Determination of g by free fall (CP1)
Determine the acceleration due to gravity by measuring the time for a falling object to travel a known distance.
Apparatus
- Metre rule or measuring tape
- Light gate and datalogger (or electronic timer with trap door)
- Steel ball bearing or opaque card
- Clamp stand
- Ruler to set drop height
Safety
- Ensure the ball lands safely and cannot strike anyone below the apparatus.
- Secure all clamp stands to prevent them toppling during the experiment.
Method
- Using light gates: hold a card of known width above the upper gate. Release from rest; the datalogger records velocity v at the lower gate after falling height h.
- Measure h between the two light gates. Calculate g using $v^2 = 2gh$, giving $g = v^2/(2h)$.
- Repeat for at least six heights by raising the upper gate. Plot $v^2$ against h.
- Alternatively, use the free-fall timer: release a ball from rest and record fall time t for height h. Use $h = \frac{1}{2}gt^2$, so $g = 2h/t^2$.
- Plot h against $t^2$; gradient $= g/2$.
Key Variables
Independent
Drop height h
Dependent
Velocity v (or fall time t)
Controlled
Same ball/card each drop; Same light gate separation (for velocity method)
Analysis and Results
- Light-gate method: $v^2 = 2gh$. Plot $v^2$ vs h: straight line through origin, gradient $= 2g$.
- Free-fall timer: $h = \frac{1}{2}gt^2$. Plot h vs $t^2$: straight line through origin, gradient $= g/2$.
- A non-zero intercept on the time-based graph indicates a systematic timing error.
Common Errors
- Not accounting for the width of the card (use centre-to-centre timing rather than leading edge).
- Air resistance becoming significant for light objects; use a dense metal ball.
- 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 0.80 m apart. A ball passes the lower gate with velocity 3.92 m s$^{-1}$ after falling from rest. Calculate g from these data.
Q23 marks
Explain why plotting $v^2$ against h is preferable to plotting v against h when analysing this experiment.
Q32 marks
State one source of systematic error in this experiment and explain how it would affect the calculated value of g.