# Conceptual Question on Kinetic Friction

1. Nov 3, 2007

### twotaileddemon

1. The problem statement, all variables and given/known data

Just wondering.. does the coefficient of kinetic friction and force of kinetic friction vary with mass?

2. Relevant equations
∑F = mg – Fk = (M + m)a
Fk = ukN
N = mg
uk = [mg – (M + m)a]/Mg

3. The attempt at a solution

I think that as the mass of an object increases, the coefficient of kinetic friction decreases and thus the force of kinetic friction decreases based on the equation Fk = ukN. This is a direct result of my lab experiment. We had a wooden block with some weights (mass M) and a weight attached to a hanger (mass m), which was attached to a string, attached to a pulley and futher attached to the end of a block of wood. We were just testing whether or not the velocity, acceleration, surface area, or mass affects the coefficient/force of kinetic friction. Based on my results, only mass varied.. but I am wondering if my statement in the first sentence is correct. Thanks

2. Nov 3, 2007

### twotaileddemon

actually, now I'm thinking that the force of kinetic friction increases with increased mass. because of Fk = ukN = ukmg.... and I also think that the coefficient of kinetic friction is indepent of mass now >_< this contradicts my previous reasoning but I did some research on sites.

3. Nov 4, 2007

### twotaileddemon

So could anyone guide me in the right direction if my claims are wrong?
the coefficient of kinetic friction is independent of mass, speed, acceleration, and surface area
the force of kinetic friction is independent of speed, acceleration, and surface area, but is proportional to the mass

4. Nov 4, 2007

### Antineutron

No the Force of friction increases, as mass increases. F=ma=mg Fk=uN=umg <----look, higher the mass, higher the force of friction becomes, the coefficient does not change, it is different for different material and is therefore have a constant value.

5. Nov 4, 2007

### twotaileddemon

My later posts confirms your response, so thank you for helping me with that! Would you happen to know if my other claims in post #3 are correct?

6. Nov 4, 2007

### Antineutron

Yes, the equation says it all, umg
depends on the material's u, g, and m. so if you have a heavier mass with small u value, ice? So does it depend on the area?

7. Nov 4, 2007

### twotaileddemon

I think surface area might affect the force of friction on ice maybe, but certainly not on a hard surface like a table... right?

8. Nov 4, 2007

### saket

If I am not mistaken following are the findings which some standard text books have quoted:
µk, for rigid bodies, depends on the two materials in contact and is independent of mass, m. Therefore, in a given problem fk is proportional to normal reaction (as fk = µkN).
But also, some have quoted that, µk may vary with increasing speed.. but for all practical purposes at this level, it may be taken as a constant.

9. Nov 4, 2007

### twotaileddemon

Yeah.. that was a problem I encountered. I must have looked at least 12 different what I consider educational/well-researched sites and some have differences of opinion with velocity, as well as mass (for the coefficient and force of kinetic friction) n_n; .. and even surface area

10. Nov 4, 2007

### saket

yeah right.. and what we do normally use is, Newtonian assumption (for dry friction): µk & fk doesnt depend upon surface area, or speed.. (µk doesnt depend upon even mass) ..but then it is just an assumption.. for we to be able to work easily, and possibly it matches agreeably (although not exactly) with experimental results.

Last edited: Nov 4, 2007
11. Nov 4, 2007

### twotaileddemon

Thanks for your reinforcements and input.
I've been searching for 6 hours and did an experiment in school several times.. and its driving me crazy xD