# Ok, a little shoe experiment!

Winner
Ok, a little experiment!

Ok, so I want to test the coefficient of static friction for two different kinds of shoes. I'll be using a runners and a formal dress shoe. Is this an ok procedure?

I'll using a wooden cherry board, and placing that against a wall. I'll slowly increase the angle of the board until the shoe in question slips. I'll measure the angle by placing a piece of paper at the side of the board and using a protractor. I'll do this a few times for each shoe to get an avg angle. I'll also have a scale for weighing the shoes. Hope you see what I'm trying to do here :rofl: Then I'm lost...

So to summarize:

What I have to work with:

board
two kinds of shoe soles
protractor
paper
scale

Now, my question is: the formula for static friction is F=uN. How can I find the u when I have two unknowns? I know N=mg, which I have but what about F?

Last edited:

Poncho
When uN = mg Sin(theta), the shoe will slip. That's assuming you're not using a shoe horn. -Dave

Homework Helper
N is not mg on an inclined plane.

Winner
right, thanks for that. Ok so I think I can find the Friction using the angle as in Wsin@=F, kinda like what Poncho said. I don't get what Poncho said in the second part though? Are you saying that when the backward force (friction) is equal to the forward force that the shoe will slip? I thought that if the friciton force is less than the forward driving force, the shoe will slip...

Winner
Päällikkö said:
N is not mg on an inclined plane.

So N is then just N=mgcos@. I see.

Staff Emeritus
Gold Member
Just a suggestion, you may be able to get a better angle measurement by measuing the length of your ramp, and its height on the wall. The ratio H/L = sin($\theta$)

Winner
Ahhh, thanks lol. Protractor...what was I thinking!

Winner
Ok so I carried out the experiment:

Code:
	Runners	Dress Shoes
Trial 	 Height of board before slip (H)	Height of board before slip (H)
1	59.9	                                                  48.5
2	57.6	                                                  48
3	58.5	                                                  48.1

Avgerage Height	58.7	                                     48.2
Angle (sin@=H/L)	42.1	                                     33.4

Length of Board: 87.6 cm
Mass of Shoes (g)
Runner:400g
Dress shoe: 480g

Ok so the data seems to make sense, I mean runners probably have greater coefficient of static friction.

Now, getting back to calculating u:

So, F=uN

and F=mgsin@
and N=mgcos@

Result: mgsin@=mgcos@ x u
since the mg's cancel out, all I need get u is sin@/cos@=u.

For the runners that is 0.903
For the dress shoes it's 0.659.

Ok, did I do this right? The results make sense, but just want to make sure.

**I didn't use mass anywhere b/c they cancelled...is that right?
**I didn't use a 1 meter board as I was supposed to...does that matter really?

Thanks all.

Last edited:
Agnostic
This can be simplified by assuming the shoe is in the shape of a sphere...

Winner
Huh? lol I don't get it ;p. Did I at least do it somewhat correct?

Poncho
Agnostic said:
This can be simplified by assuming the shoe is in the shape of a sphere...

That's funny, but I think in this case it would actually complicate the problem.

Cyrus
My god, common guys. Mu=tan(theta). Thats it, no more work involved! Its called the angle of repose, and is equal to the angle of static friciton. Experiment DONE. Doc is right, measure the length base and alittude to get a more accurate tangent.

This can be simplified by assuming the shoe is in the shape of a sphere...

Friction is INDEPENDENT of the surface area of contact, when impending motion occurs.

Last edited:
Stephan Hoyer
A simple way to test whether the coefficient of friction is indepedent of mass is to put something heavy in one of the shoes and to see if it slips at the same angle.

The length of the board doesn't matter as long as you're still finding the proper angle from the true length of the board and the height of the end of the board.

Winner
lol, all this is great discussion but did my results make sense is all I'm asking?

Cyrus
since the mg's cancel out, all I need get u is sin@/cos@=u.

100% correct.

For the runners that is 0.903
For the dress shoes it's 0.659.

Sounds good, dress shoes are smooth on the bottom.

**I didn't use mass anywhere b/c they cancelled...is that right?

Correct.

**I didn't use a 1 meter board as I was supposed to...does that matter really?

nope.

Winner
Thank you :) I'm at peace now lol.