A ballistic pendulum can be used to measure the speed of a projectile, such as a

Question

A ballistic pendulum can be used to measure the speed of a projectile, such as a bullet. The pendulum consists of a stationary 2.5 kg block of wood suspended by a wire of negligible mass. A 0.01 kg bullet is fired towards the block (see figure (a)). The bullet goes into the block and the block (with the bullet in it) swings to a maximum height of 0.65 m above the initial position (see figure (b)). Show via conservation of momentum that: V_bullet = (m_bullet + m_block/m bullet) V_block + bullet Using conservation of energy, find the velocity of the bullet.

Explanation / Answer

starting with the swing of the pendulum just after the collision until it reaches its maximum height. Conservation of mechanical energy applies here, so:

1/2(m + M)Vf^2 = (m + M)gh.

m = mass of bullet

M = mass of pendulum.

So, the speed of the system immediately after the collision is:

vf = (2gh)^1/2

Apply conservation of momentum to determine the relationship between Vf and the bullet's speed before the collision. The wood block is stationary before the collision.

Momentum before the collision = momentum after the collision

mvo = (m+M)vf

Vo = [(m + M) / m]*(2gh)^1/2

Vo = [(2.5 + 0.01) / (0.01)]*(2*9.81*0.65)^1/2

Vo = 896.35 m/s

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