What graph is plotted to obtain g from a series of heights and times, and what is its gradient?

Height is plotted against t², giving a straight line through the origin whose gradient is g/2.

Why is plotting a graph better than calculating g from a single pair of readings?

The graph uses all the data, reveals anomalous results and averages out the random errors in the timing.

State one systematic error in the trapdoor method and describe its effect on the result.

The electromagnet may hold the ball briefly after the current is switched off, so the timer starts before the ball begins to fall; the measured time is too long and the value of g comes out too small.

OCR A-Level Physics B H557

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Space, Time and Motion

Determining the acceleration of free fall

3 things to know
Components 01, 02 and 03

Overview

Recall questions on the trapdoor and electromagnet method, working from height and time, what to plot and its gradient, a systematic timing error, light gates, and why mass does not matter.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How does the trapdoor and electromagnet method measure the acceleration of free fall?

Key term

How is g calculated from the height fallen and the time taken from rest?

Numbers

A ball falls 1.5 m from rest in 0.55 s. Calculate the acceleration of free fall.

Questions from this subtopic

Each one with the model answer underneath.

1
How does the trapdoor and electromagnet method measure the acceleration of free fall?
Model answer
A steel ball is held by an electromagnet above a trapdoor; switching the magnet off starts an electronic timer, and the ball striking and opening the trapdoor stops it, giving the time to fall a measured height.
2
How is g calculated from the height fallen and the time taken from rest?
Model answer
Since s = ½gt², the value of g is twice the height divided by the square of the time.
3
A ball falls 1.5 m from rest in 0.55 s. Calculate the acceleration of free fall.
Model answer
g = 2s/t² = 3.0/0.3025 = 9.9 m s⁻².
4
What graph is plotted to obtain g from a series of heights and times, and what is its gradient?
Model answer
Height is plotted against t², giving a straight line through the origin whose gradient is g/2.
5
Why is plotting a graph better than calculating g from a single pair of readings?
Model answer
The graph uses all the data, reveals anomalous results and averages out the random errors in the timing.
6
State one systematic error in the trapdoor method and describe its effect on the result.
Model answer
The electromagnet may hold the ball briefly after the current is switched off, so the timer starts before the ball begins to fall; the measured time is too long and the value of g comes out too small.

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