The question is incomplete.
These are the parts missing.
Part A:
Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
Express your answer in newtons.
Part B:
Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
Express your answer in newtons.
Part C:
Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.50 m/s2 .
Express your answer in newtons.
Part D:
Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.50 m/s2 .
Express your answer in newtons.
Answer:
This is how you answer each part.
Part A:
Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
The acceleration is zero, so the net force is 0:
T - mg = 0
T = mg = 66kg × 9.81 m/s² = 647.46 N
Part B:
Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
The acceleration is zero too, so yet the tension is T = 647.46 N
Part C:
Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.50 m/s2 .
Now the acceleration of the gymnast is 1.50m/s², so she is adding a force of ma, which turns the equation into:
T - mg = ma
T = mg + ma = m (g + a) = 66kg (9.81 + 1.5)m/s² = 746.46N
So, the new tension is T = 746.46N
Part D:
Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.50 m/s2 .
Now, the acceleration is downward so it has the opposite sign of that of the part C.
T = m(g -a) = 66 kg (9.81 - 1.5)m/s² = 548.46
The new tension is T = 548.46N
