The ballistic pendulum (see figure a) is a device used to measure the speed of a

Question

The ballistic pendulum (see figure a) is a device used to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet is stopped by the block, and the entire system swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring h and the two masses. As an example of the technique, assume that the mass of the bullet, m1, is 4.61 g, the mass of the pendulum, m2, is 1.046 kg, and h is 5.49 cm. Find the initial speed of the bullet, v1i.

(a) Find the initial speed of the bullet-block system.

(b) Find the speed of the bullet.

Explanation / Answer

1) mass of bullet m1 = 0.00461 kg, mass of pendulam m2 = 1.046 kg, and height reached by system of pendulam and bullet goes upto height h = 0.0549 m.

By conservation of energy intial kinetic energy of bullet will be equal to final potential energy of pendulam+bullet system.

1/2*m1*v1i2 = (m1+m2)*g*h

0.5*0.00461*v1i2 = (0.00461 + 1.046)*9.81*0.0549

v1i2 = 245.48 which gives us v1i = 15.67 m/s

2) m1 = 0.00452 kg, m2 = 2.113 kg, K = 619 N/m

v1i = ?, vsi (initial velocity of bullet-block system) = ?, final velocity of bullet-block system vsf = 0 (at max compression). x (compression) = 0.0561 m

By conservation of energy initial kinetic energy of block-bullet system must be equal to potential energy of compressed spring.

1/2*(m1 + m2)*vsi2 = 1/2*K*x2

0.5*(0.00452 + 2.113)*vsi2 = 0.5*619*0.05612

vsi2 = 0.92==> vsi = 0.96 m/s (ans a)

b) By conservation of momentum

Initial momentum of bullet = combined momentum of bullet-block system

m1*Vi = (m1 + m2)*0.96

Vi = (.00452 + 2.113)*0.96/0.00452 = 449.34 m/s

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