A gymnast of mass 62.0kg hangs from a vertical rope attached to the ceiling. You

Question

A gymnast of mass 62.0kg 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.

Calculate the tension T in the rope if the gymnast hangs motionless on the rope.

Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.

Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.20m/s2 .

Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.20m/s2 .

*all answers in Newtons

Explanation / Answer

use newton's second law for all cases:

sum of forces = ma

a) accel =0, and the forces are T and W where W = 62kg or W=607.6N

T-W=0 =>T=W =607.6N

b) climbing at constant speed still means a=0, same answer as above

c) now a=+1.1m/s/s, so

T-W = ma
T-W=62kg x 1.20m/s/s
T=607.6N+74.4N=682N

d) now a=-1.2m/s/s

T-W = -62kg x 1.2m/s/s
T=607.6-74.4=533.2N

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