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Thread: collision

  1. #1
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    collision

    a smooth sphere P of mass 1 kg moving with speed u collides with a stationary sphere smooth sphere Q also of mass 1kg. the direction of motion of P before the impact makes an angle a with the lines of centers of impact. show the direction of motion of P after the impact makes and angle b with the line of centers of impact where
    tan b=2tana/1-e where e is the coefficient of restitution.

    the speed in the j direction stays the same before and after so i focus on the i direction of both the spheres before and after.so i get 2 equations.using the PCM formula.
    ucosa(1)+1(0)=y+x where y is the the velocity of P after the impact in the i direction and x is the velocity of Q in the i direction after impact. i then use the NELR formula. y-usina/ucosa-0 =-e solving both these i get x=ucosa-usina+eucosa and y=usina-eucosa so tanb=usina/usina-eucosa this does not give me the correct answer. i can explain in further detail the question and my workings in more detail if anyone needs it as i went through it quickly. i can post a diagram aswell if you need it.
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  2. #2
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    Re: collision

    see diagram for variables used ...

    $v+w=u\cos{\alpha}$

    $w-v = e \cdot u\cos{\alpha}$

    solving system for $w$ and $v$ ...

    $w = \dfrac{u\cos{\alpha}(1+e)}{2}$

    $v = \dfrac{u\cos{\alpha}(1-e)}{2}$


    $\tan{\beta} = \dfrac{u\sin{\alpha}}{v} = \dfrac{u\sin{\alpha}}{1} \cdot \dfrac{2}{u\cos{\alpha}(1-e)} = \dfrac{2\tan{\alpha}}{1-e}$
    Attached Thumbnails Attached Thumbnails collision-collision.jpg  
    Thanks from markosheehan
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