Completely inelastic collision.

[Jimmy25]

Homework Statement

A wooden block and a gun are firmly fixed to opposite ends of a long glider mounted on a frictionless air track. The block and gun are a distance L apart. The system is initially at rest. The gun is fired and the bullet leaves the gun with a velocity v_b and impacts the block, becoming imbedded in it. The mass of the bullet m_b and the mass of the gun-glider-block system is m_p.

a. What is the velocity of the glider immediately after the bullet is fired?

b. What is the velocity of the glider immediately after the bullet comes to rest in the block?

c. How far does the glider move while the bullet is in transit between the gun and the block?

Homework Equations

The Attempt at a Solution

(The bullet is fired in the positve x direction)

a. I found the the velocity of the glider after the gun is fired as (-m_bv_bx)/m_p.

b. The velocity of the glider after the bullet becomes embedded in the block should be zero.

c. After putting my algebra skills to the test, I found that the glider is displaced -m_bL/(m_p+m_b).

My problem is with C it appears the units are correct in this answer but I am not confident in that the velocity of the bullet is not contained in the equation. Is this answer possible?

 

[rl.bhat]

a) When the bullet is fired with the velocity vb, the gun, block and the glider move in the opposite direction. because the gun and the block are fixed to the glider. So vp = ...?
b)when the bullet is air born, the block is approaching with the velocity vp, so the combined velocity of the system after impact is...?
c) Since the bullet and glider are moving in the opposite direction, the relative velocity of them is...?
Finally t = L/relative velocity.

 

[tomcue]

Yes, your answer for part C is possible. In a completely inelastic collision, the total momentum is conserved but the total kinetic energy is not. This means that the final velocity of the system (in this case, the glider) will depend on the masses and velocities of the objects involved in the collision. In this case, since the bullet becomes embedded in the block, its velocity will not affect the final velocity of the glider. Therefore, your answer for part C is correct and the units are also correct.