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    A small smooth sphere A of mass 2kg moves at 4ms-1 on a smooth horizontal table. It collides directly with a second equal-sized smooth sphere B of mass 3kg, which is moving away from A in the same direction at a speed of 1ms-1. If the loss of kinetic energy due to the collision is 3J find the speeds and the directions of the two spheres after the collision.

    So I set up two equations in terms of momentum and energy.

    Let x = velocity of A after collision and y = velocity of B after collision

    Then from momentum, 2x+3y=11

    And from energy, 2x2+3y2-29=0

    Solving these simultaneously obviously gives two combinations of solutions, whereas the answer only has the answer as x (speed of A)=1ms-1 and y (speed of B)=3ms-1 with both moving in the same direction as before colliding.

    Now I can get these two answers from these equations, but I also get two others and I can't think of any reason to rule these two out. Such a situation also arose on another question. Can anybody clarify this, thanks...
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    (Original post by fayled)
    Solving these simultaneously obviously gives two combinations of solutions, whereas the answer only has the answer as x (speed of A)=1ms-1 and y (speed of B)=3ms-1 with both moving in the same direction as before colliding.

    Now I can get these two answers from these equations, but I also get two others and I can't think of any reason to rule these two out. Such a situation also arose on another question. Can anybody clarify this, thanks...
    Your other answers are x=3.4m/s and y=1.4m/s

    This would imply that both A and B are going in the same direction as before, and that A is travelling faster than B.

    This is impossible, as A would have to leapfrog over B, or somehow pass through B in some way as yet only known to science fiction.
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    (Original post by ghostwalker)
    Your other answers are x=3.4m/s and y=1.4m/s

    This would imply that both A and B are going in the same direction as before, and that A is travelling faster than B.

    This is impossible, as A would have to leapfrog over B, or somehow pass through B in some way as yet only known to science fiction.
    Silly me. Thankyou
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    (Original post by ghostwalker)
    Your other answers are x=3.4m/s and y=1.4m/s

    This would imply that both A and B are going in the same direction as before, and that A is travelling faster than B.

    This is impossible, as A would have to leapfrog over B, or somehow pass through B in some way as yet only known to science fiction.
    Actually, could you take a look at a previous question please?

    A particle of mass m moves in a straight line with velocity v when it explodes into two parts, one of mass m/3 and the other of mass 2m/3 both moving in the same direction as before. If the explosion increases the energy of the system by mu2/4, where u is a positive constant, find the velocities of the particles immediately after the explosion. Give your answers in terms of u and v.

    If x is the velocity of the particle of mass m/3 and y is the velocity of the particle of mass 2m/3, then

    x=3v-2y
    6v2+3u2=2x2+4y2

    Solving these simultaneously gives

    x=v-u, y=v+u/2
    and
    x=v+u, y=v-u/2

    Now the top combination is given as the correct answer, but I can't see a physical reason why this is the case as there is only one particle beforehand...
    Can you understand why or is my working flawed? Thanks.
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    (Original post by fayled)
    Can you understand why or is my working flawed? Thanks.
    Assuming there's no diagram. I can't see any flaw, or error in your working.

    The only flimsy thing I can see supporting their answer is that they mention the m/3 mass before the 2m/3 and interpret that as the 2m/3 is further along in the posititive v direction, and hence the m/3 mass must be the slower.
 
 
 
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