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Law of Restitution & Momentum

  1. Apr 18, 2012 #1
    Hello everyone , here we go :

    I understand that momentum is always conserved as long as no external forces act on a given system . I also understand that the law of restitution applies to the axis perpendicular to the line of impact between two objects .However i have a problem .

    For example . A ball hits the ground at an angle of 45 degrees and bounces up at an angle of 30 degrees.

    So from the law of restitution : e= - ( Vball*sin30 - Vground)/(Uball*sin45 - U ground) , the ground does not move therefore Uground = Vground=0 so

    e = - Vball*sin30/(Uball*sin45).

    My question is , why can't we apply momentum conservation on the y axis ? Is it because the reaction force when hitting the ground is considered an external force ?

    I am very confused please explain :S

    Thank you !
  2. jcsd
  3. Apr 18, 2012 #2

    Doc Al

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    Staff: Mentor

    Exactly. If you look at the ball itself, its direction reverses when it bounces. So obviously, momentum of the ball is not conserved--it's being smacked by the ground!

    If you expand your 'system' to be 'ball + ground/earth', then momentum will be conserved again. (The force between ground and ball would then be an internal force.)
  4. Apr 18, 2012 #3
    So my restitution formula is wrong and the only thing i have in my "system " is the ball , no ground etc . So it should be e= - V*sin30/(u*sin45) but e can't be negative ....argh !!! :S
  5. Apr 19, 2012 #4
    Let's assume that two balls(m1=m2=m ) collide with one another .

    The first ball is traveling at a speed u while the second ball is stationary.The first ball strikes the second one at an angle θ to the line of impact.If the coefficient of restitution is e , find the angle at which the second ball travels after the impact.

    What i don't understand in this case is why isn't momentum conserved both along the line of impact and on the axis perpendicular to it as well ? I mean , both balls are part of our system so there are no external forces ?!

    Could you please solve this exercise and explain each step thoroughly so i can finally understand ? Thank you very much !!!
  6. Apr 19, 2012 #5

    Doc Al

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    Staff: Mentor

    Why would you think that momentum isn't conserved in all directions?
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