Measurement of g by free fall
Determine the acceleration due to gravity g using a free-fall timing method.
Apparatus
- Electromagnet connected to a power supply with a switch
- Steel ball bearing
- Electronic timer (millisecond resolution) triggered by the release circuit
- Trap door or pressure pad to stop the timer on impact
- Metre rule
Safety
- Ensure the ball is caught or lands on a padded surface; a steel ball falling >1 m can cause injury.
- Secure all equipment to prevent the stand tipping when the ball is released.
Method
- Set up the electromagnet at a measured height h above the trap door. Confirm the timer starts when the magnet releases the ball and stops when the ball hits the trap door.
- Set the drop height h. Cut the current to release the ball; record fall time t.
- Repeat each height three times and take the mean t for that h.
- Vary h over at least six values from ~0.2 m to ~1.0 m. Record h and mean t.
- Plot h against $t^2$: straight line through origin with gradient g/2, giving $g = 2 \times \text{gradient}$.
Key Variables
Independent
Drop height h
Dependent
Fall time t
Controlled
Same ball each drop; Same release mechanism; Timer trigger method unchanged
Analysis and Results
- Starting from rest: $h = \frac{1}{2}gt^2$, so $t^2 = \frac{2}{g}h$.
- Plot h against $t^2$: gradient $= g/2$, so $g = 2 \times \text{gradient}$.
- The line should pass through the origin; a non-zero intercept indicates a systematic timing error.
- Compare obtained g with accepted value 9.81 m/s$^2$ and comment on sources of discrepancy.
Common Errors
- Timing starting before the ball is fully released (electromagnet retains residual magnetism), giving t values that are too large.
- Measuring h to the top of the ball rather than to its centre of mass.
- Plotting h against t (a curve) instead of h against $t^2$ (a straight line).
- Not repeating and averaging t at each height to reduce random error.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A student plots h against $t^2$ and obtains a straight line with gradient 4.82 m s$^{-2}$. Calculate the value of g obtained and suggest why it differs from 9.81 m s$^{-2}$.
Q24 marks
Describe how systematic errors in this experiment could be reduced.
Q32 marks
The graph of h against $t^2$ does not pass through the origin. Explain what this suggests.