Question

A gymnast of mass 50.0 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.

Part A

Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
Express your answer in newtons.

Part B

Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
Express your answer in newtons.

Part C

Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.30 m/s².
Express your answer in newtons.

Part D

Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.30 m/s².
Express your answer in newtons.

Answer 1

Part A Answer

The tension is just due to the force of gravity:

F = mg
T = mg
T = 50 * 9.81
T = 490.5 N
T = 491 N

Note that you should be using 9.81 m/s² for g. If you use 9.8, you’ll get the wrong answer.

491 N

Part B Answer

This is the same as Part A (491 N)

491 N

Part C Answer

You need to add the forces acting on the gymnast. First, find the gravitational force:

F = mg
F = 50 * 9.81
F = 490.5 N

Next, find the force due to the gymnast climbing:

F = ma
F = 50 * 1.30
F = 65 N

The total tension is the sum of the above forces: 490.5 + 65 = 556 N

So why add the forces if the gymnast is moving up the rope (against gravity)? Shouldn’t you subtract? You add them because the force of the gymnast climbing is applied downward, in the same direction of gravity – it is NOT opposing gravity. Remember that the gymnast must pull on the rope to climb up it. So this is the same direction as the force applied when the gymnast is merely hanging from the rope.

556 N

Part D Answer

For this part, you need to subtract the forces (since the gymnast is moving down, the climbing force is partially canceling out gravity. See the explanation for Part C).

F = ma
T = ma
T = 50 * (9.81 – 1.30)
T = 425.5 N
T = 426 N

426 N