Static Friction and angle of Repose

[genu]

I did an experiment where I had to determine the static friction of a wooden block on a horizontal wooden plank.

I determined Mu s for that to be 0.246

I then used the same block and plank, but this time I tried to determine Mu s by increasing the angle between the plank and the horizontal. I basically raised one side of the plank until the block started sliding...and recorded that angle as the angle of repose. I got Mu s for this part of the experiment to be 0.306

now I had to calculate the percent difference: ((.246-.306)/average) * 100

and I got 21.69 %

Shouldn't the percent difference be as small as possible? I assumed that Mu s would theoretically be the same no matter what angle?

 

[LowlyPion]

How did you determine the μ for the horizontal plank?

You may have lots of sources of errors.

But to answer your question, yes it is usually agreeable to be able to reconcile the theoretical with the observed.

You may want to consider how the differences in your results arose.

 

[genu]

Attached how I've setup the experiment for the horizontal. (I determined mu s by adding masses to m2 until the m1 started moving with constant speed) -- at least I tried to maintain a constant speed.

Attached is also the data for Experiment 1 and 2. (i'm comparing only the wood from experiment 2)

as you can see the Mu s is not very different from either experiment...

 

[LowlyPion]

I can't see your pics, but ...

If you were maintaining constant speed you were measuring kinetic friction that is always less than static, the point at which it begins to slide.

Other sources of error are not pulling exactly horizontal for instance. Slightly up lightens the loading, down increases the loading. Or measuring the angle ± a degree or so, as you tilt it, etc. Or reading the scale as you are pulling. etc.

 

[TVP45]

I think LowlyPion has pointed out the major source of error.

Some other things to think about:

Although I'm doing some fast hand waving about repeatability and error, someone of your level, with what I expect to be your equipment, should probably only use one significant figure for wood on wood.

What species wood? Some woods exhibit stiction.

Did you change the grain orientation?

And, did you have the same normal force each time?