A gymnast of mass 55.0kg hangs from a vertical rope attached to the ceiling. You

Question

A gymnast of mass 55.0kg 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. 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 0.500m/s2 . PArt D: Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.500m/s2 .

Explanation / Answer

F=ma , T=ma
T = (55kg)(9.81m/s^2) = 539.55 N
Constant rate would mean there is no acceleration, so T = ma + m(0)== ma

Furthermore, if the gymnast is climbing up at a certain acceleration, lets say 0.0005m/s^2, use the rate at which they climb for the acceleration in the second have of the equation. Add it because they are going up, + acceleration.
T = ma1 + ma2 == 55x9.81 + 55x0.5= 566.05 N
If the gymnast is going down, use the same formula but subtract.
T = ma1 + ma2 == 55x9.81 - 55x0.5=513.05 N

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