A particle of mass m=10g and speed Vi=5 m/s collides with and sticks to the edge

Question

A particle of mass m=10g and speed Vi=5 m/s collides with and sticks to the edge of a uniform solid sphere of mass M=1kg and radius R=20cm. If the sphere is initially at rest and is pivoted about a frictionless axle perpendicular to the plane of the paper,

a. using the fact that the angular momentum of the point mass-sphere system is conserved, find the angular velocity of the system after the collision.

b. Energy, on the other hand, is not conserved. Determine how much energy is lost in the collision.

Explanation / Answer

m = 10 g, v= 5 m/s, M = 1 kg, R = 20 cm.

moment of inertia I = 2MR2/5 = 0.016 kgm2

a) mvR = (I + mR2)

= mvR/(I + mR2) = 0.61 rad/s

b) mv2/2 - (I + mR2)2/2 = 0.122 J

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