A circus perform hangs stationary from a rope. She then begins to climb upward by pulling herself up, hand over hand. When she starts climbing, is the tension in the rope less than, equal to, greater than it is when she hangs stationary? Explain

Greater than. Tension is greater when climbing because the performer is accelerating up the rope, so the rope tension is greater when climbing.

Tension while stationary=mg*sin (theta)

Tension while climbing = m (g+a) * sin (theta)

So we can see the Tension is greater while climbing as apposed to while hanging stationary