A person weighing 500 N climbs on a rope. What is the tension on the rope?

At the times when the person is not moving up or down, the tension in

the rope is 500N. At those moments, the forces on the person consist

of 500N downward due to gravity and 500N upward due to the tension in

the rope, and with the forces balanced, the person just hangs there and

doesn't accelerate up or down.

At the times when the person is actually climbing, that is, hauling himself

upward, the tension in the rope must be greater than 500N. At those moments,

the net force on the person is upward, and the person's body accelerates upward.