Quick answer: Momentum is the product of mass and velocity, p = m v, measured in kg m/s. This Physics 11-12 lab on impulse momentum gives the aim, the equipment, the safety points, a step-by-step method, sample results and 8 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How large is the impulse when a tennis ball bounces, and how big is the average force? In this lab you film a ball bouncing from several heights, find its speeds before and after, and use the contact time to estimate the force.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB A.2
Aim
To measure the change in momentum of a tennis ball bouncing from a hard floor and to estimate the average contact force and impulse for different drop heights.
Equipment
- Tennis ball (mass 0.058 kg) and a balance
- Metre rule fixed vertically against a wall
- Phone that records slow-motion video at 960 frames per second
- Hard floor or tile, and a few books to prop up the phone
Safety
Clear the floor of obstacles and keep your head away from the path of the ball. Do not stand on a chair to release the ball from above 1.5 m; hold the ball at arm height next to the rule instead.
Method
- Measure the mass of the ball. Prop the phone on the books so its lens is level with the floor, about 1 m from the rule.
- Hold the ball so that its bottom edge is at 0.50 m on the rule and start the video.
- Release the ball without pushing it. Play the video frame by frame to read the highest rebound height and to count the frames from first touching the floor to leaving it.
- Repeat from 1.00 m, 1.50 m and 2.00 m.
- Calculate the speed just before and after the bounce from √(2 g h).
Results
Sample results recorded by Mei and Aarav (m = 0.058 kg, 960 frames per second, g = 9.81 N/kg). Take upward as positive when you work out Δp.
| drop height (m) | rebound height (m) | frames in contact | contact time (ms) | speed before (m/s) | speed after (m/s) | Δp (kg m/s) | average F (N) |
|---|---|---|---|---|---|---|---|
| 0.50 | 0.30 | 5 | 5.21 | 3.13 | 2.43 | 0.322 | 62 |
| 1.00 | 0.60 | 5 | 5.21 | 4.43 | 3.43 | 0.456 | 88 |
| 1.50 | 0.88 | 6 | 6.25 | 5.42 | 4.16 | 0.556 | 89 |
| 2.00 | 1.18 | 6 | 6.25 | 6.26 | 4.81 | 0.642 | 103 |
Analysis questions
Question 1 Speed before and after
Show how the speeds in the first row were obtained, and state why the ball’s speed after the bounce is smaller.Question 2 Change in momentum
Calculate Δp for the 1.00 m drop. Explain why the speeds are added.Question 3 Average force
Calculate the contact time and the average force for the 1.50 m drop.Question 4 Graph of Δp
Describe a graph of Δp against √h (drop height) and explain the shape.Question 5 Force and weight
Compare the average force for the 2.00 m drop with the weight of the ball.Question 6 Uncertainty in contact time
The contact time is read to ±1 frame. Calculate the percentage uncertainty for the 0.50 m drop and its effect on the force.Question 7 Coefficient of restitution
Calculate e = speed after ÷ speed before for each drop and comment on the trend.Question 8 Improvement
Suggest two improvements to the method.
