This problem has two parts. The questions of both parts along with additional info will be listed in "Description".

Question

Suppose a 57.5 kg gymnast is climbing a rope. Therefore, m = 57.5 kg.

Part a) What is the tension in the rope, in newtons, if he climbs at a constant speed?

Part b) What is the tension in the rope, in newtons, if he accelerates upward at a rate of 1.7 m/s²?

Answer 1

Consider the two free body diagrams below where the only forces are

tension (T) in the rope and gravitational force (mg) exerted on the gymnast.

In the first FBD, tension balances gravitational force giving a net force of zero.

In the second FBD, tension is greater than gravitational force giving a nonzero, net upward force.

How do these relate to the gymnast climbing the rope? Can you use these and the information given in the question to determine the tension on the rope in parts a and b?

Answer 2

Maybe we can start by considering the gymnast as a point particle. What are the forces experienced by the gymnast as he climbs? We know about gravity but there must be something that counteracts gravity to allow him to climb up.

Once we have the forces on the gymnast, we can think about using Newton's 2nd Law, i.e. the sum of all forces on a system should equal mass times acceleration of the system.

Hint: Each part has a different acceleration for the climber