Comparing static friction on two surfaces
Same block, same loads, two different surfaces. Tilt the board slowly, record the angle where the block first slides, and the coefficient of static friction falls out of one tangent. The mass cancels, so changing the load should change nothing.
Why one angle is all you need
As the board tilts, static friction grows to match the pull of gravity down the slope. It can only grow up to μsN. The angle where it runs out gives μs directly (Giancoli, §4–8).
The mass cancels. Move the mass slider on the right: both curves stretch, but the point where they cross stays put.
Force budget on the block
HoldsTilt the board yourself
Grab the purple knob on the raised end, or use the slider. Raise slowly and use the 0.1° nudges near the sliding point, as in step 4 of the procedure. When the block slips, its angle goes onto the sheet. Lower the board to put the block back for the next trial.
Measurement sheet
Simulated| Trial | θc (°) | μs = tan θc | Observation |
|---|---|---|---|
| Mean ± SD | — | — |
Does mass matter?
Mean μs for each of the six conditions, with error bars of one sample standard deviation. A flat row of points means no mass dependence, which is what μs = tan θc predicts.
Mean μs vs total mass
Summary · Appendix C
Simulated| Cond. | n | θ̄c (°) | μ̄s | SD |
|---|
These numbers come from the simulation: typical friction values for each material plus random trial-to-trial scatter. They show how the analysis works. They are not lab data.
What does one degree cost?
An angle reading of θ ± Δθ puts μs between tan(θ − Δθ) and tan(θ + Δθ). The same Δθ costs more on a grippy surface, because tan θ gets steeper as θ grows.
The project's own example, 30° ± 1°, gives a coefficient between tan 29° and tan 31°. Drag the reading to 45° with the same ±1° and the band gets noticeably taller.
Here Δθ is in radians. At 30°, sec²θ is about 1.33; at 45° it is 2. This is why the analysis compares the spread of repeated trials with the spread that the angle device alone would cause: if two surfaces or two masses differ by less than both, the difference means nothing.
Relative uncertainty here: —
Procedure
Board about 0.5–1.0 m long, a short wide block with extra weights near its centre, two surface materials, a balance, and a protractor or calibrated inclinometer.
Prepare surface A
Record the material, check it lies flat on the board, and mark the starting position.
Weigh the masses
Weigh the block alone and with its added loads. Record M1, M2 and M3 and keep the same totals on both surfaces.
Zero the angle device
Zero it on a horizontal reference. A phone used as an inclinometer stays clear of the sliding path.
Raise the board slowly
Start M1 at the mark. Lift without pushing the block, and use only small angle changes near the sliding point.
Read θc
Record the angle at the first continuous slide. A brief jump does not count.
Repeat five times
Reset and repeat for five readings, then do M2 and M3 with the same contact face and orientation.
Switch to surface B
Record the new material and repeat all fifteen measurements with the same block, masses and method.
Note anything odd
Toppling, a moving surface sheet, or any unexpected result goes in the observations column.