A ballistic pendulum is a device for measuring bullet speeds. One of the simplest versions consists of a block of wood hanging from two long cords. (Two cords are used so that the bottom face of the block remains parallel to the floor as the block swings upward.) A 0.013-kg bullet traveling at 280 m/s hits a 2.0-kg ballistic pendulum. However, the block is not thick enough for this bullet, and the bullet passes through the block, exiting with one-third of its original speed. How high above its original position does the block rise?

1 answer

The initial kinetic energy of the bullet is given by:

KE = 0.5 * m * v^2

KE = 0.5 * 0.013 kg * (280 m/s)^2

KE = 15.84 J

The final kinetic energy of the bullet is given by:

KE = 0.5 * m * v^2

KE = 0.5 * 0.013 kg * (93.3 m/s)^2

KE = 4.35 J

The change in kinetic energy of the bullet is given by:

ΔKE = KEf - KEi

ΔKE = 4.35 J - 15.84 J

ΔKE = -11.49 J

The change in kinetic energy of the bullet is equal to the change in potential energy of the block. The change in potential energy of the block is given by:

ΔPE = m * g * h

Where m is the mass of the block, g is the acceleration due to gravity, and h is the height the block rises.

We can rearrange this equation to solve for h:

h = ΔPE / (m * g)

h = (-11.49 J) / (2.0 kg * 9.8 m/s^2)

h = -0.58 m

The block rises 0.58 m above its original position.