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    A small smooth phere of mass 3kg moving on a smooth horizontal plane with speed 8ms^(-1) collides directly with a sphere of mass 12kg which is at rest. Given that the spheres move in opposite directions after the collision, obtain the inequality satisfied by e
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    By conservation of momentum
    24 = 12V2 - 3V1
    8 = 4V2 - V1
    V2 = (8+V1)/4


    also, coefficient of restitution
    e = (V2+V1)/8
    so V1 = 8e - V2
    sub in V2

    V1= 8e - (8+V1)/4
    4V1 = 32e - 8 + V1
    3V1 = 32e - 8

    But V1 < 0 as spheres r moving in opposite direction as shown in diagram where towards right is the positive direction
    so 32e - 8 < 0
    e<1/4

    and 0<e<1

    0 < e < 1/4
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    Hajira, if you are treating V1 as a vector quantity and assigning it a sign (-ve quantity), then you would have had to write ...

    24 = 12V2 + 3V1
    and
    e = (V2 - V1)/8

    rewriting what you did,

    By conservation of momentum
    24 = 12V2 + 3V1
    8 = 4V2 + V1
    V2 = (8-V1)/4

    also, coefficient of restitution
    e = (V2 - V1)/8
    so V1 = V2 - 8e
    sub in V2

    V1= (8-V1)/4 - 8e
    4V1 = 8 - V1 - 32e
    5V1 = 8 - 32e

    Min value of V1 is V1 = 0, giving
    0 = 8 - 32e
    e = 8/32 = 1/4

    but particle is actually moving, so e ≠ 1/4, and e < 1/4 gives a +ve value for V1 (wrong direction!) so e > 1/4

    and 0<e<1

    so

    1/4 < e < 1
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    (Original post by Fermat)
    Hajira, if you are treating V1 as a vector quantity and assigning it a sign (-ve quantity), then you would have had to write ...

    24 = 12V2 + 3V1
    and
    e = (V2 - V1)/8
    e=speed of separation/speed of approach

    as its the speed of separation...u add them because of the fact that they r in opposite directions
    think about two particles moving in opposite directions at speeds 1m/s and 3m/s
    the speed by which they r separating is actually 3 + 1, n not 3 - 1...even tho being in opposite directions would make one of em negative as a vector!
 
 
 
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