Let\'s consider the ballistic pendulum apparatus as pictured on previous page. A

Question

Let's consider the ballistic pendulum apparatus as pictured on previous page. A spring gun project!* the ball horizontally, into a hollow bob that catches the ball. Below is a drawing of the three stages of this action. In an inelastic collision, what is conserved and what is not conserved? Explain. Use m_1 for the mass of the ball and for the mass of the pendulum v_1 for the velocity of the ball and v_2 for the velocity of the ball and pendulum together. For the drawings above, assuming a completely inelastic and instantaneous collision, derive an equation for the momentum of the system, at the instant just before the collision. Derive an equation for the final velocity of hall and bob immediately after collision. Show how you arrived at this. A completely inelastic collision often refers to a collision where the two objects stick together. Derive an equation for the total mechanical energy of the ball and bob combination immediately after collision

Explanation / Answer

1.

In an inelastic collision , Momentum is conserved but kinetic energy is not conserved. Kintic energy is nbot conserved because some amount of energy is lost during the collision.

2.

a. Momentum just before collision is given as

Pi = m1 v1

b)

momentum after the collision is given as
Pf = (m1 + m2 ) v2

using conservation of momentum

Pf = Pi

(m1 + m2 ) v2 = m1 v1

v2 = m1 v1 /(m1 + m2 )

c)

Total mechanical energy = (0.5) (m1 + m2 ) v22 = (0.5) (m1 + m2 ) m21 v21 /(m1 + m2 )2

Total mechanical energy = m21 v21 /2(m1 + m2 )

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