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?
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
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