One dimensional motion with friction

[mahdilm]

Hello,

I was wondering if someone could help me out with this one. Its been years since I've done physics and this problems is bugging the hell out of me.

A can of pop is given a shove. It slides across a table, eventually coming to a stop. If its initial velocity is 2.0 m/s, and the coefficient of kinetic friction between the two surfaces is 0.30, how far will it travel across the table.

Thanks

 

[GeoMike]

Hello,
I was wondering if someone could help me out with this one. Its been years since I've done physics and this problems is bugging the hell out of me.
Thanks

Hint:
You know the coefficient of friction, but you don't know the frictional force, nor do you know the normal force. You do have a common element to both the frictional force and the normal force though. Try eliminating it and then working from there.

GM

 

[mahdilm]

Hint:
You know the coefficient of friction, but you don't know the frictional force, nor do you know the normal force. You do have a common element to both the frictional force and the normal force though. Try eliminating it and then working from there.
GM

Could you elaborate more please?

 

[LeonhardEuler]

There are several different models for kinetic friction. In some cases it is assumed to increase as velocity increases, but I suspect that this is not the model you are intended to use as this would result in a differential equation, which seems to be more advanced than the level of the question. In that case, you are probably expected to assume that the force of friction is proportional to the normal force and directed against the velocity, but independent of its maginitude. This means that
$$F_{f}= \mu N$$
Where F_f is the friction force, mu is the coefficient of friction and N is the magnitude of the normal force. You know the normal force cancels out the force of gravity because the can is not accelerating in the vertical direction. So N=m(mass of can)*g(acceleration due to gravity). You don't know the mass, but work the problem out as if you did and you will see that it does not matter.