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!

 

[Nickie]

I would suggest the following procedure to determine the coefficient of kinetic friction between the block and plank of wood:

1. Place the plank of wood on a horizontal surface and measure its length and width. This will be used to calculate the surface area of the plank.

2. Place the block on the plank and measure its mass. This will be used to calculate the normal force acting on the block.

3. Slowly raise one end of the plank to create an incline. Use a protractor to measure the angle of incline, θ. This will be the same angle used for determining the coefficient of static friction.

4. Begin slowly sliding the block down the incline, taking care to keep the motion smooth and consistent.

5. Use a stopwatch to measure the time it takes for the block to slide a certain distance, Δd. This will be used to calculate the acceleration of the block.

6. Using the equations of motion, specifically the equation a_x = gsin(θ) - μ_k gcos(θ), solve for the coefficient of kinetic friction, μ_k.

7. Repeat the experiment multiple times and calculate the average value of μ_k to reduce any errors.

In response to question #5, it is not necessary to know the mass of the object to determine the coefficient of kinetic friction. This can be proven by the fact that in the equation used to solve for μ_k, the mass of the object does not appear. This means that as long as the angle of incline, θ, and the acceleration, a_x, are known, the coefficient of kinetic friction can be determined without knowing the mass. However, knowing the mass of the object can still be helpful in confirming the accuracy of the results and reducing errors in the experiment.

I hope this helps and good luck with your experiment!