A ballistic pendulum, as shown in the figure, was a device used in the past cent

Question

A ballistic pendulum, as shown in the figure, was a device used in the past century to measure the speed of bullets. The pendulum consists of a large block of wood suspended from long wires. Initially, the pendulum is at rest. The bullet strikes the block horizontally and remains stuck in it. The impact of the bullet puts the block in motion, causing it to swing upward to a height h. If the bullet has a mass of 8.2 g, and the block of mass 4.5 kg swings up to a height of h = 11.000 cm, what was the speed of the bullet before impact?

Explanation / Answer

Mass of Bullet = m= 8.2 g = 8.2 X 10^(-3)Kg

Mass of Block = M = 4.5 Kg

Height gained by block after bullet is embedded = h = 11cm = 11 X 10^(-2) mrs

Let the speed of bullet before impact be = v m/s

Initial momentum carried by bullet = mv

Final momentum of bullet+block system = (m+M) Vf

By conservation of momentum

mv = (m+M) Vf

Now theKinectic energy imparted by bullet to the bullet+Block system = (1/2) (m+M) Vf^2

This KE results in Potential energy of the bullet+block system raising it by height h

(1/2) ( m+M) Vf^2 = (m+M) g h

Vf^2 = (2gh)

mv/(M+m) = sqrt(2gh)

v = [(M+m)Sqrt(2gh)] /m = [(4.5+8.2 X 10^(-3) Kg)/(8.2 X 10^(-3) Kg)]Sqrt( 2 X 9.8 m/s^2 X 11 X 10^(-2) mrs)

= 807.3m/s

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