A gymnast of mass 69.0 kg hangs from a vertical rope attached to the ceiling. Yo

Question

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.

Explanation / Answer

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

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