Question

topic: Ballustic Pendulum Lab.
why does the total momentum before the collision include only the momentum of the ball? why is the momentum of the pendulum included?

Answer 1

The ballistic pendulum is used to measure the launch velocity of a high speed projectile.

Working: A projectile launcher fires a steel ball mass of the ball is m velocity V₀. The pendulam is kept in the path and the ball is caught by a pendulum of mass m_pend.When the ball is hit on the pendulam the momentum of the ball is transferred to the pendulam and the pendulum swings freely upwards, raising the center of mass of the system by a distance h. The pendulum rod is hollow so the mass is low, and most of the mass is concentrated at the end so that the entire system approximates a simple pendulum. During the collision of the ball with the catcher, the total momentum of the system is conserved. Thus the momentum of the ball just before the collision is equal to the momentum of the ball-catcher system immediately after the collision:

=> m_ballV₀ = MV

where V is the speed of the catcher-ball system just after the collision,

the total mass M = m_ball + m_pend

After the ball hitting

This collision is a totally inelastic collision. Because the pendulum is at rest before the bullet hits it, the speed of block plus bullet is V = m_ballv₀/m_ball + M_pend where v₀is the speed of the bullet before it hits the block, and is the speed of the block and bullet system right after impact.

Initially the pendulum is at rest, and when gun fires the ball collides with the pendulum and is trapped in the catcher.

Divide the experiment into two parts. First, When gun fires ball of mass m_ball travels with velocity v₀ in the absence of external forces,so no change in horizontal velocity

So p=m_ball *v₀

Secondly, ball collide with the catcher of mass Mpend ,the ball will get trapped. But the linear momentum is conserved

So P_f=(M_ball+m_pend)V