How high can Jill reach on the swing after Jack jumps off?

[Summer202]

hey everyone
I am so glad I found this forum
I just have this one question that I need help with:

two circus performers, Jack and Jill, whose total mass is 120 Kg, start a swing which is 5.0 m long such that initially the rope attatched to their swing makes an angle of 36 degrees with the horizontal. At the bottom of the arc, Jack, whose mass is 65 Kg, steps off. What is the maximum height of a landing ramp that Jill can reach as the swing continues?

 

[jgm340]

Well, this is slightly tricky!

Usually you would use conservation of energy: the sum of kinetic and potential energy remains unchanged in a closed system. The problem is that since Jack steps off, the system isn't closed!

However, notice that Jack "steps" off, so he doesn't change the speed of the swing at the bottom.

I will pose two questions to you, and your answers to them ought to lead you to the answer to your question.

First: Would the swing have been going any faster at the bottom if Jack had never been on the swing at all?

Second: If no one jumps off, is there any difference between Jack and Jill being on the same swing versus separate swings side by side?

 

[Summer202]

hm thankyou
I got the et=et prime
everyones getting different answers so its kinda of confusing

 

[jgm340]

Ok, then I'll give you another hint.

A system is not closed if energy leaves or enters the system. In this case, no energy enters the system, but energy does leave.

At the bottom of the swing, there is only one form of energy: kinetic. This can be broken up into the kinetic energy Jack is contributing and the kinetic energy Jill is contributing. When Jack leaves the swing, all his kinetic energy goes with him (and dissipates into the ground, as he breaks his crown). This leaves only Jill's kinetic energy left.

However, note that the amount of kinetic energy Jill has at the bottom of the swing is exactly the same amount she would have had at the bottom of the swing if she had been swinging along all along. In other words, Jack's presence on the swing did not affect the amount of kinetic energy accumulated by Jill as gravity worked it magic.

This means that there IS a closed system we can consider, namely Jill swinging by herself. Since Jack's body never interacted with Jill's swinging in any way, the system consisting only of Jill's kinetic and potential energy IS closed.

This means that there is conservation of energy with respect to the system consisting of Jill. You can fill in the rest, I'm sure.

 

[Summer202]

ok so basically
this is what I did

mgh=1/2mv^2

through that i calculated v and got an answer of 7.59 m/s

and then during the swing after jack leaves i calculated the kinetic energy
1/2mv^2=mgh where m=55 and the velocity stays the same

and i got 2.94 m

but then.. it seems wrong. LOL