Determining the Coefficient of Kinetic Friction on an Incline

[Polus]

Homework Statement

I am conducting an experiment to determine the coefficient of static and kinetic friction between 2 objects I've arbitrarily chosen. I have a block and a plank of wood. I have been raising the plank to an incline to determine at what angle the block will begin sliding.

I was given no data, I'm measuring everything myself. I have determined that the angle of incline or θ = 18°. I then drew a FBD and determined the coefficient of static friction which I found to be 0.32.

The part I'm stuck on is question #3: "Now, using the same tools, figure out a procedure to determine the coefficient of kinetic friction. State your procedure."

I'm stuck because question #5 then asks: "Was it necessary to know the mass of the object to perform this activity? State how you can prove that mass is/is not necessary"

I've been trying to solve the coefficient of kinetic friction between the block and plank of wood without mass first because I don't want to lose marks by arguing the incorrect conclusion.



2. The attempt at a solution
I attached the FBD, it's not the best image but I thought it'd be worth it to upload it. :P

I tried to come up with an equation which would let me solve for μ_k. The best I could come up with was: a_x = gsin(θ) - μ_k gcos(θ)

I assumed that F_{netx} = F_{gx} - F_k

I feel as if I'm on the right track (if it is even possible to find μ_k like this) as I have eliminated mass but I don't know what to do with the a_x.

Also, 18° was the angle I used for determining the coefficient of static friction. Am I wrong to use 18° for determining kinetic friction?


By the way, my tools are a protractor, ruler, my horizontal plane (the plank), and object used to slide (block). If I take question #3 literally I don't know how I would be able to determine the mass of my object. Although, I do roughly know the mass of my object. I was also thinking I could use Δd to determine acceleration but without a watch of some sort included in my list of tools I don't know if I am meant to use Δt in my equations.

This is my first post so I am sorry if it is formatted improperly (I tried my best!). Critiques to the formatting of my post would be much appreciated. Thanks!

 

[TSny]

I tried to come up with an equation which would let me solve for μ_k. The best I could come up with was: a_x = gsin(θ) - μ_k gcos(θ)

I assumed that F_{netx} = F_{gx} - F_k

I feel as if I'm on the right track (if it is even possible to find μ_k like this) as I have eliminated mass but I don't know what to do with the a_x.

Hello, Polus, and welcome to PF!

I think you have a very good start! Suppose you fiddle with the angle so that, after giving the block a little push to get it started, it slides with a slow constant speed down the slope. Would this help with what to do with a_x? Of course, there will be some error in deciding whether or not the speed is constant. But if you play around with it, I think you can get a decent result.

 

[Polus]

Thanks, TSny. I consulted my teacher and she told me exactly what you did. :P

 

[TSny]

That's good. Have fun with the experiment!