Determining g

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.12Sections 2.12

Goal: Describe a free-fall experiment to find g, and get g from a graph of s against t².

01The big picture

Drop a small steel ball from rest from an electromagnet. Switching off the magnet starts a timer; the ball hitting a trapdoor stops it. Measure the height $s$ with a metre rule and repeat each height, averaging $t$ .

From rest, $s = \tfrac12 g t^2$ , so a graph of $s$ against $t^2$ is a straight line through the origin with gradient $g/2$ . Light gates with a falling card, or video, can also be used.

Free fall [paraphrase]: Falling with only the weight acting: acceleration $g$ , no air resistance.

Fig. 1 · s against t²

A straight line through the origin: gradient

= g/2

02Key equations

From rest

s = \tfrac{1}{2}gt^{2}

One drop

g = \frac{2s}{t^{2}}

From the graph

g = 2 \times \text{gradient of } s\text{–}t^{2}

Symbols and units

$s$ height fallen $\mathrm{m}$
$t$ time to fall $\mathrm{s}$
$g$ acceleration of free fall $\mathrm{m\,s^{-2}}$

03Sample problems with solutions

Sample 1 · One drop
A ball falls 1.20 m from rest in a mean time of 0.495 s. Calculate $g$ .

Rearrange $s = \tfrac12 gt^2$ :
$g = \frac{2s}{t^{2}} = \frac{2 \times 1.20}{0.495^{2}} = 9.79\ \mathrm{m\,s^{-2}}$

Answer:

g = 9.79\ \mathrm{m\,s^{-2}}

(3 s.f.)

Unit check:

\frac{\mathrm{m}}{\mathrm{s^{2}}} = \mathrm{m\,s^{-2}}\ \checkmark

04Practice problems

P1
The gradient of a graph of $s$ against $t^2$ is 4.95 m s⁻². Find $g$ .
Final answer
9.90 m s⁻²
Answer: 9.90 m s⁻²
P2
A ball falls 0.80 m from rest in 0.40 s. Find $g$ .
Final answer
10 m s⁻²
Answer: 10 m s⁻²
P3
Why use a small, dense ball?
Final answer
Air resistance is negligible compared with its weight
Answer: Air resistance is negligible compared with its weight
P4
Why repeat each height and average the times?
Final answer
To reduce the effect of random errors
Answer: To reduce the effect of random errors

05Other useful information

Common mistakes

✗ Wrong: Plot $s$ against $t$ and take the gradient as $g$ .
✓ Right: That curves; plot $s$ against $t^2$ and double the gradient.

Exam tips

Measure $s$ from the bottom of the ball to the trapdoor.

What the syllabus asks

9702 topic 2: describe an experiment to find g using a falling object. Coursebook 2.12.

Explore: Practice questions for this lesson