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    M2 exercise 4d Q6

    Three small smooth spheres A,B and C, of equal size and of mass 2m, 7m and 14m respectively, are at rest on a smooth horizontal floor with their centres in that order on a straight line. The coefficient of restitution between each pair of spheres is 1/2. Sphere A is projected so that it collides with sphere B.
    a) show that, after two collisions that have taken place, sphere B is at rest and spheres a and C are moving in oppsite directions with equal speeds.
    b) find what fraction of the orginal kinetic energy remains after the two collisions?
    Please help, have no idea!
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    (Original post by Sarah1101)
    M2 exercise 4d Q6

    Three small smooth spheres A,B and C, of equal size and of mass 2m, 7m and 14m respectively, are at rest on a smooth horizontal floor with their centres in that order on a straight line. The coefficient of restitution between each pair of spheres is 1/2. Sphere A is projected so that it collides with sphere B.
    a) show that, after two collisions that have taken place, sphere B is at rest and spheres a and C are moving in oppsite directions with equal speeds.
    b) find what fraction of the orginal kinetic energy remains after the two collisions?
    Please help, have no idea!
    What have you tried so far? What do you know about coefficients of restitution?
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    (Original post by morgan8002)
    What have you tried so far? What do you know about coefficients of restitution?
    For the first collision i have the equation 2u1+7u2+ 2v1+7v2

    And the coeffcient equation:

    2v2-2v1=u2-u1
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    (Original post by Sarah1101)
    For the first collision i have the equation 2u1+7u2+ 2v1+7v2

    And the coeffcient equation:

    2v2-2v1=u2-u1
    An equation equates two expressions. I assume you mean 2u_1 + 7u_2 = 2v_1 + 7v_2.

    The second equation is incorrect. Start again from e = \dfrac{v_1 - v_2}{u_2 - u_1}. You seem to have dropped a negative.
    Once you've got the right second equation, you have two simultaneous equations, so can solve for v_1 and v_2.
    And then again for the second collision.
 
 
 
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Updated: October 26, 2015
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