**A Gymnast on a Rope**

Part A = 491 N

Part B = 491 N

Part C = 556 N

Part D = 426 N

**Solution Below:**

Part A

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/s^{2} for g. If you use 9.8, you’ll get the wrong answer.

491 N

Part B

Express your answer in newtons.

This is the same as Part A (491 N)

491 N

Part C

^{2}.

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

^{2}.

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