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 h and the two masses. As an example of the technique, assume that the mass of the bullet, m1, is 4.71 g, the mass of the pendulum, m2, is 1.051 kg, and h is 5.25 cm.

(a) Find the velocity of the system after the bullet embeds in the block

(b) Calculate the initial speed of the bullet.

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

(b) Find the speed of the bullet.

Explanation / Answer

Here ,

after the embedding of the bullet in the block

let the speed is v

Using conservation of energy

0.50 * m * v^2 = m * g * h

0.5* v^2 = 9.8 * 0.0525

v = 1.014 m/s

the velocity of the system is 1.014 m/s

b)

let the initial speed of the bullet is u

0.00471 * u = (0.00471 + 1.051) * 1.014

u = 227.4 m/s

the initial speed of the bullet is 227.4 m/s

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