Question

A m2 = 6 kg block of clay is suspended from the ceiling by a long cord, as seen in the following figure. A m1 = 210 gram bullet, fired horizontally, imbeds itself into the clay, causing both masses to rise to a height of 4 m. What is the velocity of the bullet?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the bullet = m₁ = 210 g = 0.21 kg

Mass of the block of clay = m₂ = 6 kg

Firing velocity of the bullet = V₁

Velocity of the bullet and the block of clay after the collision = V₂

By conservation of linear momentum,

m₁V₁ = (m₁ + m₂)V₂

Height the both masses are raised to = H = 4 m

The kinetic energy of the block of clay and the bullet after the collision is converted into potential energy as they rise up.

(m₁ + m₂)V₂²/2 = (m₁ + m₂)gH

V₂² = 2gH

V₁ = 261.97 m/s

Velocity of the bullet = 261.97 m/s