RP3, RP4Required Practicals and Data AnalysisCore

Required Practicals 3–4: Free Fall and Young Modulus

Good mechanical measurements distinguish the quantity you want from offsets in the apparatus. Timing delays affect free fall; support movement and wire diameter affect Young-modulus measurements.

40 min 8.2–8.3 Required Practicals and Data Analysis

What you'll be able to do

Choose a free-fall method and determine g from a gradient
Calculate Young modulus from force–extension data
Explain zero errors, controls and uncertainty contributions

RP3: determine g by free fall

Release a ball from rest and measure the time to fall through known vertical heights using electronic timing with a release switch and trapdoor or appropriate light-gate setup. Measure height consistently between the positions used by the timer. A stopwatch is poor for a short fall because reaction time is a large fraction of the interval.

For a release-from-rest height–time method, plot h against t²: gradient is g/2. Repeat each height and cover a substantial height range. A non-zero release speed, trigger delay or wrong height reference can bias the result. A light gate measuring speed from interrupt time uses v≈flag length/time only when speed does not change too much during interruption.

h=\tfrac12gt^2

This model assumes negligible drag and zero initial vertical speed.

RP4: determine Young modulus

Clamp a long thin wire securely, measure its original test length, and add known loads in steps. A small preload removes initial slack; record the extension relative to that state. Measure diameter with a micrometer at several positions and orientations, check zero error and calculate area $A=\pi d^2/4$ .

Measure extension with a suitable fine scale or travelling microscope. A reference wire can help reveal support movement or thermal expansion. Keep loads below the elastic limit, record unloading data to check recovery, secure the stand and use a catch tray for masses. Plot force against extension; gradient is EA/L, so E equals gradient times L/A.

E=\frac{F/A}{\Delta L/L}=\frac{FL}{A\Delta L}

Use the gradient of the straight elastic region rather than one noisy point.

Use uncertainty to choose improvements

For $g=2h/t^2$ , the approximate percentage uncertainty is the percentage in h plus twice that in t under the usual worst-case propagation. A longer timed interval therefore helps if absolute timing uncertainty is fixed.

For Young modulus, diameter contributes twice its percentage uncertainty because area depends on d². Repeated diameter readings help assess variation; a longer wire gives a larger extension at the same stress. Merely repeating a force reading does not fix a micrometer zero error or a slipping clamp.

Work through the reasoning

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.

Example 1A plot of h in metres against t² in s² has gradient 4.88 m s⁻². Find g.

1Gradient

=g/2

g=2(4.88)=9.76

m s⁻².

Answer9.76 m s⁻².

Example 2A wire is 2.0 m long and 0.50 mm in diameter. Its force–extension gradient is 20000 N m⁻¹. Find E.

A=\pi(0.50\times10^{-3})^2/4=1.96\times10^{-7}

m².

E=(20000)(2.0)/(1.96\times10^{-7})

Answer

2.04\times10^{11}

Pa.

Equation recap

h=\tfrac12gt^2

This model assumes negligible drag and zero initial vertical speed.

E=\frac{F/A}{\Delta L/L}=\frac{FL}{A\Delta L}

Use the gradient of the straight elastic region rather than one noisy point.

Common mistakes to avoid

Using gradient g for h versus t².

The gradient is g/2.

Using diameter as the radius in πr².

Divide diameter by two, or use πd²/4.

Key takeaways

Define release conditions and timing references for free fall.
Young modulus comes from stress divided by strain in the elastic region.
Squared dimensions amplify fractional uncertainty.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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