[] An Experiment to Determine the Coefficient of Friction

[Yellowkies_3275]

Homework Statement

So in physics we have this lab. Its simple, I'm just bad at physics...so bare with me.
The objective of the lab is find the coefficient of friction (on a flat surface not on inclined planes and such not sure if this makes a difference (I should know if it does but I don't and so I will say as clarification, that we only did this experiment on level surfaces)). I need help with the procedure for this. So what our group did was:

As instructed: get a wooden block with a known mass (40g -> 0.04kg) and get several cylinders with varying (known) masses:

Record their individual mass and weight and then their combined mass and weight.

The cylinder masses we used (for each surface the experiment is run several times with different cylinder masses) were

Mass: 0.5 kg ---the weight----> 4.9 N
Mass: 1 kg ---the weight----> 9.8 N
Mass: 0.2 kg ---the weight----> 1.96 N
Mass: 0.05 kg ---the weight----> 0.49 N
Mass: 0.1 kg ---the weight----> 0.98 N

and since our blocks mass was 0.04 kg ; the weight being 0.39 N, our total weight for each trial (per surface) is as follows:

5.29 N
10.19 N
2.35 N
0.88 N
1.37 N
~~~~~~~~~~~~~~~~~
Our first surface was our desk. So, we hooked the block with the cylinder mass on top (starting with 5.29 N as our combined total weight) to a spring scale to measure F_app . On our lab worksheet it is listed in the table where our measurements were recorded, that F_app = F_f
So using the spring scale and dragging the block and cylinder across a flat surface, we recorded our F_app, for all of the total weights.

For the Table:
Total weight (F_n): 5.29 N ---F_app----> 2 N
Total weight (F_n): 10.19 N ---F_app----> 2.8 N
Total weight (F_n): 2.35 N ---F_app----> 0.8 N
Total weight (F_n): 0.88 N ---F_app----> 0.2 N
Total weight (F_n): 1.37 N ---F_app----> 0.4 N

For a piece of Cardboard:
Total weight (F_n): 5.29 N ---F_app----> 1 N
Total weight (F_n): 10.19 N ---F_app----> 2 N
Total weight (F_n): 2.35 N ---F_app----> 0.4 N
Total weight (F_n): 0.88 N ---F_app----> 0.1 N
Total weight (F_n): 1.37 N ---F_app----> 0.2 N

For a piece of Styrofoam:
Total weight (F_n): 5.29 N ---F_app----> 1.4 N
Total weight (F_n): 10.19 N ---F_app----> 2.6 N
Total weight (F_n): 2.35 N ---F_app----> 0.6 N
Total weight (F_n): 0.88 N ---F_app----> 0.15 N
Total weight (F_n): 1.37 N ---F_app----> 0.25 N

We used the same weight combinations for each surface. And experimented with 3 surfaces.

Homework Equations

[/B]
F_n = mg
F_f = μk*F_n

The Attempt at a Solution

With F_app being stated on the worksheet as equal to F_f we used the equation:
F_f = μk*F_n
We divided both sides by F_n so that :

F_f
------------------- = μk
F_nSo for the Table we got:
2 N
------------------- = 0.38
5.29 N

2.8 N
------------------- = 0.29
10.19 N

0.8 N
------------------- = 0.34
2.35 N

0.2 N
------------------- = 0.23
0.88 N

0.4 N
------------------- = 0.29
1.37 N
For the Cardboard:

1 N
------------------- = 0.19
5.29 N

2 N
------------------- = 0.20
10.19 N

0.4 N
------------------- = 0.17
2.35 N

0.1 N
------------------- = 0.11
0.88 N

0.2 N
------------------- = 0.15
1.37 NFor the Styrofoam:

1.4 N
------------------- = 0.26
5.29 N

2.6 N
------------------- = 0.26
10.19 N

0.6 N
------------------- = 0.26
2.35 N

0.15 N
------------------- = 0.17
0.88 N

0.25 N
------------------- = 0.18
1.37 NFor the Table:

See how different all of those μk's are? Ahh :''

It was at this point we asked our physics teacher, not exactly for an answer, but for any advice. What he gave us was as such:
"When I apply to a job I have to submit paper work
When I apply (insert example I have to (insert relevant, corresponding factor)
When you apply force you have *pause* do something. That's as big of a hint as I can possibly give you"

I still don't know what he meant. I've thought about all the things I could possibly be doing that, as of current, were not done. I've come up with several things maybe but I think they are not exactly relevant, and I'm just reaching past what I need to into something unnecessary. I don't know which is why I consult the friendly users of PhysicsForums. I will finish listing my data in spoilers before I pose my final question.

For the Cardboard:

Closer than the first set of data, but still to distant to be reliable. There is still a very obvious flaw...one I cannot myself identify.

...and now my n key is stuck :' (rip)

For the Styrofoam:

As you can see with this last set of data, on the Styrofoam, three resulting μk's all had the exact same value. I would like to believe this to be a sign that our procedure was correct ad that inaccurate results previously can be attributed solely to massive human error, which will be corrected later in a redo experiment if that is the case.

My confusion is simply trying to understand whether or not, it was only human error responsible for our drastically varying results, or our procedure was flawed. Like our teacher said, did we have to do more with F_app? Was it not directly equivalent to F_f, despite the worksheet saying as such? What should we have done instead if our procedure contained the inaccuracies? For once I can't be led with hints to find the answer myself. I've evaluated every aspect and I myself cannot come up with a solution so simple, clarification instead of hints would be greatly appreciated.

Spoiler: As a gift for helping me

 

[Merlin3189]

I've no idea what your teacher was talking about.
I'd plot them on a graph and look for a pattern. You know what sort of pattern to expect.

Edit: "them" being your original data.

 

[Yellowkies_3275]

I've no idea what your teacher was talking about.

me neither

I have plotted them on a graph and for the last one, it is consistent the pattern I expect is what I got.. Thats what has lead me to believe the first two were human error, causing inaccuracies (since they don't line up with a graph well either), so I just wanted to check if my procedure was correct :)

 

[kuruman]

So using the spring scale and dragging the block and cylinder across a flat surface, we recorded our F_app, for all of the total weights.

This is a key part of the procedure that is not very clear. The coefficient of kinetic friction is the ratio of the pulling force to the weight only if the acceleration of the mass is zero. What measurements did you make to ensure that it was?
When you apply force, you have acceleration. (unless the net force is zero).

 

[Merlin3189]

So you expected a straight line?
If you made some (small) random errors, what would that do to the points?

When there is random error, we can plot the points and try to guess where the line should be.

 

[Yellowkies_3275]

This is a key part of the procedure that is not very clear. The coefficient of kinetic friction is the ratio of the pulling force to the weight only if the acceleration of the mass is zero. What measurements did you make to ensure that it was?
When you apply force, you have acceleration. (unless the net force is zero).

we did not make any measurements to ensure that we just tried our best to keep the motion constant.

 

[kuruman]

Did you take more than one measurements for each set of total weight and surfaces rubbing together to see how reproducible your results are? Say you measured the cardboard at 5.29 N total weight 10 times and found that the highest value of μ_k is 0.20 and the lowest value is 0.13 with an average of 0.16. What then? As @Merlin3189 suggested, there could be random error in your procedure or the procedure itself cannot be any more accurate than that. A significant systematic error is pulling the block at angle θ above the horizontal. Then the force gauge may say F however the normal force is not mg but mg - F sinθ. Another source of random error could be stick-and-slip behavior that might give you a range of values for the pulling force depending on when you read it.

https://en.wikipedia.org/wiki/Stick-slip_phenomenon