The method and the results are on the torque lab. Do the analysis yourself first, then check the answers below.
Quick answer: Torque is the turning effect of a force, τ = r F sin θ, measured in newton metres. These answers go with the AP Physics 1 lab on torque: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The answers use the sample data. The torques should match within a few per cent, the graph should be a straight line through the origin with gradient close to the ratio of the masses, and the main errors come from reading the balance point and from friction at the pivot.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 5
Left = 0.200 × 9.81 × r; right = 0.100 × 9.81 × d. Values in N m: r = 0.050: left 0.098, right 0.099; r = 0.100: left 0.196, right 0.195; r = 0.150: left 0.294, right 0.299; r = 0.200: left 0.392, right 0.390; r = 0.250: left 0.491, right 0.493. Left and right agree closely.
Question 2 Percentage difference
First trial: (0.0991 − 0.0981) ÷ 0.0981 = 1.0 %. Last trial: (0.4934 − 0.4905) ÷ 0.4905 = 0.6 %. Both are within the reading uncertainty, so the rule is in equilibrium within error.
Question 3 Graph of d against r
The graph is a straight line through the origin. Gradient = (0.503 − 0.101) ÷ (0.250 − 0.050) = 0.402 ÷ 0.200 = 2.01. The mass ratio is 0.200 ÷ 0.100 = 2.0, so they agree.
Question 4 Reading uncertainty
Percentage uncertainty in r = 0.002 ÷ 0.050 × 100 = 4 %. The masses are known well, so the torque of the load has the same 4 % uncertainty.
Question 5 Why the pivot is at the centre
The weight of a uniform rule acts at its centre. With the pivot there, the rule’s weight has a zero lever arm and no torque, so only the two hung masses matter. Otherwise the rule’s own torque must be included.
Question 6 Predict a new balance
From the gradient 2.0: d = 2.0 × 0.180 = 0.36 m. Check with torques: 0.200 × 0.180 = 0.100 × d gives d = 0.36 m.
Question 7 Improving the method
Use a sharper pivot to cut friction, and read the positions from the centre of each thread loop. Repeat each balance several times and average, and use a larger range of r to reduce the effect of reading error.
