Question

Suppose a 65.5 kg gymnast climbs a rope. What is the tension in the rope if she climbs at a constant speed

Answer 1

The tension in the rope when the gymnast climbs it at constant speed is 641.9 N.

Given:

Mass of gymnast, m = 65.5 kg

The speed 'v' of gymnast is constant

Solution:

Consider the free-body diagram of the system as shown below.

Balancing forces along the vertical axis we get:

ΣFy = 0

Thus, we get:

F = ma     - (1)

where, m is mass of gymnast

            a is acceleration of gymnast (a = 0m/s², as the speed is constant)              

Also,

F = T - mg          -(2)

where, T is tension in the rope

           g is acceleration due to gravity

Equating (1) & (2), we get:

ma = T - mg

Re-arranging the equation, we get:

T = m(a+g)

Applying values in above equation we get:

T = (65.5 kg)(0 m/s²+9.8 m/s²)

T = 641.9 N

Therefore, the tension in the rope when the gymnast climbs it at constant speed is 641.9 N.

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