Required Practicals / AQA / Practical 3
3 AS 3.4.1.1

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

  1. 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.
  2. Set the drop height h. Cut the current to release the ball; record fall time t.
  3. Repeat each height three times and take the mean t for that h.
  4. Vary h over at least six values from ~0.2 m to ~1.0 m. Record h and mean t.
  5. 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.

Q1 3 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$^{-2}$.

Q2 4 marks

Describe how systematic errors in this experiment could be reduced.

Q3 2 marks

The graph of h against $t^2$ does not pass through the origin. Explain what this suggests.