Two small flat disks, one with a mass of 300 grams and the other with a mass of

Question

Two small flat disks, one with a mass of 300 grams and the other with a mass of 200 grams are connected by a low-mass rod with length of 150. cm and are at rest on a frictionless horizontal table as shown on the right. A third mass of 400 grams is moving at 3.00 m/s perpendicular to the rod and strikes and sticks to the 200. gram disk in a perfectly inelastic collision.
a) What is the speed at the center of mass immediately after the collision?
b) What is the angular speed of the rod about the systems CM after the collision?
c) What percentage of the initial KE is converted into heat and sound during the collision?

Explanation / Answer

a) it is 3*0.4/(0.4+0.3+0.2)=1.33(m/s) b) center of mass. G distance between G and the 0.2kg disk 1.5*0.3/(0.2+0.3+0.4)=0.5(m). so angular momentum. 0.4*3*0.5=0.6. ------- moment of inertia 0.2*0.6^2+(0.3+0.4)*0.9^2=0.64. so w=0.6/0.64=0.94(rad/s). c) K_inti=0.4*3^2/2=1.8(J) K_final = 0.94^2*0.64/2+K1. where K1=P^2/2M=(0.4*3)^2/2(0.4+0.3+0.2)=0.8 so K_final=1.08(J) so Q=1.8-1.08=0.72(J)

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