Two skaters each of mass 50 kg approach each other along prallel paths separated

Question

Two skaters each of mass 50 kg approach each other along prallel paths separated by 3 m . hey have oppsite velocities of 1.4 m/s each. one skater holds the end of a long pole of negligable ass, and the other skater grabs the other end of it as she passes. assume  the ice provides frictionless surface. (a) describe quantitativley the motion of the skaters after they have become connected by the pole. (b) what is the knietic energy of the system? (c) if the skaters pull on the pole so as to reduce thier separation to 1 m what are thier angular speed. (d) what the new kinetic energy of the system?

Explanation / Answer

a.)After the skater grabs the pole the entire translational energy converts into rotational energy

b.) E = 1/2*mv^2 + 1/2*mv^2 = mv^2 = 50*1.4^2 = 98J

c.) Conservation of angular momentum

mv1r1 = mv2r2

50*1.4*(3/2) + 50*1.4*(3/2)= 50*v*(1/2) + 50*v*(1/2)

v = 4.2m/s

d.) The energy, E = 1/2mv^2 + 1/2*mv^2 = mv^2 = 50*(4.2)^2 = 882J

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