Static Friction Experiment: Help Result interpretation

[Jaimie]

Hello, I hope someone can help me with this question.
"Design a simple experiment that you could carry out in your home to
i) determine the coefficient of static friction between an object and a surface.
ii) prove that the coefficient of static friction is dependent only on the surfaces in contact, and is not affected by any change in the mass of your object"

This is what I came up with.
1) Obtain and tape down with painter’s tape the architectural scale (ruler) so that the edge is 90degrees with the edge of the table top.

2) Obtain and tape protractor along the edge of the table so that the ‘x’ mark is aligned to the front edge of the scale and to the table top. Both taped scale and protractor will act as a jig to ensure there is little movement when raising the textured surfaces.

3) Place a piece of painter’s tape on the edge of the cutting board (closest to you) to mark the point at which the box will be placed at the start of each trail.

4) Place the wood cutting board flat on the table so that the front edge fits snuggly between the protractor and scale’s front edge. Align the full box of screws on the cutting board so the longest front edge is aligned with the tape marker.

5) Slowly raise the end of the cutting board surface just until the box just begins to slide downwards. Record the angle at which this occurs in the data table.

6) Repeat steps 4-5 two more times for a total of three trials and calculate the average angle value. (This angle will be used to calculate the static friction coefficient).

7) Calculate the static friction coefficient using the equation u= sin(theta) as derived from -Ff + Fgx = 0 for the surface and using the average angle value.

8) Repeat steps 4-7 with the box of screws 1/2 –full, then with the box empty. Record all values and calculations in the data table.

9) Obtain the plexiglass sheet clip it, with the binder clips, to on the board’s edge (closest to you). Repeat steps 4-8 and record all values and calculations in the data table.

10) Obtain the sheet of white paper and clip it (with the binder clips) to the cutting board. Repeat steps 4-8 and record all values and calculations in the data table.

Here are my results
Surface Average angle Static coefficient
Wood cutting board (w/Full box of screws)- 20.0 0.364
" (w/1/2 box of screws)- 20.8 0.380
" (empty) 22.8 0.420
Plexiglass (w/Full box of screws) 28.3 0.538
" (w/1/2 box of screws)- 34.0 0.674
" (empty box) 40.7 0.860
Paper (w/Full box of screws)- 20.0 0.364
" (w/1/2 box of screws)- 28.0 0.532
" (empty) 30.3 0.584

The Attempt at a Solution

 

[Simon Bridge]

Uncertainties are reported to no more than 2 sig fig and usually just one.

Have you done hypothesis testing yet? Do you know how to combine errors?
The hypothesis being tested is that there is no difference in the coefficient if friction for different weights.
Clearly there is a difference - but it could be due to random variations in the measurement.
You need to see if the difference is close enough to zero to call it at 95% confidence level.

The simplest approach is to plot a graph of coefficient vs mass, with 95% error bars, and see if a horizontal line can be drawn through all the errorbars.

Note: what did you do to account for the sliding of the box changing the surface (scratching it etc)?

 

[Jaimie]

Yes, this is what I thought as mathematically, mg cancels out, so the static coefficient should be the same with same surfaces in contact with varying weights. I do believe that there were a lot of errors as a result of movement while taking mesurements, not enough trials perhaps, inaccuracies in equipment,etc.
Thank you also for the tip about the percentage error (Will keep this in mind when studying further). I didn't account for the sliding of the box changing the surface. Good to know! Typically was is done to account for this...or do you just wipe both surfaces in contact before sliding?

 

[Simon Bridge]

You certainly have too few trials.

I suspect your surfaces got rougher with use - increasing the coefficient of friction perhaps.
Plastics tend to have more stiction with more sharp edges for example. (You know how friction happens?)

You'd account for this by having more trials - identifying outliers - and repeating the runs for different weights.

The most common mistakes made in this sort of thing is just getting relaxed as you go through the trials - when you start you are usually very careful and as you get used to the work, you get a bit more careless.

Pointers:
- You should make a statement if your overall strategy at the start of your description of the experiment - before you go into details. The important details are in how you identify control the variables in an experiment.

- you don't need the protractor or any measurement of the angle to the horizontal.
measure the distance along the rap to the start position of the box - call this d
measure the height (to the ramp) of the box when the box just starts to move - call this h
the sine of the angle is h/d
... so you keep d the same, and record h and m for each run.

- make a graph as you go - this can be quite untidy so you won;t hand it in, but it helps you identify when you have a mistake or a systematic error.

 

[Jaimie]

Thank you Simon. Very helpful. I will make the adjustments as noted. Thanks again.