A projectile of mass m =1.00 kg is traveling at a constant velocity of 4.00 m/s

Question

A projectile of mass m =1.00 kg is traveling at a constant velocity of 4.00 m/s toward (and tangent to) the edge of a stationary, solid disk of mass M =3.00 kg and radius R=2.00 m that is free to rotate about its axis. The projectile strikes the disk tangent to the edge and sticks to it. Model the projectile as a point mass.
(a) Before impact, what is the total angular momentum L0 of the disk-projectile system about the axis?
(b) What is the angular speed ? of the disk- projectile system just after the impact?
(c) What is the kinetic energy of the disk-projectile system after impact?
(d) How much mechanical energy is lost in this collision?

Explanation / Answer

a) it is 1*4*2=8(kgm2/s). b) we have that 8=(1*2^2+3*2^2/2)*w. so w=0.8(rad/s). c) it is (2^2+3*2^2/2)*0.8^2/2=3.2(J). d). initial energy 1*4^2/2=8(J). so energy lost ?Q=8-3.2=4.8(J)

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