A gymnast of mass 53.0 Kg hangs from a vertical rope attached to the ceiling. Yo

Question

A gymnast of mass 53.0 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 9.81 m/s^2 for the acceleration of gravity. 1)Calculate the tension T in the rope if the gymnast hangs motionless on the rope. 2)Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate. 3) Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 0.800 m/s^2 . 4)Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.800 m/s^2 .

Explanation / Answer

1) T - m g = 0
T = mg = 53*9.81=519.93 N
2) if constant rate, a = 0
so T = 519.93 N
3) a = 0.8
T - mg = 0.8*m
T =53*9.81+0.8*53=562.33 N
4) a = -0.8
T =53*9.81-0.8*53=477.53 N

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