Pre-laboratory Work Part P-1: Let\'s consider the ballistie pendulum apparatus a

Question

Pre-laboratory Work Part P-1: Let's consider the ballistie pendulum apparatus as pictured on peevious page. A spring gun projects the ball horizontally, into a hollow bob that catches the ball. Below is a drawing of the three stages of this action 1. In an inelastic collision, what is conserved and what is not conserved? Explain. 2. Use mi for the mass of the ball, m for the mass of the pendulum, vi for the velocity of the ball and v for the velocity of the ball and pendulum together For the drawings above, assuming a completely inelastic and instantaneous collision, derive an A completely inelastic collision equation for the momentum of the system, at the often refers to a collision where a. instant just before the collision. the two objects stick together b. Derive an equation for the final velocity of ball and bob immediately after collision. Show how you arrived at this c. Derive an equation for the total mechanical energy of the ball and bob combination immediately after collision Last revised 7/17/2015 Projectiles and Pendulums 7.2

Explanation / Answer

1.

Momentum : conserved

since initial total Momentum = final Total momentum

Kinetic energy : not conserved

since some energy is lost during the collision and hence the kinetic energy before and after the collision does not remain same

2

a)

initial momentum = m1 v1

b)

final momentum = (m1 + m2) v2

final momentum = initial momentum

(m1 + m2) v2 = m1 v1

v2 = m1 v1 /(m1 + m2)

c)

E = (0.5) (m1 + m2) v22 = (0.5) (m1 + m2) (m1 v1 /(m1 + m2) )2 = m21 v21 /2(m1 + m2)

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