# Conservation of Momentum / Kinetic Energy - What am I doing wrong?

I have a problem, I'm trying to work out this simple equation and I'm confusing myself.

This is the question: a white snooker ball hits a stationary red ball elastically at speed of 50cm/second, and both move off at different velocitys. if the balls are the same mass(50g) and the final velocity of the white ball is 20 cm/seconds, what is the final speed of the red ball.

If I use the conservation of momentum equation or equal the KE on both sides of the equation I get different answers? Do i assume that the white balls velocity will be positive on the left side of the equation and negative on the right because the question specifies it's moving in 'different velocities'.

Then if I use ½mv² = ½mv² I get a different answer.

Can someone explain what I am doing wrong?

Thanks!

Hootenanny
Staff Emeritus
Gold Member
Do i assume that the white balls velocity will be positive on the left side of the equation and negative on the right because the question specifies it's moving in 'different velocities'.
You needn't assume anything, just solve the consevation of momentum equation and it will return both the speed and direction of the ball. Different velocities simply means that their velocities are different, but not nesscarily in the opposite direction. Note that momentum is a vector quantity and hence will give you a velocity. However, kinetic energy is a scalar, which means it will return it's speed only and therefore will give you no information regarding the ball's direction.

Notice that the question gives both the final and intial velocities of the white ball as positive, which means that it continues in the same direction.

If you post your working, perhaps we could point out where you're going wrong.

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I'm using m1u2+m2u2=m1v1+m2v2

So I substitute in my values and get:

0.05x0.5 + 0.05x0 = 0.05x0.2 +0.05v

0.025 = 0.01 + 0.05v

0.015 = 0.05v

v=0.30 m/s

But if you equate KE, assuming ½mv²=½mv² so v²=v², 50^2 = 20^2 + v^2

v^2 = 2100

v = 45.38.

Why am I confusing myself?

if you look at http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html#c2, you see that the final velocity for the white ball should be zero. that's a problem. if the problem is inelastic, then your okay(because you have solved for conserved momentum), but even for an elastic collision in which the red ball goes 0.2m/s you will still have anomoulous velocities.

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alphysicist
Homework Helper
I think this is a two-dimensional problem; the white ball hits the red ball off-center.

The unknowns are the final speed of the red ball and the two angles of the final velocities. With conservation of momentum and kinetic energy you can write three equations (momentum in x-direction, momentum in y-direction, and KE) and solve for the unknowns.