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? 發問於 科學及數學其他 - 科學 · 1 十年前


A sphere X of mass m, travelling with speed u ,makes a collision with a sphere Y of mass 2m which is at rest. After the collision ,the velocities of X and Y are V1 and V2 respectively .Which of the followings is a possible pair of values V1 and V2 ?

_____V1____________V2 _________


B.___1.5u_________ - 0.25u_______



2 個解答

  • 1 十年前

    conservation of momentum

    initial momentum = mu

    final momentum = mv1+2mv2

    u = v1 +2v2

    using above forumla, eliminating ans A

    conservation of kinetic energy: final energy must be less than initial energy

    initial energy = 1/2 m u^2

    final energy = 1/2 m v1^2 + m v2^2

    u^2 = v1^2 + 2v2^2

    ans B & D, final energy > initial energy --> rejected

    right answer should be C

  • 1 十年前

    According Conservation of momentum, the total momentum of a closed system of objects (which has no interactions with external agents) is constant.

    So, before collision

    total momentum = mu+2m*0=mu

    After collision, the total momentum should also be mu too

    A 0.5u*m+0.5u*2m=1.5mu

    B 1.5u*m-0.25u*2m=mu

    C 0+2m*0.5*u=mu

    D -0.5u*m+0.75u*2m=mu

    However, B is impossible since the direction is wrong.

    D is also impossible, consider the kinetic energy

    Before collision

    kinetic energy=(1/2)mu^2

    After collision

    kinetic energy=(1/2)m(-0.5u)^2+1/2(2m)(0.75u)^2=0.6875mu^2>0.5mu^2

    The kinetic energy has increased and this should be ipossible

    The answer is C

    2007-03-04 04:20:44 補充:

    in B, I mean the velocity direction of X and Y is wrong