Displacement of an object with certain Ek stopped by Frictional Force

[elia07]

Please do excuse if certain terms are not the most technical ones as I am translating the problem from another language. Do feel free to kindly inform me of the more technical term that substitues the sloppy one I've used. (And do excuse the generally bad English overall :-))

1. Homework Statement
A certain body of mass with the beginning kinetic energy of 48 J is moving along a horizontal surface and then stopping due to the effect of the friction force of onstant 6 N.
Calculate the path along which the body was stopping (in meteres).

Homework Equations

Ek = m x v^2 / 2
Wk = Ek

Ffr = G x mi
Ffr = Wfr / d

The Attempt at a Solution

I was working through the formulas and managed (I think) to extract the mass from both Ek and Ffr and got m = 96 J / v^2 and m = 0,6 kg & mi. However, I don't think this will be of any help, and conceptually I feel I should be looking somewhere else - unfortunately my imagination isn't working well at the moment.
What should I do?
Also, I was thinking perhaps if Wk is F times d, then I can somehow use that as well, although I feel this might reflect my faulty understanding of this formula.

Please help!

 

[gneill]

Also, I was thinking perhaps if Wk is F times d, then I can somehow use that as well, although I feel this might reflect my faulty understanding of this formula.

Actually, this is a good thought and a better approach. What does the work-energy theorem say about the relationship between kinetic energy and force x distance?

 

[elia07]

Actually, this is a good thought and a better approach. What does the work-energy theorem say about the relationship between kinetic energy and force x distance?

Well, it says, if I'm not mistaken, that the kinetic energy and the force x distance are equal.
(Btw, what force? The one that is moving the object, yes? How do we call it? In order to differentiate it from the Ffr.)
So just to confirm, I can use this formula for work when just calculating the work of kinetic energy as well? I thought W = m x v^2 / 2 was exclusive to it.

Some newer attempts of mine are extractions of distance according to this theorem:
d = 48 J / F
d = Wfr / 6N

Now what! I was thinking maybe I can tie it all together by the energy conservation theorem, since we know that the work of friction will be equal to the change of total energy. However, I'm not sure how to calculate this change. Is it possible that if Ek is 0 in the end, then Egp is 48J? Well, I guess not, because some of the energy will be lost through friction, right?

 

[gneill]

Well, it says, if I'm not mistaken, that the kinetic energy and the force x distance are equal.
(Btw, what force? The one that is moving the object, yes? How do we call it? In order to differentiate it from the Ffr.)

Any external force acting on the object. This includes friction forces.

So just to confirm, I can use this formula for work when just calculating the work of kinetic energy as well? I thought W = m x v^2 / 2 was exclusive to it.

That is how to calculate the kinetic energy held by a moving mass. But energy can be converted between forms, too, hence conservation of energy. When a force is involved in doing work on an object, the change in kinetic energy is equal to the force multiplied by the distance over which the force operates on the object.

Some newer attempts of mine are extractions of distance according to this theorem:
d = 48 J / F
d = Wfr / 6N

Now what! I was thinking maybe I can tie it all together by the energy conservation theorem, since we know that the work of friction will be equal to the change of total energy.

Yes.

However, I'm not sure how to calculate this change. Is it possible that if Ek is 0 in the end, then Egp is 48J?

Yes.

Well, I guess not, because some of the energy will be lost through friction, right?

But that is the point! The kinetic energy is being lost to friction, mediated by the friction force. When all of the KE has been lost to friction, the object has stopped moving.