Work-energy theorem and Tension Force

[RedDanger]

Homework Statement

While running at a speed of 5.0m/s Tarzan grabs a 9.0m long vine hanging vertically from a tall tree in the jungle and swings on it. As he swings on the vine, how much work is done on him by the tension force in the vine? To what maximum vertical height can he swing if he masses 95Kg?

Homework Equations

KEi + PEi = KEf + PEf

Work = F*deltaX*cos(angle)

The Attempt at a Solution

Well, because the tension force is acting at 90 degrees from the direction of motion, doesn't it do 0J of work on Tarzan because cos(90) = 0?

On the second part, when I apply the work-energy theorem, I end up with (0.5Vi² - 0.5Vf²)/g = height final, which would go to zero because Tarzan is an object in motion and is not being acted on by any force except gravity and the tension force, which if the vine does not break then it cancels out the Fg on Tarzan. Therefore, Tarzan's final velocity = initial velocity and height final = 0.

Is this correct?

 

[Doc Al]

Well, because the tension force is acting at 90 degrees from the direction of motion, doesn't it do 0J of work on Tarzan because cos(90) = 0?

Good!

On the second part, when I apply the work-energy theorem, I end up with (0.5Vi² - 0.5Vf²)/g = height final,

Good. That follows from conservation of energy.

which would go to zero because Tarzan is an object in motion and is not being acted on by any force except gravity and the tension force, which if the vine does not break then it cancels out the Fg on Tarzan. Therefore, Tarzan's final velocity = initial velocity and height final = 0.

No. The tension force does not cancel out Fg. (Is your answer reasonable, based on your experience?) While the tension does no work on Tarzan, gravity does. Thanks to the swinging vine, his initial KE is converted to gravitational PE.