Question

Shown below is a small particle of mass 21 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.7 kg and a radius of 20 cm and is initially at rest.

What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) answer unit israd/sec

How much kinetic energy (in J) is lost in the collision? answer unit is in J

Answer 1

Considering conservation of angular momentum of system

Initial angular momentum of system = final angular momentum of system

mv r = ( 0.5 M r^2 + m r^2) w

0.021* 10 = ( 0.5 * 0.7* 0.2 + 0.021* 0.2) w

w = 2.83 rad /s

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Initial KE of system

KE i = 0.5 m v^2

KEi = 0.5 * 0.021*10^2 = 1.05 J

Final KE of system

KEf = 0.5 (0.5 Mr^2 + mr^2) w^2

KE f = 0.5 ( 0.5*0.7*0.2^2 + 0.021* 0.2^2)*2.83^2

KEf = 0.0594 J

Energy lost = 1.05 - 0.0594 = 0.9906 J

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