Max Tension in Rope Supporting Bungie Jumper (75kg)

[lovemake1]

Homework Statement

Find the maximum Tension in the rope that supports the bungie jumper.
mass of the jumper is 75kg. neglet air resistance.

Homework Equations

would it be Fnet = ma
Fgravity - F Tension = ma

The Attempt at a Solution

I am not sure how to approach this.
i know that when the jumper reaches the bottom. the rope flicks and for a moment it gains quite a bit of tension i believe? how would you approach this problem?
is it possible to find out ?

 

[jegues]

The point at which the rope is stretched the most will be the point of maximum tension. When he reaches this point he won't be moving up or down. (Try to imagine this)

With that said, we can conlcude that at that point $$a = 0$$

So using Newton's 2nd law,

$$\sum F = 0$$

This should be enough information for you to solve the problem. Give it a shot!

 

[JaWiB]

The point at which the rope is stretched the most will be the point of maximum tension. When he reaches this point he won't be moving up or down. (Try to imagine this)

With that said, we can conlcude that at that point $$a = 0$$

So using Newton's 2nd law,

$$\sum F = 0$$

This should be enough information for you to solve the problem. Give it a shot!

I disagree. In order for the jumper to come to a stop, the tension force must be greater than the weight force at some point or his acceleration is downward or zero during the entire jump and he'll splat.

The maximum tension will most likely occur at the point where the rope is stretched the most (so long as it obeys Hooke's law, which I imagine is a good approximation as long as the bungee doesn't break)

Were you given any more information for this problem?

 

[jegues]

In order for the jumper to come to a stop, the tension force must be greater than the weight force

You aren't going to look at the point when the tension is greater than the jumpers weight, you are going to look at the point when they are equal.

The maximum tension will most likely occur at the point where the rope is stretched the most

Thus, $$\sum F = 0$$

 

[JaWiB]

The rope is stretched the most at the bottom of the fall, when the jumper's velocity is zero. A moment after the jumper hits the bottom of the jump, he starts going back up.

Since the velocity goes from zero to nonzero in an upward direction, the change in velocity is also nonzero upward, and the acceleration must also be upward at the bottom of the jump, and from Newton's second law the net force must also be upward.

 

[jegues]

acceleration must also be upward at the bottom of the jump

At the bottom of the jump the jumper will not have any acceleration, for a small fraction of time he will be suspended in air with 0 velocity it both directions(downward and upward).

There is an acceleration upward immediately after the bottom of the jump, not at the bottom of the jump.(the point at which there is maximum tension)

 

[JaWiB]

At the bottom of the jump the jumper will not have any acceleration, for a small fraction of time he will be suspended in air with 0 velocity it both directions(downward and upward).

There is an acceleration upward immediately after the bottom of the jump, not at the bottom of the jump.(the point at which there is maximum tension)

How can there be an upward acceleration at any time if the maximum tension force has the same magnitude as the weight force?

 

[jegues]

How can there be an upward acceleration at any time if the maximum tension force has the same magnitude as the weight force?

You're right.

But there is still 0 acceleration at the point where the cord is extended to its maximum length.

I can't see how to go about solving for the maximum tension now though. Perhaps I let my intuition and reason fly out the window when I was unable to conjure an answer.

Thank you for the discussion/clarification JaWiB, sorry if I was any source of confusion.