Kinetic friction in a two mass, one pulley problem

[StonedPhysicist]

Homework Statement

I have solved the problem where one mass m₁ is on a horizontal frictional table connected to a mass m₂ which is hanging off the table by a string over a pulley (assuming pulley massless), assuming that m₂ is greater than m₁ there is a net acceleration causing the mass 2 to fall down and the mass 1 to follow. The problem is that the equations suggest that an increased pulling force (i.e. larger m₂) causes an increased coefficient of kinetic friction, furthermore I apply this formula to the data I have and indeed a larger hanging mass gives a greater kinetic friction coefficient. Is this correct? I would have thought it should not effect the coefficient.

Homework Equations

The Attempt at a Solution

Solution already obtained, the question is about the solution.

 

[RUber]

If you hold your coefficient constant, what would have to change? Is there another term that might be variable in your equation?

 

[StonedPhysicist]

If you hold your coefficient constant, what would have to change? Is there another term that might be variable in your equation?

the only other variables are m₂ and of course the acceleration, but using the data i have for the acceleration which was found using a camera and tracking software, i still find an increasing coefficient of kinetic friction with increasing m₂

 

[RUber]

That is interesting. You have data for the two different masses and the acceleration terms are the same?
I would recommend running a third test -- maybe with masses that are close to each other -- clearly acceleration will need to change at some point.

 

[UchihaClan13]

Coefficient of friction depends on the surface on which the mass under consideration moves/undergoes relative motion
It has nothing to do with the mass of the body which experiences the frictional force!

 

[StonedPhysicist]

That is interesting. You have data for the two different masses and the acceleration terms are the same?
I would recommend running a third test -- maybe with masses that are close to each other -- clearly acceleration will need to change at some point.

no, the acceleration does increase with increasing m₂, but so does the kinetic friction coefficient. My understanding is that the kinetic friction should be independent of m₂ and thus independent of the acceleration but this does not seem to be the case.

 

[StonedPhysicist]

Coefficient of friction depends on the surface on which the mass under consideration moves/undergoes relative motion
It has nothing to do with the mass of the body which experiences the frictional force!

i agree, but the formula and my data do not seem to suggest this, my question is why

 

[UchihaClan13]

Could you provide an actual picture of the data you possess??
thanks
UchihaClan13

 

[StonedPhysicist]

Could you provide an actual picture of the data you possess??
thanks
UchihaClan13

Here is the data:

where the paper types are what m₁ is being dragged over, and 30,40 and 50g corresponds to mass m₂.

 

[StonedPhysicist]

any more ideas?