A gymnast of mass 64.0 kg hangs from a vertical rope attached to the ceiling. Yo

Question

A gymnast of mass 64.0 kg hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value 9.81m/s2 for the acceleration of gravity.

Part A
Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
Part B
Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
Part C
Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.30 m/s2

Part D

Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.30 m/s2 .

Explanation / Answer

a) T = mg = 64 x 9.81 =627.84 N
(b) T = 627.84 N [as v = constant=>acceleration= 0=>F = 0]
(c) T = m x (g+a) = 64 x (9.81+1) = 691.84 N
(d) T = m x (g-a) = 64 x (9.81 - 1) = 563.84 N

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