Question

A gymnast of mass 63.0 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.

A)Calculate the tension T in the rope if the gymnast hangs motionless on the rope.Express your answer in newtons.
B)Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.Express your answer in newtons.
C)Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 0.600 m/s2 .Express your answer in newtons.
D)Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.600 m/s2 .Express your answer in newtons

Answer 1

Answer:

Explanation:

A ) When gymnast is motionless , he is in equilibrium

T = mg

= 63 x 9.81

= 618.03 N

B )

When gymnast climbs up at a constant rate , he is still in equilibrium ie net force acting on it is zero as acceleration is zero.

T = mg

= 618.03 N

C ) If the gymnast climbs up the rope with an upward acceleration of magnitude 0.600 m/s2

Net force on it = T - mg   , acting in upward direction

T - mg = m a

T =  mg + m a

= m ( g + a )

= 63 ( 9.81 + .6)

= 655.83 N

D )  If the gymnast slides down the rope with a downward acceleration of magnitude 0.600 m/s2

Net force acting in downward direction

mg - T = ma

T = m ( g - a )

= 63 x ( 9.81 - .6 )

= 580.23 N