How Do You Solve Momentum and Elastic Collision Problems in Physics?

[krypt0nite]

A steel ball of mass 10kg moves due east at 5.0m/s. It collides with a rubber ball of mass 5.0 kg moving at 10m/s due north. After the collision the steel ball moves at an angle of 60 degrees East of North with a speed of 4.0 m/s.
If the collision were perfectly elastic what would be the speeds of the two balls after the collision?

Where do I start. I know total momentum before = total momentum after. But there seems to be 2 variables. vafter for steel ball and v after for rubber ball.

Can an elastic collision have the 2 objects even stick together?
If so then i got 1.92m/s.

 

[LENIN]

If the collision is elastic the 2 objects won't stisk together.

Try thinking of momentum as a vector. You can use triginometry for the angel, but I don't think it's really necesry.

P.S. don't forget that the mass of the 2 balls is constant.

 

[HallsofIvy]

You have two unknowns so you need two equations. Yes, one of the equations is "momentum before= momentum after", conservation of momenum. Since this collision is "elastic", the other is "kinetic energy before= kinetic energy after": conservation of energy.

Momentum is a vector quantity so you will need to consider x and y components separately. Kinetic energy is a "scalar" quantity so you really have 3 equations for 4 unknowns (x and y components of both velocities) but fortunately you are given the angles.

 

[krypt0nite]

I need help on another question
A ball of mass 3.0kg moving at a speed of 3.0ms has a head-on collision with a stationary ball of mass 4.0kg.

If the collision were perfectly elastic what would be the speeds of the two balls after the collision?

I used the momentum before=momentum after equation and the KE before= Ke after equation.

I get weird answers. I get 2 answers. I get the velocity of the 3kg ball at -.42m/s and 3m/s. So what's the answer? If i know the velocity of the of this ball I can find the velocity of the other.

 

[arildno]

I need help on another question
A ball of mass 3.0kg moving at a speed of 3.0ms has a head-on collision with a stationary ball of mass 4.0kg.

If the collision were perfectly elastic what would be the speeds of the two balls after the collision?

I used the momentum before=momentum after equation and the KE before= Ke after equation.

I get weird answers. I get 2 answers. I get the velocity of the 3kg ball at -.42m/s and 3m/s. So what's the answer? If i know the velocity of the of this ball I can find the velocity of the other.

Using only considerations of energy&momentum conservation before and after collision will always yield two sets of possible answers (solutions):
1) There hasn't been any interacting force between the two objects in the collision period.
That is, there wasn't any collision after all.
2) There has been a net momentum transfer (through a non-zero force) during collision.

Your 3m/s possibility is clearly of the trivial 1)-type.