Energy conservation: sled on a hill

[tomgackle]

Hi there, I'm studying for mechanics final and I came across a question I can't figure out how to do. The question is as follows:

A person is on a sled of mass 10 kg that’s moving to the right on a frictionless surface at 4 m/s. Just before the sled goes down a hill the person of mass 50 kg jumps off the sled with a speed of 3 m/s relative to the sled, to the left. After the sled slides down the hill it comes in contact with a rough surface of u = 0.3 and is brought to a momentary stop by compressing a spring of force constant 1000 N/m, by 30 cm.

How far did the sled travel on the rough surface at the instant the spring was fully
compressed?


To start with, I found the change in velocity of the sled after the person jumped off, but I'm stymied as to how I can do the rest without being given the height of the hill.

any help is greatly appreciated!

thanks,

tom

 

[TxRationalist]

Since they give you the spring constant and the amount of compression, couldn't you figure out what the gain in kinetic energy was from going down the hill? Just a thought, I'm at work and can't spend time on it. Let me know how this works out!

 

[tomgackle]

I'm just thinking that if the hill was a lot higher than it is, then the sled would have to travel a lot farther on the frictional surface in order to compress the spring the same amount. If they wanted the answer in terms of 'h' the height of the hill it would be no problem, but I'm pretty sure it's supposed to be a numerical value.

Anyway, no need to risk it for my sake if you're at work, I'll just move on to the next few questions :)

 

[TxRationalist]

I have to agree with you. seems they left some info out...maybe I'll print this out and look at it at home tonight...good luck

 

[tomgackle]

Thank you and thank you!

 

[dumbatphysics]

umm...its been a long time but can you please tell me how you calculated the speed of the sled immediately after the person jumps off?

thankyou :)

 

[tomgackle]

It has been a while, but I remember have trouble with this question. I ended up going to my professor, and he told me that a value had indeed been left out. So if I remember correctly, the height should be given as 10m. Hope that helps.

Whoops, I guess that doesn't actually answer your question, does it?
To find the speed of the sled after the person jumps off, I think you can use the conservation of kinetic energy:
Ek = (1/2)mv^2

Energy of person relative to sled: Ep/s = 0.5*50*3^2
Then use that energy to find the change in velocity of the sled: 0.5*10v^2 = Ep/s by solving for v.

Add that value to the original speed. I'm not 100% sure on this, but I'm just on my way to bed, so it'll have to do. Final tomorrow!

 

[dumbatphysics]

omg thanku so much :)
and goodluck on your final :)