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
- 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.
- Calculate $g = (v_2^2 - v_1^2)/(2h)$ or use $g = 2h/t^2$ if releasing from rest above the upper gate.
- Repeat for at least six heights. Plot appropriate graph (see analysis) to find g.
- 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.
- 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.
Q13 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.
Q22 marks
Explain one advantage of using light gates over a ticker-tape timer for this experiment.