Question

A gymnast of mass 62.0kg 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 the tension T in the rope if the gymnast hangs motionless on the rope.

Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.

Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.20m/s2 .

Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.20m/s2 .

*all answers in Newtons

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A gymnast of mass 69.0 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 9.81 m/s2 for the acceleration of gravity.

Calculate in Newtons:

The tension T in the rope if the gymnast hangs motionless on the rope.

The tension T in the rope if the gymnast climbs the rope at a constant rate.

The tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 0.700 m/s2.

The tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.700 m/s2.

Given that the mass of gymnast is m = 69.0 kg
Acceleration due to gravity is a = 9.81 m/s^2
--------------------------------------------------------------
The weight of the gymnast acting down wards and tension in the string acting upwards.

When the gymnast hangs motionless tension in the string is
T = mg
= (69.0 kg)(9.81 m/s^2)
= 676.9 N
When the gymnast climbs the rope at a constant rate tension in the string is
T = mg
= (69.0 kg)(9.81 m/s^2)
= 676.9 N
When the gymnast climbs up the rope with an upward acceleration of magnitude
a = 0.700 m/s2 the tension in the string is
T - mg = ma (Since acceleration a is upwards)
T = ma + mg
= m (a + g )
= (69.0 kg)(9.81 m/s^2 + 0.700 m/s^2)
= 725.19 N
When the gymnast climbs up the rope with an downward acceleration of magnitude
a = 0.700 m/s2 the tension in the string is
mg - T = ma (Since acceleration a is upwards)
T = mg - ma
= m (g - a )
= (69.0 kg)(9.81 m/s^2 - 0.700 m/s^2)
= 628.6 N