Quick answer: Projectile motion is two-dimensional motion under gravity alone. This AP Physics 1 lab on projectile motion gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A steel ball rolls down a ramp and leaves a table horizontally. By measuring where it lands, you find its launch speed and test how that speed depends on the release height. The lab uses only projectile equations, a metre rule and carbon paper.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 1
Aim
To find how the launch speed of a rolling ball depends on its release height, using the range of a horizontal projectile.
Equipment
- steel ball (about 2 cm diameter)
- grooved ramp and clamp stand
- bench or table, height measured with a metre rule
- carbon paper and white paper
- plumb line, masking tape, metre rule
Safety
Stop the ball with a tray or a box so it does not roll across the floor, and clear the landing area of bags so nobody slips on a loose ball.
Method
- Fix the ramp so the end is level with the table top and the ball leaves horizontally.
- Use the plumb line to mark on the floor the point directly below the table edge, and measure the table height H.
- Tape the white paper to the floor 0.4 m from the mark and cover the expected landing area with carbon paper.
- Release the ball from a height h = 0.10 m above the table top, measured to the ball centre, and repeat five times.
- Measure the range x from the plumb mark to the centre of the group of marks.
- Repeat for h = 0.15, 0.20, 0.25 and 0.30 m.
Results
The table height was H = 0.90 m. Sample averages of five trials:
| h (m) | x (m) | x² (m²) |
|---|---|---|
| 0.10 | 0.49 | 0.240 |
| 0.15 | 0.60 | 0.360 |
| 0.20 | 0.69 | 0.476 |
| 0.25 | 0.77 | 0.593 |
| 0.30 | 0.84 | 0.706 |
Analysis questions
Question 1 Fall time
Calculate the time the ball takes to fall from the table edge to the floor.Question 2 Launch speed
Calculate the launch speed of the ball for h = 0.20 m.Question 3 Why x²
Show that x² = (v²) × (2H ÷ g) and explain why x² against h should be a straight line through the origin.Question 4 Gradient
Calculate the gradient of the x² against h graph using the first and last data points.Question 5 Energy check
Use the gradient to find v² ÷ h, then compare with the value 14.0 m/s² expected for a solid ball rolling without slipping (v² = 10gh ÷ 7).Question 6 Uncertainty
Estimate the percentage uncertainty in x if the five marks for h = 0.20 m spread over 0.67 to 0.71 m.Question 7 Improvement
Suggest two improvements that would make the experiment more accurate.
