The method and the results are on the work energy theorem lab. Do the analysis yourself first, then check the answers below.
Quick answer: Work done by a variable force is the integral W = ∫F dx, the area under the force–position graph. These answers go with the AP Physics C lab on work energy theorem: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Here are the work energy theorem lab answers for AP Physics C: graph, calculations, uncertainties and conclusion. First do the lab yourself, then compare, and go back to the lesson if needed.
Model answers based on the sample data. The gradient should come out near 25 N/m and the measured drop extension a few per cent below the prediction. If your own spring differs, check that your units are in metres and newtons before comparing.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 3
Work energy theorem lab answers: the analysis explained
Question 1 Spring constant
Points lie on a straight line through the origin. Gradient = 2.45/0.098 = 25 N/m, and Hooke’s law holds over this range.
Question 2 Area under the graph
Triangle area = ½ × 2.45 × 0.098 = 0.120 J, and ½kx² = ½ × 25 × (0.098)² = 0.120 J, so they agree: 0.12 J.
Question 3 Predicted drop
mgx = ½kx² gives x = 2mg/k = 2 × 0.100 × 9.81/25 = 0.0785 m, so the predicted extension is 7.8 cm.
Question 4 Measured against predicted
Mean = (7.7 + 7.5 + 7.6)/3 = 7.6 cm. Difference = (7.85 − 7.6)/7.85 = 3.2 % lower than predicted.
Question 5 Energy accounting
Gravitational energy lost = mgx = 0.981 × 0.076 = 0.0746 J. Elastic energy = ½ × 25 × (0.076)² = 0.0722 J. Missing energy = 0.0024 J, about 3 % of the loss.
Question 6 Uncertainty
0.001/0.020 = 5 %, so the 50 g point carries 5 % uncertainty. Larger loads have smaller percentage uncertainty, so the best-fit gradient is dominated by the larger loads.
Question 7 Evaluation
Air resistance and internal friction in the spring remove a little energy, and the spring’s own mass was ignored. Using a higher frame-rate video reduces the reading error: smaller than predicted because of energy losses.
