A gymnast of mass 68.0kg hangs from a vertical rope attached to the ceiling. You

Question

A gymnast of mass 68.0kg 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 climbs up the rope with an upward acceleration of magnitude 0.800m/s2 .

Express your answer in newtons.

Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.800m/s2 .

Express your answer in newtons.

Explanation / Answer

F=ma , T=ma
T = (61kg)(9.81m/s^2) = ? N (do the math)
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, 0.800 m/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 == 68x9.81 + 68x0.800 =721.48 N
If the gymnast is going down, use the same formula but subtract.
T = ma1 + ma2 == 68x9.81 - 68x0.800 = 612.68N

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