AP Physics 1 · Free-response skill

Design and analyze a friction experiment

The move. Plan and analyze a force experiment: link what is measured to the quantity wanted, calculate it from data, interpret a trend, and say how a procedure error would bias the result.

How to do it

  1. Before any numbers, be clear about the relation that links what you measure to what you want, and use it the same way for every trial.
  2. When several trials give nearly the same value, you may average them; say why that is reasonable.
  3. To judge whether a result depends on a variable, compare how much the result changes with how much the variable changes, and check whether the result rises or falls steadily.
  4. For a procedure error, decide which way it pushes the measured value, too large or too small, and then follow that through to the calculated result.
  5. To get a value from a graph, choose axes so the slope is the quantity you want: if the theory says y = (constant)x, plot y on the vertical axis and x on the horizontal axis.

Practice prompt Try it

A team wants to find the coefficient of static friction between a rubber-soled shoe and a wooden board. The board is 1.20 m long and hinged at one end, so its other end can be raised. The empty shoe has a mass of 0.40 kg, and slotted masses can be packed inside it. For each load, the team sets the shoe on the board, slowly raises the free end, and records the height h of the raised end, measured straight up from the level of the hinge, at the moment the shoe starts to slide. The 1.20 m board is the long side of the right triangle formed by the board, the height h and the level line from the hinge. At the moment the shoe starts to slide, the coefficient of static friction equals tan⁡θ\tan\theta, where θ is the board’s angle above the horizontal.

Height of the raised end when the shoe starts to slide

Mass added to the shoe (kg)h (m)
00.62
0.500.61
1.000.63
1.500.62

Use the setup and the data to respond to each part.

  1. Use the data to calculate the coefficient of static friction. The four heights agree closely, so you may average them or use any one trial.
  2. Does the coefficient change as the load in the shoe changes? Cite the measurements that tell you.
  3. One student reads the height a moment after the shoe has started to slide, while the board is still rising. Would her h values be too large or too small, and how would that change the coefficient she calculates?
  4. The team plots the friction force at slipping, Mgsin⁡θMg\sin\theta, on the vertical axis, where M is the total mass of the shoe and its load. What quantity should go on the horizontal axis so that the slope of the line is the coefficient of static friction?

Write each part, then check yourself against the checklist. Nothing you type here is saved or graded.

Check yourself and see a model answer

Checklist

Our own checklist of what a full answer does, one line per point. Tick each one your response earns.

0 of 6 points

Model answer, annotated

(a) The four heights agree closely, so average them: 0.62 + 0.61 + 0.63 + 0.62/4 = 0.62 m. Then sin⁡θ=0.62/1.20=0.517\sin\theta = 0.62/1.20 = 0.517, so θ = 31.1° and μs=tan⁡31.1∘≈0.60\mu_s = \tan 31.1^\circ \approx 0.60.

  • Point 1 Averages the trials, finds the angle from the board length, then takes the tangent.

(b) The coefficient does not depend on the load. As the added mass goes from 0 to 1.50 kg, so the total mass grows about fivefold from 0.40 kg to 1.90 kg, h stays between 0.61 m and 0.63 m, within about 0.01 m of its mean of 0.62 m, with no trend, so the slipping angle, and with it the coefficient, stays the same.

  • Point 2 States the conclusion plainly: no dependence on the load.
  • Point 3 Quotes the measured heights, 0.61 to 0.63 m, to back it up.

(c) Her h values would be too large, because the board keeps rising between the moment the shoe starts to slide and the moment she reads the height. A larger h gives a larger angle, so the coefficient she calculates would be too large.

  • Point 4 Says the heights come out too large and why.
  • Point 5 Follows the error through: a larger angle means a larger tangent, an overestimate.

(d) Put the normal force, Mgcos⁡θMg\cos\theta, on the horizontal axis, with M equal to 0.40 kg plus the added mass and θ found from sin⁡θ=h/1.20\sin\theta = h/1.20. At slipping the friction force equals μs\mu_s times the normal force, so the points fall on a line through the origin whose slope is μs\mu_s.

  • Point 6 Names the normal force for the horizontal axis, so the slope is the coefficient.