The ballistic pendulum (Figure a) is a device used to measure the speed of a fas

Question

The ballistic pendulum (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 hand the two masses. As an example of the technique, assume that the mass of the bullet, m1, is 5.41 g, the mass of the pendulum, m2, is 1.022 kg, and h is 4.99 cm.

(a) Find the velocity of the system after the bullet embeds in the block.
m/s

(b) Calculate the initial speed of the bullet.
m/s

Explanation / Answer

)
Let

m = 5.41 g = 0.00541 kg

M = 1.022 kg

h = 4.99 cm = 0.0499 m

Let V is the velocity of the system after the bullet embeds in the block.

Apply conservation of energy after the collsion.

initual kinetic energy = final potetail energy

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

v^2 = 2*g*h

V = sqrt(2*g*h)

= sqrt(2*9.8*0.0499)

= 0.99 m/s

b) Let u is the initial speed of the bullet

Apply conservation of momentum

m*u = (m + M)*v

u = (m + M)*v/m

= (0.00541 + 1.022)*0.99/0.00541

= 188 m/s

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