Quick answer: Newton's law of gravitation says two masses attract with force F = G m₁m₂/r². This Physics 11-12 lab on gravitational field 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 strong is the Earth’s gravitational field in your classroom? In this lab you film a ball falling from several heights, count frames to find the fall times and calculate g. You then use g and the Earth’s radius to estimate the mass of the Earth.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.1
Aim
To measure the gravitational field strength g near the Earth’s surface from the fall times of a ball, and to use your value to estimate the mass of the Earth.
Equipment
- Steel ball (about 20 g) or a marble
- Metre rule and masking tape for marks at every 0.40 m up a wall
- Phone that records slow motion at 240 frames per second
- Soft mat or folded towel on the floor
- Books to prop up the phone
Safety
Stand on a stable step only if the height is below 1.0 m; otherwise ask a partner to release from a higher mark with a long-handled tool. Keep feet away from the landing zone and pick the ball up straight after each drop so nobody trips on it.
Method
- Fix the tape marks on the wall from the floor up at 0.40, 0.80, 1.20, 1.60 and 2.00 m. Place the mat at the foot of the wall.
- Put the phone on the books 2 m away, level with the middle mark, and start the slow-motion video.
- Release the ball from the 0.40 m mark so that it drops straight down without being pushed.
- Play the video frame by frame. Count the frames from the frame when the ball first moves to the frame when it first touches the mat.
- Repeat from each height. Divide the number of frames by 240 to obtain the time.
Results
Sample results from Emma’s physics club in Leeds. The time is t = frames ÷ 240.
| height h (m) | frames | time t (s) | t² (s²) | g = 2h ÷ t² (m/s²) |
|---|---|---|---|---|
| 0.40 | 68 | 0.2833 | 0.0803 | 9.97 |
| 0.80 | 97 | 0.4042 | 0.1634 | 9.79 |
| 1.20 | 118 | 0.4917 | 0.2417 | 9.93 |
| 1.60 | 138 | 0.5750 | 0.3306 | 9.68 |
| 2.00 | 153 | 0.6375 | 0.4064 | 9.84 |
Analysis questions
Question 1 Time from frames
Calculate the time for the 1.20 m drop and explain why the ball can be treated as starting from rest.Question 2 Value of g
Calculate g for the 0.40 m drop and check the entry in the table.Question 3 Mean value
Calculate the mean of the five values of g and its percentage difference from the accepted 9.81 N/kg.Question 4 Graph
Describe a graph of h against t² and say what its gradient gives.Question 5 Field strength and the Earth
Use g = 9.81 N/kg, R = 6.37 × 10⁶ m and G = 6.67 × 10⁻¹¹ to estimate the mass of the Earth.Question 6 Uncertainty in frames
The frame count is uncertain by ±1 frame. Calculate the percentage uncertainty in g for the 0.40 m drop.Question 7 Air resistance
Explain the effect of air resistance on the values of g and why it is small here.Question 8 Improvements
Suggest two improvements that would make the result more accurate.
