A gymnast of mass 61.0 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.

Question

How do I calculate the tension T in the rope if the gymnast hangs motionless on the rope?
Also, what if the gymnast climbs the rope at a constant rate. How would I calculate that?

Thanks in advance!

Answer 1

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, lets say 2.1 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 == 63x9.81 + 63x2.1
If the gymnast is going down, use the same formula but subtract.
T = ma1 + ma2 == 63x9.81 - 63x2.1

Answer 2

If motionless or moving at constant speed T=ma where m is mass of object and a is 9.8