Solving Elastic Collision Problems

[definition]

Homework Statement

A 4kg ball moves moving to the east with a speed of 3m/s has an elastic collision with a 2kg ball moving to the west with a speed of 4 m/s.

What is the total momentum of the system after collision?
Determine the velocities of each ball after collision.

Homework Equations

p = mv
KE = (1/2)mv^2

The Attempt at a Solution

So I know that since momentum is always conserved, I can say that:
Momentum Initial = Momentum Final, therefore:

p = mv :: (4kg)(3m/s) + (2kg)(-4m/s) = 4 kgm/s

I think that's correct. But what I'm having trouble on is solving for the velocities
for the balls after the collision. I think the professor said to do it in terms of energy,
but if it's possible to do it with momentum as well, that'd be great.

I'm currently trying to do KE(Initial) = KE (Final)

So, I have 34 J = (1/2)(4kg)v^2 + (1/2)(2kg)(V^2), but there are two unknown variables?

Thank You!

 

[CxStrike]

You'll have two equations, one equating momentum, and one equating KE. Two equations, two variables. Solve for one, then substitute.

 

[definition]

ah! so i plugged solved for a velocity using

4 = mv + mv and plugged it in.

Thank You!

 

[cashmoney805]

Would you mind providing the solution to the problem?

I understand the momentum part:
4=M(1)*V1f + M(2)*V2f

And the energy part is

M1*V1i² + M2*V2i² = M1V1f² + M2*V2f²

I'm having a hard time doing the math though/figuring out which is easiest to isolate and plug in for.

 

[definition]

What I did was: Since it was an elastic collision, energy is conserved.

KE Initial = KE Final
KE Initial came out to be, 34 J.

Therefore:
34J = (1/2)(4kg)(v1)^2 + (1/2)(2kg)(v2)^2

Momentum is conserved as well, and therefore Momentum Initial = Momentum Final, which
came out to be 4 kgm/s.

Therefore:
4 kgm/s = (4kg)(v1) + (2kg)(v2)

v1 = (4kg) - (2(v2)) / 4 kg

Substitute v1 in the KE equation, and solve for V2.

Then solving v2, use the v1 substitution to solve for v1.

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Hope it helped!

 

[MakyBee]

Elastic Collision

Regarding elastic collision. How about if a Ball A and Ball B are supported by two strings and the larger ball is pulled to its center of gravity raised to nth cm and then released. How can I solve for the final velocities now?

 

[gneill]

Regarding elastic collision. How about if a Ball A and Ball B are supported by two strings and the larger ball is pulled to its center of gravity raised to nth cm and then released. How can I solve for the final velocities now?

First find the speeds of the balls at the instant of collision, then analyze the collision as usual assuming that it takes place in essentially zero time. Then take care of whatever dynamics transpire post-collision to determine the velocities at some time after collision (for example, the balls will both change height as they swing on their strings). Conservation laws are your friend

 

[Arkavo]

or use momentum conservation And coefficient of restitution this should give u 2 eqns 2 vars solve to get (i usually don't use energy cause its a quadratic)