Regular lab. You turn in the part you worked on. In a group of two, each of you turns in your own part plus CON.
At a glance
- Question. How does the friction force on a block depend on the normal force pressing it into the track, for static and for kinetic friction, on two different pairs of surfaces?
- You measure. The peak force just before the block slips and the average force while it slides, for five loads, three trials each, on two surface combinations.
- You calculate. The total mass on the track and the normal force.
- You graph. Friction force against normal force: four data sets on one graph, four linear trendlines. The four slopes are the four coefficients of friction.
- You conclude. The relationship in words, the four equations, the four coefficients, static against kinetic, surface against surface.
QPD
The question
What is the relationship between the magnitude of the normal force (\(F_N\)) and the magnitude of the friction force (\(f_s\) and \(f_k\)) between horizontal surfaces of A on B and C on B?
Fill in the surfaces with their names, felt on poplar or cork on oak, using the same names you put in the Excel header and the graph legend. The symbols go in brackets after the words, not instead of them.
What the procedure must make clear
- Which two surface combinations you tested, and which face of the block was down for each.
- How the block was loaded: the box, then bars of 0, 0.25, 0.5, 1.0 and 1.5 kg on top, three trials at each.
- How the pull was done: the force sensor hooked to the block, zeroed before each run, pulled horizontally and slowly until the block breaks free, then kept moving at a steady speed.
- Where each number came from on the force–time graph: the maximum static friction force is the peak just before the block slips, read from a Statistics box over the peak; the kinetic friction force is the mean of the plateau while it slides, from a Statistics box over the plateau.
| Symbol | Quantity | How it is measured | Unit |
|---|---|---|---|
| \(M_\text{bars}\) | mass added on top of the box | given, 0 to 1.5 kg | kg |
| \(M_\text{box}\) | mass of the box | given on the template, 0.11 kg | kg |
| \(f_{s,\max}\) | maximum static friction force | peak of the force–time graph | N |
| \(f_k\) | kinetic friction force | mean of the sliding plateau | N |
The diagram
A photo of the block on the track with the sensor attached, labelled with: the block and which surface is down, the track surface, the sensor and the direction of pull, the added masses, and the direction of motion. The report’s QPD section also wants a screenshot of the force–time graph with both Statistics boxes open, one over the peak and one over the plateau, so it is clear where \(f_{s,\max}\) and \(f_k\) came from.
UDA
In Excel
| Column | Formula | Unit | Sample calculation on the board |
|---|---|---|---|
| \(M_\text{TOTAL}\) | \(M_\text{bars} + M_\text{box}\) | kg | yes |
| \(F_N\) | \(M_\text{TOTAL} \times 9.81\ \text{m/s}^2\) | N | yes |
| \(f_{s,\max}\), \(f_k\) | measured | N | no, but both need uncertainty rows |
The mass columns come with their uncertainty filled in. For the two force columns the reading wobbles, so the standard deviation from the Statistics box is a sensible \(\delta_a\); the uncertainty guide has that branch.
The graph. Friction force in newtons on the vertical axis, normal force in newtons on the horizontal. Four series on one chart: combination 1 static, combination 1 kinetic, combination 2 static, combination 2 kinetic. A linear trendline on each with its equation displayed, and a legend that names the combination and whether it is static or kinetic. The relationship is linear, so this graph is also the linearized graph.
On the board
Left half, derivation. Draw the block being pulled, with four forces: the normal force \(F_N\) up, the weight \(F_g\) down, the tension \(F_T\) from the sensor along the pull, and friction \(f\) opposing it. Vertically nothing accelerates, so \(F_N - F_g = 0\) and \(F_N = M_\text{TOTAL}\,g\). Horizontally, at the instant before slipping and again while sliding at constant speed, \(F_T - f = 0\), so \(f = F_T\): the sensor reading is the friction force. The model under test is \(f = \mu F_N\), a straight line through the origin whose slope is \(\mu\).
Right half, sample calculations. One for each calculated column, from a real row of your sheet:
\[M_\text{TOTAL} = 0.25\ \text{kg} + 0.11\ \text{kg} = 0.36\ \text{kg}, \qquad F_N = (0.36\ \text{kg})(9.81\ \text{m/s}^2) = 3.5\ \text{N}.\]
CON
The questions as they are handed out, each with the sentence it becomes. The numbers are invented.
- What relationship did you find between the normal force and the friction force, both static and kinetic? → “The relationship between the normal force on the block and the friction force on it is linear, for both static and kinetic friction and for both surface combinations.”
- What were your two static-friction trendlines and your two kinetic-friction trendlines? Physical variables, not \(x\) and \(y\). → “For cork on oak the trendlines were \(f_s = (0.31)\,F_N\) and \(f_k = (0.24)\,F_N\), and for felt on oak they were \(f_s = (0.42)\,F_N\) and \(f_k = (0.35)\,F_N\).” If Excel gives an intercept, keep it, with its unit: \(+\,0.05\ \text{N}\).
- What were your four friction coefficients? → “The coefficients were \(\mu_s = 0.31\) and \(\mu_k = 0.24\) for cork on oak and \(\mu_s = 0.42\) and \(\mu_k = 0.35\) for felt on oak, to two significant figures; they are unitless because each is a force divided by a force.”
- Were the kinetic or the static coefficients greater in general? → “For both combinations the static coefficient was larger than the kinetic one.”
- Which surface combination had the larger coefficients? → “Felt on oak had the larger coefficients for both static and kinetic friction.”
There is no outside reference value in this lab. The comparison is between your own results.
Common slips
- Writing \(y = 0.314x + 0.02\) instead of \(f_s = (0.314)\,F_N + 0.02\ \text{N}\).
- Four trendlines and no legend, so nobody can tell which is which.
- Leaving the box out of the total mass.
- Reading \(f_k\) off the peak, or \(f_{s,\max}\) off the plateau.
- Pulling at an angle or in jerks. The sensor measures tension, and tension only equals friction when the pull is horizontal and the block is not accelerating.
- Coefficients quoted to five figures. Two is what is asked for, and two is what the data support.
Going deeper
Why the coefficient has no units. It is the ratio of two forces, so the newtons cancel. That also tells you what it measures: how many newtons of sideways push each newton of squeeze can resist before the surfaces let go.
Why static beats kinetic. When the block sits still, the high points of the two surfaces settle into each other and tiny bonds form. Breaking them takes more force than keeping them broken; once the block is sliding, it rides over the high points before new contacts can fully form. So \(\mu_s \ge \mu_k\), and your fourth sentence is checking exactly that.
Why the contact area never appears. Guillaume Amontons wrote this down in 1699, two centuries after Leonardo da Vinci sketched it: friction depends on the load and not on the apparent area of contact. The real contact area, the tips of the bumps that actually touch, is a tiny fraction of the apparent one, and it grows in proportion to the load. Double the squeeze, double the real contact, double the friction. Area drops out.