strikes a smooth vertical wall at right angles.

    Its kinetic energy after impact is one-half of its initial kinetic energy.

    Find the coefficient of restitution between the ball and the wall.


    This is what I have got so far:
    Let speed of approach be u and speed of separation be v

    KE = 1/2 mv^2

    so therefore

    1/2 m (2)^2 = 1/2 * 1/2 m (v) ^2

    Then I just do not have a clue what to do from there.
    If it helps the textbook tells me the answer is e = 1/√2, I just don't know how to get there...
    Any help will be appreciated
    Coefficient of restitution = (rebound speed)/(inbound speed)

    where these are realy the components of the after and befor velocities normal to the plane of impact. So in this case:

    Coefficient of restitution = sqrt(rebound KE)/sqrt(inbound KE) = sqrt[(rebound KE)/(inbound KE)] =sqrt(1/2)

    RonL
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