Compute all parts of given question:
Question: A gymnast of mass 55.0kg 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 9.81 m/s2 for the acceleration of gravity.
Part I: Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
Part II: Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
Part III: Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 0.500m/s2.
Part IV: Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 0.500m/s2.
Please show all work and explain your methods for above question.