Question

A gymnast of mass 67.0 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. Use the value 9.81m/s2 for the acceleration of gravity.

Calculate in Newtons:

a. The tension T in the rope if the gymnast hangs motionless on the rope.
b. The tension T in the rope if the gymnast climbs the rope at a constant rate.

Answer 1

Step-by-step explanation:

Given that,

Mass of the gymnast, m = 67 kg

Acceleration due to gravity,
`a=9.81\ m/s^2`

(a) We need to find the tension T in the rope if the gymnast hangs motionless on the rope. In this case, the tension in the rope is equal to its weight. So,

`T=mg\\\\T=67* 9.81\\\\T=657.27\ N`

(b) In this case, we need to find the tension T in the rope if the gymnast climbs the rope at a constant rate. So, the value of acceleration, a = 0. So,

`T=mg\\\\T=67* 9.81\\\\T=657.27\ N`

Hence, this is the required solution.