of which i thought was an ellastic collision problem

[rottenapple]

Homework Statement

Ball A moving at 12m/s collides elastically with ball B as shown. If both balls have the same mass, what is the final velocity of ball A? ***theta = 60***

Homework Equations

Ui + Ki = Uf + Kf

The Attempt at a Solution

I could only think of the above equation when I read elastic collision. However, the solution in the back of the book suggested using conservation of momentum, which I thought is only applicable to inelastic collision. The numerical answer is 6m/s which can be figure out using mv = mv and breaking it down to x and y components.
I can see how they get to the numerical answer but I am lost as to why? Can someone please explain why I would use the formula for conservation of momentum? And also, I'm at a complete loss on how to approach a problem like this so can you also explain what I would need to solve the problem if it is an elastic collision?

Thank you!

 

[diazona]

Conservation of momentum applies to all collisions. Conservation of energy applies to only elastic collisions.

So in summary,
Elastic:
$$K_i + U_i = K_f + U_f$$
$$\vec{p}_i = \vec{p}_f$$

Inelastic:
$$\vec{p}_i = \vec{p}_f$$ only

 

[ben.zhang98]

The forces due to the collision among particles(interior forces) are always larger than exterior forces, and they are so large that we can always omit the exterior forces. According to Newton's second law, F=d(mv)/dt, if F(exterior force) is zero , mv(momentum) must be a constant, i.e. momentum is conservertive. So the conservertion of momentum on collision is always valid.

 

[inky]

Homework Statement

Ball A moving at 12m/s collides elastically with ball B as shown. If both balls have the same mass, what is the final velocity of ball A? ***theta = 60***

Homework Equations

Ui + Ki = Uf + Kf

The Attempt at a Solution

I could only think of the above equation when I read elastic collision. However, the solution in the back of the book suggested using conservation of momentum, which I thought is only applicable to inelastic collision. The numerical answer is 6m/s which can be figure out using mv = mv and breaking it down to x and y components.
I can see how they get to the numerical answer but I am lost as to why? Can someone please explain why I would use the formula for conservation of momentum? And also, I'm at a complete loss on how to approach a problem like this so can you also explain what I would need to solve the problem if it is an elastic collision?

Thank you!

For elastic collision, you may use both law of conservation of momentum and law of conservation of energy.
Ui + Ki = Uf + Kf

For inelastion collision , you can use only law of conservation of momentum. In inelastic collision , energy lost or gained. If you want to use law of conservation of energy,
Ui + Ki= Uf + Kf +energy lost