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    I've been looking through the text book and some tricky mechanics questions for M1 and I am frustrated by my lack of ability to do this one, if someone could be kind enough to explain it to me I'd be more than grateful.

    Two smooth spheres A and B, of equal radii and masses m1 and m2 respectively, are moving towards each other along the same horizontal line each with speed u. After collision both spheres have reversed their original directions of motion and A now travels with speed u/2.
    Show that 3m1>2m2
    Sphere B then strikes a fixed wall at right angles, the impact reversing the direction of motion of B and halving it's speed. Show that B will again collide with A provided that 3m1>4m2.
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    (Original post by Lucykathryn)
    I've been looking through the text book and some tricky mechanics questions for M1 and I am frustrated by my lack of ability to do this one, if someone could be kind enough to explain it to me I'd be more than grateful.

    Two smooth spheres A and B, of equal radii and masses m1 and m2 respectively, are moving towards each other along the same horizontal line each with speed u. After collision both spheres have reversed their original directions of motion and A now travels with speed u/2.
    Show that 3m1>2m2
    Conservation of linear momentum: um_1 - um_2 = -\frac{um_1}{2} + m_2 v_b

    So: um_1 \left(1 + \frac{1}{2}\right) = m_2 (u + v_b) \iff um_1 = \frac{2m_2}{3}(u+v_b) \iff 3m_1 = \frac{2m_2}{u}(u+v_b)

    So...?

    Remember that \frac{u+v_b}{u} = 1 + \text{something} > 1.

    So 3m_1 = 2m_2 \times (\text{something bigger than 1})
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    (Original post by Zacken)
    Conservation of linear momentum: um_1 - um_2 = -\frac{um_1}{2} + m_2 v_b

    So: um_1 \left(1 + \frac{1}{2}\right) = m_2 (u + v_b) \iff um_1 = \frac{2m_2}{3}(u+v_b) \iff 3m_1 = \frac{2m_2}{u}(u+v_b)

    So...?
    I am really unsure of how to decide whether a collision will occur just from the momentum. I managed to prove the first part.
    Sorry I should have specified where I needed help
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    (Original post by Lucykathryn)
    I am really unsure of how to decide whether a collision will occur just from the momentum. I managed to prove the first part.
    Sorry I should have specified where I needed help
    Sphere B will collide with Sphere A if and only if the speed of Sphere B after colliding with the wall is greater than the Speed of A, this then means that B will be able to "catch up" with A. So find an expression for the velocity of B and set it greater than u/2.
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    (Original post by Zacken)
    Sphere B will collide with Sphere A if and only if the speed of Sphere B after colliding with the wall is greater than the Speed of A, this then means that B will be able to "catch up" with A. So find an expression for the velocity of B and set it greater than u/2.
    Oh god that is so simple. Thankyou so much, I over complicated that loads.
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    (Original post by Lucykathryn)
    Oh god that is so simple. Thankyou so much, I over complicated that loads.
    No problem, let me know if it works out!
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    (Original post by Zacken)
    No problem, let me know if it works out!
    It worked perfectly, thankyou
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    (Original post by Lucykathryn)
    It worked perfectly, thankyou
    Awesome, glad I could help!

    Welcome to TSR, hope to see you around the maths forum more.
 
 
 
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