I need help with A and C but if you could explain B too that would be great. Two

Question

I need help with A and C but if you could explain B too that would be great.

Two friends hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about an axis through the center of the rope and perpendicular to the ice. The mass of one friend is 78.0 kg and the other has a mass of 125.0 kg. The rope of negligible mass is 3.5 m long and they move at a speed of 4.80 m/s.

(a) What is the magnitude of the angular momentum of the system comprised of the two friends?   kg · m2/s

(b) They now pull on the rope and move closer to each other so that the rope between them is now half as long. Determine the speed with which they move now. 9.6 m/s (correct)

(c) The two friends have to do work in order to move closer to each other. How much work did they do?
J

Explanation / Answer

a) magnitude of the angular momentum of the system = m1*v*(d/2) + m2*v*(d/2)

= 78*4.8*(3.5/2) + 125*4.8*(3.5/2)

= 1705.2 kg.m^2/s

b) Let v' is the speed in this case

Apply conservation of angular momentum

(m1+m2)*v'*(d/4) = (m1+m2)*v*(d/2)

v' = 2*v

= 2*4.8

= 9.6 m/s

c) Workdone = change in kinetic energy

= 0.5*(m1+m2)*(v'^2 - v^2)

= 0.5*(78+125)*(9.6^2 - 4.8^2)

= 7015.7 J

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