# Ok, a little shoe experiment!

1. Sep 25, 2005

### 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: Sep 25, 2005
2. Sep 25, 2005

### Poncho

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

3. Sep 25, 2005

### Päällikkö

N is not mg on an inclined plane.

4. Sep 25, 2005

### 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...

5. Sep 25, 2005

### Winner

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

6. Sep 25, 2005

### Integral

Staff Emeritus
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($\theta$)

7. Sep 25, 2005

### Winner

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

8. Sep 25, 2005

### Winner

Ok so I carried out the experiment:

Code (Text):

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: Sep 25, 2005
9. Sep 25, 2005

### Agnostic

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

10. Sep 25, 2005

### Winner

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

11. Sep 25, 2005

### Poncho

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

12. Sep 25, 2005

### 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.

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

Last edited: Sep 25, 2005
13. Sep 25, 2005

### 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.

14. Sep 25, 2005

### Winner

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

15. Sep 25, 2005

### Cyrus

100% correct.

Sounds good, dress shoes are smooth on the bottom.

Correct.

nope.

16. Sep 25, 2005

### Winner

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