The method and the results are on the impulse momentum theorem lab. Do the analysis yourself first, then check the answers below.
Quick answer: Linear momentum is the product of mass and velocity, p = mv, a vector in kg m/s. These answers go with the AP Physics 1 lab on impulse momentum theorem: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
The model answers use the sample data above, with the up direction as positive. Your numbers will differ with your ball and surfaces, but the ranking of forces and the discussion of frame-count uncertainty should be similar.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 4
Question 1 Speed before impact
v = √(2gh) = √(2 × 9.81 × 1.50) = √29.43 = 5.42 m/s downward.
Question 2 Speed after impact
v = √(2gh₂). Tile: √(2 × 9.81 × 0.83) = 4.04 m/s. Carpet: √(2 × 9.81 × 0.62) = 3.49 m/s. Foam: √(2 × 9.81 × 0.35) = 2.62 m/s, all upward.
Question 3 Impulse on the ball
Take up as positive, so vi = −5.42 m/s. J = m(vf − vi). Tile: 0.057 × (4.04 + 5.42) = 0.539 N s. Carpet: 0.057 × (3.49 + 5.42) = 0.508 N s. Foam: 0.057 × (2.62 + 5.42) = 0.459 N s, all upward.
Question 4 Contact times
Each frame is 1/240 s = 0.00417 s. Tile: 3 frames = 0.0125 s. Carpet: 4 frames = 0.0167 s. Foam: 6 frames = 0.0250 s.
Question 5 Average force
F = J/Δt. Tile: 0.539 ÷ 0.0125 = 43.1 N. Carpet: 0.508 ÷ 0.0167 = 30.5 N. Foam: 0.459 ÷ 0.0250 = 18.3 N. The weight is mg = 0.56 N, only 1 to 3 % of these values, so it is negligible.
Question 6 Trend
From tile to foam the impulse decreases a little (0.539 to 0.459 N s), contact time doubles and the force falls to less than half. The softer surfaces absorb more of the ball’s energy as thermal energy, so the ball rebounds more slowly. A longer contact time at a similar impulse gives a lower average force on softer surfaces.
Question 7 Uncertainty in contact time
±1 frame on 3 frames is 1 ÷ 3 = 33 %. The force is inversely proportional to the time, so the force has about the same percentage uncertainty: 43.1 N ± 14 N. The foam result (±1 on 6 frames, 17 %) is more reliable.
Question 8 Improvements
Use a higher frame rate or a high-speed camera, so that the contact time is counted over more frames. Repeat each drop several times and average the heights and frame counts. Both reduce the uncertainty in the average force.
