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# M2 collisions Watch

1. 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...
2. (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...

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.
3. (Original post by ghostwalker)

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
4. (Original post by ghostwalker)

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.
5. (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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