Required Practicals / OCR A / Practical 1
1 AS PAG 1

Determination of g by free fall (PAG 1)

Measure the acceleration due to gravity using a free-fall method with light gates or a ticker-tape timer.

Apparatus

  • Light gates (two) and datalogger, or ticker-tape timer (50 Hz) and power supply
  • Steel ball or card of known width
  • Metre rule and clamp stand
  • Ruler for measuring drop height

Safety

  • Ensure the dropped object lands safely and cannot injure anyone.
  • Secure clamp stands so they cannot topple.

Method

  1. Light-gate method: position two light gates a measured distance h apart. Drop the ball through both. Datalogger records velocities $v_1$ (upper gate) and $v_2$ (lower gate) and time t between them.
  2. Calculate $g = (v_2^2 - v_1^2)/(2h)$ or use $g = 2h/t^2$ if releasing from rest above the upper gate.
  3. Repeat for at least six heights. Plot appropriate graph (see analysis) to find g.
  4. Ticker-tape method: attach a length of ticker tape to a falling mass. Analyse the tape to find acceleration from the increasing spacing of dots.
  5. Measure distances between successive groups of dots (e.g. every 5 intervals); use $s = ut + \frac{1}{2}at^2$ to find g.

Key Variables

Independent Drop height h
Dependent Fall time t (or velocity v)
Controlled Same ball each drop; Same release mechanism

Analysis and Results

  • Light-gate (from rest): $v^2 = 2gh$. Plot $v^2$ vs h: gradient $= 2g$.
  • Ticker-tape: plot velocity v against time t for uniformly accelerating motion; gradient $= g$.
  • Compare with accepted value $g = 9.81$ m s$^{-2}$; comment on sources of discrepancy.

Common Errors

  • Air resistance on the falling object, which is more significant for light or large-surface-area objects.
  • Tape friction in the ticker-tape method adds a retarding force, reducing the measured acceleration.
  • Measuring h between the wrong reference points on the light gates.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 3 marks

A student uses two light gates 0.60 m apart. A ball falls from rest above the upper gate and passes the lower gate at $3.43$ m s$^{-1}$. Calculate g.

Q2 2 marks

Explain one advantage of using light gates over a ticker-tape timer for this experiment.