A puck of mass m = 54/0 g is attached to a taut cord passing through a small hol

Question

A puck of mass m = 54/0 g is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). the puck is initially orbiting with speed V_i = 1.60 m/s in a circle of radius r_i = 0.320 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.130 m. What is the puck is speed at the smaller radius? Find the tension in the cord at the smaller radius. How much work done by the hand pulling the cord so radius the pucks manages from 0.370 m to 0.130 m? Two astronauts (figure), each having a mass of 76.0 kg are connected by a sigma = 11.11 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.30 m/s.

Explanation / Answer

part 1 )

a )

angular momentum is conserve

mvr = mvi*ri

v = vi*ri/r

v = 1.60 * 0.320 / 0.130

v = 3.94 m/s

part b )

T = mv^2/r = (54 x 10^-3) * (3.94)^2 / 0.130

T = 6.44 N

part c )

W = dKE ( change in kinetic energy )

1/2* m(v^2 - vi^2)

W = 0.35 J

part 2 )

L = mrv + mrv

L = 2mrv

m = 76 kg

r = 11.11/2 = 5.555 m

v = 5.30 m/s

L = 4475.108

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