Mastering Physics Solutions: A Gymnast on a Rope

Mastering Physics Solutions: A Gymnast on a Rope

On September 22, 2013, in Chapter 04: Force and Motion, by Mastering Physics Solutions

A Gymnast on a Rope

Part A = 491 N Click to use the calculator/solver for this part of the problem
Part B = 491 N Click to use the calculator/solver for this part of the problem
Part C = 556 N Click to use the calculator/solver for this part of the problem
Part D = 426 N Click to use the calculator/solver for this part of the problem

Solution Below:

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.

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

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

This is the same as Part A (491 N)

491 N

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.

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? The reason you add them is 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, in order 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

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.

For this part, you need to subtract the forces (since the gymnast is moving down, the climbing force is partially cancelling 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

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