Energy and momentum conservation

[Cc518]

Homework Statement

An object with a mass of 5kg is placed on a horizontal surface and it has a semi-circular orbit with radius 1m. Its left end is close to a baffle fixed on the ground. A ball with a mass of 1kg is released from the point A by static. The surface and the groove are both smooth. Ignore the air resistance. Calculate the maximum height at which the ball rises.

Homework Equations

From A to B:
mgR=1/2 (VB)2
VB = √2gR
From B to C:
mVB = (M + m) VC
mgR=mgh+1/2(M+m) * (VC)² where h is the height

The Attempt at a Solution

I can use these relationships to get the answer, but I don understand why I can use these 2 equations in the same problem:
mVB = (M + m) VC which is an equation for inelastic collision,
mgR=mgh+1/2(M+m) * (VC)² which represents the energy is conserved

If I assume this is an inelastic collision, then the energy will not be conserved. mgR=mgh+1/2(M+m) * (VC)² This equation will not be true if it's an inelastic collision.

I also thought this is an elastic collision, and the two objects just move at the same final velocity. But how can I tell this is an inelastic or elastic collision?

 

[Doc Al]

mVB = (M + m) VC which is an equation for inelastic collision,

That equation is a statement of momentum conservation. There's no inelastic collision here. (Energy is conserved.)

 

[Cc518]

That equation is a statement of momentum conservation. There's no inelastic collision here. (Energy is conserved.)

Oh, I see
Thank you for reply.

 

[haruspex]

To elaborate on @Doc Al 's reply, all conservation laws come with conditions attached. The conditions which are satisfied in a given situation can be any combination.
In the present problem, conditions for work conservation are satisfied throughout, whereas conditions for linear momentum conservation of the particle+block system are only satisfied after the particle reaches B. Why not before that?

 

[Cc518]

To elaborate on @Doc Al 's reply, all conservation laws come with conditions attached. The conditions which are satisfied in a given situation can be any combination.
In the present problem, conditions for work conservation are satisfied throughout, whereas conditions for linear momentum conservation of the particle+block system are only satisfied after the particle reaches B. Why not before that?

Because the object cannot move with the ball from point A to B, the momentum is not conserved?

 

[Doc Al]

Because the object cannot move with the ball from point A to B, the momentum is not conserved?

Yes. While the ball moves from point A to B there is an external force on the system (from the fixed baffle), so momentum is not conserved.

 

[Cc518]

Thank you so much!