The method and the results are on the impulse momentum lab. Do the analysis yourself first, then check the answers below.
Quick answer: Momentum is the product of mass and velocity, p = m v, measured in kg m/s. These answers go with the Physics 11-12 lab on impulse momentum: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
The answers use the sample table, so your own readings will differ a little. Check the signs of the velocities, the units of time (milliseconds against seconds) and the uncertainty from counting frames.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB A.2
Question 1 Speed before and after
Speed before = √(2 g h) = √(2 × 9.81 × 0.50) = 3.13 m/s; speed after = √(2 × 9.81 × 0.30) = 2.43 m/s. Kinetic energy is lost as thermal energy and sound in the bounce, so the ball rebounds more slowly.3.13 m/s down, 2.43 m/s up.
Question 2 Change in momentum
Δp = m (v + u) = 0.058 × (3.43 + 4.43) = 0.456 kg m/s. The velocity reverses, so with up as positive the change is +v − (−u) = v + u.Δp = 0.456 kg m/s upwards.
Question 3 Average force
t = 6 frames ÷ 960 = 6.25 ms. F = Δp ÷ Δt = 0.556 ÷ 0.00625 = 89 N.F average = 89 N.
Question 4 Graph of Δp
Δp is proportional to the speed before impact, which is √(2 g h), so Δp against √h is a straight line through the origin. The gradient is m √(2 g) (1 + √(hr ÷ h)), which depends on the rebound fraction.straight line through the origin.
Question 5 Force and weight
Weight = 0.058 × 9.81 = 0.569 N. The average force is 103 N, about 181 times the weight, so during contact the floor force is far larger than the weight.about 181 times the weight.
Question 6 Uncertainty in contact time
One frame is 1.04 ms and the contact is 5 frames, so the uncertainty is 1 ÷ 5 = 20 %. The force is inversely proportional to the time, so the average force has the same percentage uncertainty (about ±20 %).±20 %.
Question 7 Coefficient of restitution
e = √(hr ÷ h): 0.77, 0.77, 0.77, 0.77. The values lie between 0.75 and 0.78, so e is nearly constant and the bounce loses a similar fraction of speed at each height.e ≈ 0.77.
Question 8 Improvement
Film from a greater distance with zoom to reduce parallax in height readings, and measure the contact time with a force sensor or a microphone trace, which is more precise than counting frames. Repeat each drop three times and average the heights.reduce parallax and use a force sensor.
