Physics · Lesson 30

Practical 3: pendulum, loaded spring and moments

WAECNECO

What the syllabus asks

WAEC: simple pendulum (determination of g), Hooke’s law and the spiral spring (spring constant; oscillating spring), principle of moments with a metre rule (centre of gravity, mass of the rule). Theory links: p-units on SHM, elasticity and equilibrium.

NECO: simple pendulum (determination of g), Hooke’s law and the spiral spring (spring constant; oscillating spring), principle of moments with a metre rule (centre of gravity, mass of the rule). Theory links: p-units on SHM, elasticity and equilibrium.

What you will learn

Set up and carry out the simple pendulum experiment and deduce g.
Carry out the loaded-spring experiment and deduce the spring constant.
Apply the principle of moments to a metre rule and deduce its mass.
Linearise the formulae for each experiment.
Calculate slopes and intercepts with correct units.
State precautions and sources of error for each experiment.
Answer the short theory items that follow each experiment.
Read stopwatches and scales in alternative-to-practical diagrams.

Key points

Pendulum: plot T² against l; g = 4π²/slope.
Sample result: slope 4.03 s² m⁻¹, g = 9.80 m s⁻².
Spring: plot e against m; k = g/slope in SI units.
Sample result: slope 0.390 m kg⁻¹, k = 25.1 N m⁻¹.
Moments: find G first; m x = M y about the knife edge.
1/x against m: M = c/s; sample M = 109 g.
Check every row against the physics law.
Precautions: small amplitude; elastic limit; sharp knife edge; parallax.
Part (b): define SHM, Hooke’s law, principle of moments.
Do sense checks on every final answer.

Start here: Concept summary: the three mechanics experiments

Three mechanics experiments dominate the WAEC and NECO physics practical: the simple pendulum, the loaded spiral spring and the principle of moments with a metre rule. They may appear in many disguises: a pendulum whose length is varied, or whose bob is changed; a spring that is loaded and measured at rest, or loaded and set oscillating; a metre rule balanced on a knife edge with one mass, two masses, or a mass immersed in water. Behind every disguise is the same physics and the same skills from units pp1 and pp2.

In this unit each experiment is treated in the same five steps: theory (the formula and how to linearise it), procedure (what you actually do at the bench), sample readings (a complete, realistic table produced and checked by computer), graph and deduction (slope, intercept and the constant), and precautions, errors and part (b) items.

The sample readings are realistic: they contain the small scatter you would get with real apparatus in a Nigerian school laboratory, for example a 50 g slotted mass that is really 50.3 g, or a balance point judged to within 0.1 cm. Do not expect your own readings to match them exactly. The examiner’s scheme sets a tolerance around the expected values, and honest readings within that tolerance score full marks.

One word on g. In calculations from your experiment you will deduce g yourself (about 9.8 m s⁻²). When a question instructs you to use g = 10 m s⁻² (as many WAEC questions do), use exactly that value in that question, and use 9.8 m s⁻² only when told to or when no value is given. In this unit the spring calculation uses g = 9.8 m s⁻²; using 10 m s⁻² would give k about 2 % larger, and an examiner would accept either if the question did not specify.

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Practice questions

1. A pendulum of length 0.800 m makes 20 oscillations in 35.9 s. Find T, T² and g.

Show worked answer

T = 1.795 s ≈ 1.80 s; T² = 3.22 s²; g = 4π² × 0.800/3.222 = 9.80 m s⁻².

2. A graph of T² against l has slope 4.10 s² m⁻¹. Find g.

Show worked answer

g = 39.48/4.10 = 9.63 m s⁻².

3. State three precautions for the simple pendulum experiment.

Show worked answer

Small amplitude (under 10°); time 20 oscillations from a fiducial mark at the centre; rigid split-cork clamp; swing in one vertical plane.

4. Unloaded pointer reading 12.5 cm; with 150 g it reads 18.4 cm. Find the extension and k (g = 9.8 m s⁻²).

Show worked answer

e = 5.9 cm = 0.059 m; k = 0.150 × 9.8/0.059 = 24.9 N m⁻¹.

5. Why is the spring unloaded at the end and the pointer read again?

Show worked answer

To check it returns to its original reading, showing the elastic limit was not exceeded.

Key words

Simple pendulum: Small dense bob on a light inextensible string.
Period: Time for one complete oscillation.
Amplitude: Maximum displacement from the rest position.
SHM: Acceleration proportional to displacement and directed to a fixed point.
Spring constant: Force per unit extension, in N m⁻¹.
Elastic limit: Greatest load from which a body fully recovers.
Limit of proportionality: End of the straight-line part of a force–extension graph.
Moment: Force × perpendicular distance from the pivot.
Centre of gravity: Point where the whole weight appears to act.
Knife edge: Sharp pivot giving a definite point of support.
Fiducial mark: Reference mark for timing.
Effective mass: Part of a spring’s mass that moves with the load.

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