Friction and Incline Lab
Adam Seering
In this lab, we investigated static and kinetic friction, and we measured the effect of the angle of an inclined plane on the "downhill" force acting on an object on that plane.
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Part I
Part II
Error Analysis
For the first part of the lab, we measured the downhill force on an object resting on an inclined plane, or ramp. This force should be equal to the difference between FN and mg; this difference is equal to mg(sinq) (see diagram). We did this by attaching a cart with a significant mass (1 kg) to a force probe, and anchoring the probe at the top of a ramp. This way, the force probe measured the "downhill" force on the cart. This force is also the net force, because in this setup, all other forces cancel each other out (see diagram).
Why the downhill, and net, force equals mg(sinq)
Sample picture of the setup (taken from the lab page, http://doversherborn.org/~bridgerj/physics/labs/inclinefriction/inclinefriction.htm)
We recorded the force measured by the force probe at 5? increments, from 0? to 90?. At 90?, the force was, logically, the weight of the cart; at 0?, it was, also logically, zero. We then plotted this information, as force vs. angle. The data was clearly nonlinear; this was not surprising, though, as we expected it to be in the form F=mg(sinq ) (where F=y and q=x, on an x/y plane), and we graphed F vs. q; this is a variant on a simple, non-linear sine function.
To get a linear function, one must have a graph of the form y = mx + b (there are other ways to get a linear graph, but this is the simplest). We wanted to get a linear graph because it is much easier to find a line of best fit for a linear function, and a line of best fit can be very useful in interpereting a relation. We therefore set y equal to F and x equal to sinq (as opposed to just q, like before), and let a computer calculate m and b, and generate a line of best fit.
Here is our data, as entered in the graphing program:
| Row #: | X | Y | sin(x) column |
| 1 | 0 | 0 | 0.0 |
| 2 | 5 | 0 | 0.08716 |
| 3 | 10 | 0.4 | 0.1736 |
| 4 | 15 | 1.5 | 0.2588 |
| 5 | 20 | 2.5 | 0.3420 |
| 6 | 25 | 3.3 | 0.4226 |
| 7 | 30 | 4.1 | 0.5000 |
| 8 | 35 | 4.9 | 0.5736 |
| 9 | 40 | 5.6 | 0.6428 |
| 10 | 45 | 6.3 | 0.7071 |
| 11 | 50 | 6.8 | 0.7660 |
| 12 | 55 | 7.5 | 0.8192 |
| 13 | 60 | 7.8 | 0.8660 |
| 14 | 65 | 8.2 | 0.9063 |
| 15 | 70 | 8.5 | 0.9397 |
| 16 | 75 | 8.7 | 0.9657 |
| 17 | 80 | 8.9 | 0.9848 |
| 18 | 85 | 9.1 | 0.9962 |
| 19 | 90 | 9.2 | 1.0 |
Force (Newtons; Y-axis) vs. sin(Angle) (degrees; X-axis):
This data does appear to be roughly linear. B is less than the margin of error for our measuring equipment, so it can be safely disregarded. M, according to our prediction, should be equal to mg; since the mass of the cart was 1kg, mg = 1(9.8) = 9.8. M differs by 0.1; this is, again, less than the accuracy of our measuring equipment, so it is reasonable to assert, using this data, that our predicted equation, F=mg(cosq ), is correct.
To make the graph somewhat more useful, we returned it to its original form, as F vs. q. The graphing software that we used has the nice feature that, once a line of best fit is found, it is maintained correctly even if the data is de-linearized. So this graph has a Sin-curve of best fit for the original data:
Force (Newtons; Y-axis) vs. Angle (degrees; X-axis):
This graph shows that the weight of the cart is roughly 9 newtons; its weight is the measure of the force at q =90?. This verifies our mass estimate of 1kg; 9 newtons * 1kg/9.8newtons = 0.9, or roughly 1.
The next part of the lab was to calculate static and dynamic coefficients of friction for different weights and surfaces. We used a scale with weights stacked on it for our "weight"; it was the easiest thing that we could find to push with the force probe.
Here is a sample picture of the arrangement, with weights stacked on a piece of wood instead of a scale:
Sample picture of the setup (taken from the lab page, http://doversherborn.org/~bridgerj/physics/labs/inclinefriction/inclinefriction.htm)
We then tried to push our "weight" with the force probe, graphing the force exerted on the force probe. We exerted just enough force to get the weights moving, and then reduced the exerted force so that it was just enough to keep it moving, without accelerating. As a result, the peak on the graph represented the amount of force necessary to overcome static friction, and the portion of the graph after the peak represented the amount of force necessary to balance dynamic friction. We ended up with a set of graphs, one for each configuration of materials that we tried.
The scale weighed 12.5N; this is a graph of the scale with a 9N weight on it, so it is for a total weight of 21.5N. It is on a piece of wood. The peak force is roughly 7.2N; Ff = mFN, so m = Ff / FN = 0.33. The scale started to slip down the board when it was angled at 20°; tan(q) = 0.36 = m. This is close enough to indicate that our force measurement is the actual measurement of static friction.
The force needed to overcome kinetic friction here looks to be roughly 4.7N, so mkinetic = Ff / FN = 0.22.
This was a graph made from measurements on a different piece of wood. Also, the scale only had a 4.5N weight on it, so the net weight was 17N. The peak force for static friction is 7.3N; therefore, m = Ff / FN = 0.43. The scale started to slide at 24°; tan(24) = 0.45. 0.43 is close enough to 0.45 to indicate a correlation.
The force of kinetic friction is roughly 3.5N here; therefore, m = Ff / FN = 0.20.
This graph was based on measurements from the stone surface of a lab table; it also made use of a different weight, 4.5N instead of 9N, for a total weight of 17N. The peak force is 2.7N; m = Ff / FN = 0.16. We realized, unfortunately, that it is not possible to safely lift up the table high enough to get the scale to start moving; had we been able to lift the table enough, we should have found the angle to be 9°.
The force needed to overcome kinetic friction here is about 1.8N; so m kinetic = Ff / FN = 0.11.
In this lab, there were relatively few sources of error. Almost every part of the lab was done at least in part on the computer; the computer, with its attached probes, seems to provide consistently accurate data to at least two significant figures. The only real significant source of error in the lab was in the protractors; they were quite small, so it was difficult to get readings accurate to within more than a degree or two. Air resistance was also neglected, but it is probably safe to say that it is negligible under the circumstances of this lab.