What is the force exerted by the rope?

[pivoxa15]

Homework Statement

Jo decides to try bungy jumping while on an overseas holiday. A rope that could be easily stretched was tied to her ankles and she jumped off a bridge high above a river. Model this as an ideal spring with a spring constant of 20N/m. Jo has a mass of 60kg and, after she jumps, her centre of mass falls vertically a distance of 12m before there is a force exerted on her by the rope.

When the rope reaches maximum extension Jo will be momentarily at rest. What is the upward force that the rope exerts on Jo?

Homework Equations

Assume g=10m/s^2

The Attempt at a Solution

When Jo is at rest there is a 600N force downward so the reaction is a tension force of 600N in the rope. This tension is the upward force that the rope exerts on Jo. But the answers suggested the force is 5.4*10^2N. How did they get that?

 

[AlephZero]

When Jo is at rest, she is accelerating upwards, otherwise she would not "bounce" up again. So the force in the rope is greater than her weight.

Hint: use conservation of energy.

 

[arildno]

pivoxa:
Remember that "balance of forces" means "no acceleration", whereas "at rest" means "no velocity".

Do not confuse velocity and acceleration, nor the states when either of them has the value 0!

 

[jeroen]

A similar situation.
https://www.physicsforums.com/showthread.php?t=157395

 

[pivoxa15]

I get it now. It is a good problem since it uses many concepts. The person falls 12m without any external forces for a total time of 1.55seconds. The speed at the end of this fall is 15.5m/s with a total of 7200J. All this energy must be converted into elastic potential energy and the string is stretched by 26.83m (fairly elatic rope - can stretch for such a long length in reality?). This amounts to a total upward force of 536.7N exerted on Jo.