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 5.47 g, the mass of the pendulum, m2, is 1.070 kg, and h is 4.63 cm. Find the initial speed of the bullet, v

Explanation / Answer

:  Momentum

v1m1 = v2m2
v1m1/m2 = v2
v2 = v1(m1)/(m1+m2)<-- As it is the mass of the bullet and block


Energy
1/2 m v^2 = mgh
1/2 v^2 = gh
v^2 = 2gh
v = sqrt(2gh)
Substitute in v
v1(m1)/(m1+m2) = sqrt(2gh)

v1 = (m1+m2)sqrt(2gh)/m1
Plug in known values
v1 = (0.00547kg + 1.070kg)sqrt(2(9.8N/kg)(0.0463m) / (0.00547kg)
v1 = 187.29m/s

The bullet was going at187.29m/s

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