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.
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?
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