24 The 1.7 kg balls are attached to the ends of a thin rod of length 50.0 cm and

Question

24

The 1.7 kg balls are attached to the ends of a thin rod of length 50.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (as shown), a 59.0 g wad of wet putty drops onto one of the balls, hitting with a speed of 4.00 m/s and then sticking to it.ion (a) What is the angular speed of the system just after the putty wad hits? rad/s (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? K^after/^before = (c) Through what angle will the system rotate before it momentarily stops?

Explanation / Answer

I1 = 2*1.7*0.5² = 0.85 kgm²
I2 = I1 + 0.059*0.5² = 0.8647 kgm²

L = m*v*r = 0.059*4.0*0.5 = 0.118 kgm²/s

A.

w = L/I2 = 0.118/0.8647= 0.136 rad/sec

KE2 = ½*I2*w² =0.5*0.8647*0.136^2 = 0.00805 J
KE1 = ½mV² = 0.5*0.059*4^2 = 0.472 J

B.

R = KE2/KE1 = 0.472/0.00805 = 58.63

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