Measuring the Young Modulus | CAIE 9702 Paper 1 Notes

Paper 1

Physics9702

Measuring the Young Modulus

The experiment must provide four quantities: force, original length, cross-sectional area and extension.

A long, thin wire gives a larger measurable extension for a given load.

A hand-drawn long horizontal wire is clamped at one end, passes a pointer beside a vertical scale, continues over a pulley and supports a stack of masses.

fixed endlength Lpointer reads xforce F from load

Measure the wire's original length L, its extension x for each load, and its diameter d with a micrometer. The diameter gives cross-sectional area A = πd²/4.

Measure each quantity for a reason

E=\frac{FL}{Ax}

Symbols

$F$ = force produced by the added load (N)
$L$ = original test length of the wire (m)
$A$ = cross-sectional area (m²)
$x$ = extension caused by the load (m)

Measure the original test length $L$ with a metre rule.
Measure the wire diameter $d$ with a micrometer at several positions and in two perpendicular directions. Use the mean to find $A=\pi d^2/4$ .
Record the pointer reading before adding load. Add known masses in small steps; each total mass gives $F=mg$ .
Record the new pointer reading after each load settles. Subtract the initial reading to obtain extension $x$ .
Plot force against extension. Use the gradient of the straight region as $k=F/x$ , then calculate $E=kL/A$ .

Do not use one force-extension reading when several are available. A best-fit gradient uses all the data in the proportional region and is less affected by one uncertain reading.

Control the experiment and reduce uncertainty

Keep the same wire and temperature throughout. Add loads gently and remain below the limit of proportionality.
The extension is small, so use a pointer beside a fine scale or a travelling microscope. Read at eye level to avoid parallax.
Diameter uncertainty is important because area depends on $d^2$ . Repeat diameter measurements and use their mean.
A long, thin wire increases extension, which reduces the percentage uncertainty in $x$ . It must still be strong enough not to exceed its elastic range.

Your turnCAIE-style experiment question

Describe how to determine the Young modulus of a metal wire. State the measurements, graph and two ways to reduce uncertainty. [7]

Show worked answer

Measure $L$ with a metre rule.
Measure $d$ repeatedly with a micrometer and calculate $A=\pi d^2/4$ .
Add known masses gradually, calculate $F=mg$ , and record the extension $x$ from the change in pointer reading.
Plot $F$ against $x$ , find the best-fit gradient $k$ , and use $E=kL/A$ .
Use a long wire and a fine extension scale; repeat diameter readings in different positions and directions.