Mechanics - Momentum question

Particles of mass 5m and m moving directly towards each other and immediately before they collide the particles have speeds u and 2u respectively. Immediately after they collide the particle of mass m has speed 2u in the opposite direction to that in which it was initially travelling. Find the speed of the 5m mass immediately after the collision.

thanks for any help

Quote:

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Originally Posted by gracey

Particles of mass 5m and m moving directly towards each other and immediately before they collide the particles have speeds u and 2u respectively. Immediately after they collide the particle of mass m has speed 2u in the opposite direction to that in which it was initially travelling. Find the speed of the 5m mass immediately after the collision.

thanks for any help

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First let's check that I am reading your problem correctly (and give the masses names).

Mass A has a mass of 5m and moves from left to right at speed u.
Mass B has a mass of m and moves from right to left at speed 2u.

Now if we define left to right as the positive direction we can re-state this as:

Mass A has a mass of 5m and moves with velocity u.
Mass B has a mass of m and moves with velocity -2u.

So
Mass A has momentum 5*1=5
Mass B has momentum 1*(-2)=-2
Therefore before the collision the total momentum is 5+(-2)=3.

After the collision mass B has changed direction so its velocity has changed from -2u to +2u. Its momentum has changed to +2.

The total momentum of the system is constant so mass A must have a post collision momentum of 1. Therefore, 5*u=1 and hence the velocity of mass A has reduced from u to u/5.