Conservation of momentum, elastic collision, find other mass? help

[nchin]

conservation of momentum, elastic collision, find other mass? help!

Two titanium spheres approach each other head-on with the same speed and collide elastically After the collision, one of the spheres, whose mass is 300 g, remains at rest.

What is the mass of the other sphere?

What i did:

m1v1 + m2v2 = m1u1 + m2u2
v1 = 0 b/c at rest

m2v2 = m1u1 + m2u2

m2v2 - m2u2 = m1u1

m2(v2 - u2) = m1u1 ? This is where I got stuck!

please help!

 

[Fightfish]

Two titanium spheres approach each other head-on with the same speed and collide elastically

What is the relationship between u1 and u2?

The collision is elastic. What can you say about the relative speeds of approach and separation?

 

[nchin]

What is the relationship between u1 and u2?

The collision is elastic. What can you say about the relative speeds of approach and separation?

Momentum is the same so initial speed equals final speed?

 

[nchin]

So I looked up the solution and it uses v=2u
(m1-m2)u = m2(2u)

So why is it 2u? I know that m1v1 is at rest. Is it because when m1 collides with m2 it gave its speed to m2 so you multiply by 2?

 

[Doc Al]

You applied momentum conservation. What else is conserved in an elastic collision?

Also, redo your momentum conservation equation. The spheres approach each other with the same speed, thus they move in opposite directions.

 

[nchin]

You applied momentum conservation. What else is conserved in an elastic collision?

Also, redo your momentum conservation equation. The spheres approach each other with the same speed, thus they move in opposite directions.

I know that p and ke is comserved. I'm not sure what else.

m2v2 = m1u1 - m2u2

 

[Doc Al]

I know that p and ke is comserved. I'm not sure what else.

Make use of the fact that KE is conserved.

m2v2 = m1u1 - m2u2

Better. Note that the speeds of the balls before colliding are the same. Use that fact.

 

[nchin]

Make use of the fact that KE is conserved.


Better. Note that the speeds of the balls before colliding are the same. Use that fact.

How can we use ke in this?

m2v2 = (m1 - m2)u?

 

[Doc Al]

How can we use ke in this?

Calculate the KE before and after. Set them equal to each other.

m2v2 = (m1 - m2)u?

OK.

There's a quicker way to solve this (hinted at by Fightfish), but I suggest doing it this way.

 

[nchin]

1/2m1vi + 1/2m2vi = 1/2m2vf

1/2vi(m1 + m2) = 1/2m2vf --> mult each side by two

vi(m1 + m2) = m2vf ??

 

[Doc Al]

1/2m1vi + 1/2m2vi = 1/2m2vf

1/2vi(m1 + m2) = 1/2m2vf --> mult each side by two

vi(m1 + m2) = m2vf ??

Two things:
(a) KE = 1/2 mv², not 1/2 mv.
(b) Use the same symbols for the speeds that you used in the momentum equation.