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How are moments, stress, strain, mechanical advantage and gear ratios calculated in product design?

Structural and mechanical calculations: the moment of a force and equilibrium, stress, strain and Young's modulus, mechanical advantage, velocity ratio and gear and pulley ratios, with formulae, units and worked applications to products.

A focused answer to Eduqas A-Level Product Design on structural and mechanical calculations: the moment of a force and equilibrium, stress, strain and Young's modulus, mechanical advantage, velocity ratio and gear and pulley ratios, with formulae, units and worked product examples.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

The key formulae: the moment of a force is $M = F \times d$ (force times perpendicular distance), in newton metres, and a structure is in equilibrium when clockwise moments equal anticlockwise and forces balance. Stress is $\sigma = \frac{F}{A}$ in pascals; strain is $\varepsilon = \frac{\Delta L}{L}$ (no units); Young's modulus (stiffness) is $E = \frac{\sigma}{\varepsilon}$ in pascals. Mechanical advantage is $MA = \frac{\text{load}}{\text{effort}} = \frac{\text{effort arm}}{\text{load arm}}$ (no units). The gear ratio (velocity ratio) is $\frac{\text{driven teeth}}{\text{driver teeth}}$ , and a pulley ratio uses diameters; a reduction (ratio greater than one) slows the output and increases torque. Convert lengths to metres and areas to square metres, keep strain and ratios unitless, and show the working.

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What this dot point is asking
Moments and equilibrium
Stress, strain and Young's modulus
Mechanical advantage
Velocity ratio, gear and pulley ratios

What this dot point is asking

Eduqas wants you to perform the structural and mechanical calculations of the paper: the moment of a force and equilibrium, stress, strain and Young's modulus, mechanical advantage, and velocity ratio and gear and pulley ratios, with the right formulae, units and a product application. A calculator is allowed and working and units carry marks, so this is the quantitative heart of the technical principles, drawn from the structures and mechanisms topics.

Moments and equilibrium

Stress, strain and Young's modulus

Definition

Stress is the internal force per unit area in a loaded material: $\sigma = \frac{F}{A}$ , with force in newtons and area in square metres, giving pascals (Pa) (often megapascals, MPa). Strain is the fractional change in length: $\varepsilon = \frac{\Delta L}{L}$ , the extension divided by the original length, which is dimensionless (no units). Young's modulus measures stiffness, the resistance to elastic deformation: $E = \frac{\sigma}{\varepsilon}$ , also in pascals (often gigapascals, GPa), and it is the gradient of the straight (elastic) part of the stress-strain graph. A high Young's modulus means a stiff material (steel, about $200$ GPa) that barely stretches; a low one means a flexible material. To calculate, convert all lengths to metres and areas to square metres first, find stress and strain, then divide stress by strain for $E$ .

Mechanical advantage

Key fact

Mechanical advantage (MA) is how much a machine multiplies force: $MA = \frac{\text{load}}{\text{effort}}$ , or for a lever, $MA = \frac{\text{effort arm}}{\text{load arm}}$ . It has no units. An MA greater than one means the machine multiplies force (a small effort lifts a large load), as in a second-class lever or a force-multiplying gear train; an MA less than one means it multiplies movement at the cost of force (a third-class lever such as tweezers). From the MA you can find the effort needed: $\text{effort} = \frac{\text{load}}{MA}$ . The law of the lever ( $E \times d_E = L \times d_L$ ) underlies it. Use MA to size a lever or estimate the effort a user must apply, and remember it is a ratio, so do not give it a unit.

Velocity ratio, gear and pulley ratios

The gear ratio, also called the velocity ratio, relates input and output speeds and is the number of teeth on the driven (output) gear divided by the teeth on the driver (input) gear: a 20-tooth driver and a 60-tooth driven gear give $\frac{60}{20} = 3$ , or 3:1. A ratio greater than one is a reduction: the output turns slower (the input speed divided by the ratio) but with more torque; a ratio less than one speeds the output up and reduces torque. A pulley and belt system uses the ratio of the pulley diameters in the same way (driven diameter over driver diameter). Compound gear trains multiply ratios. These calculations let a designer set the output speed and torque: for example, a winch uses a large reduction for slow, strong lifting. Keep the ratio unitless, and remember that slowing the output increases torque and vice versa, because energy is conserved.

Combining structural and mechanical calculations

Calculate a moment for a fixing

A bracket carries a $120$ N load at $0.30$ m from its wall fixing. The moment is $M = F \times d = 120 \times 0.30 = 36$ N m, the turning effect the fixing must resist.

Calculate stress in a member

A tie in the bracket of area $4.0 \times 10^{-5}$ square metres carries $1600$ N. The stress is $\sigma = \frac{F}{A} = \frac{1600}{4.0 \times 10^{-5}} = 4.0 \times 10^{7}$ Pa, which is $40$ MPa, well within steel's strength.

Calculate mechanical advantage of an operating lever

A lever opening the bracket's clamp has an effort arm of $0.40$ m and a load arm of $0.08$ m, so $MA = \frac{0.40}{0.08} = 5$ : a $50$ N effort holds a $250$ N load.

Calculate a gear ratio in the drive

A 15-tooth driver turns a 45-tooth driven gear, so the gear ratio is $\frac{45}{15} = 3$ (3:1), slowing the output threefold and roughly tripling the torque. State every unit (N m, Pa, none, none) and show the working, because that is what the marks reward.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20204 marksA steel tie of cross-sectional area

2.5 \times 10^{-5}

square metres carries a tensile force of 5000 N. Calculate the stress, and the strain if the tie stretches by 0.5 mm over an original length of 1.0 m.

Show worked answer →

A Component 1 stress and strain calculation. Marks for the stress and the strain with correct units.

Stress is force per unit area: $\sigma = \frac{F}{A} = \frac{5000}{2.5 \times 10^{-5}} = 2.0 \times 10^{8}$ pascals, which is $200$ MPa. Strain is the extension divided by the original length (no units): convert $0.5$ mm $= 5.0 \times 10^{-4}$ m, so $\varepsilon = \frac{\Delta L}{L} = \frac{5.0 \times 10^{-4}}{1.0} = 5.0 \times 10^{-4}$ .

Award marks for $2.0 \times 10^{8}$ Pa (200 MPa) and $5.0 \times 10^{-4}$ (dimensionless). A common dropped mark is leaving the area in the wrong units (it must be square metres for pascals) or forgetting to convert the extension to metres.

Eduqas 20226 marksA first-class lever has an effort arm of 0.50 m and a load arm of 0.10 m. A gear train then connects a 16-tooth driver to a 48-tooth driven gear. Calculate the mechanical advantage of the lever and the gear ratio, and state the effect of each.

Show worked answer →

A Component 1 mechanical advantage and gear ratio calculation. Marks for the MA, the gear ratio and the interpretations.

Mechanical advantage of the lever is the effort arm divided by the load arm: $MA = \frac{0.50}{0.10} = 5$ (no units), so the lever multiplies the effort five times (a load equals five times the effort). The gear ratio is the driven teeth over the driver teeth: $\frac{48}{16} = 3$ , written 3:1, a reduction, so the output turns three times slower with about three times the torque.

Award marks for $MA = 5$ , gear ratio $3:1$ , and the effects (force multiplied five times; speed down and torque up three times). A common dropped mark is inverting either ratio or giving them units.

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Sources & how we know this

Eduqas A Level Design and Technology specification (Product Design) — Eduqas (2017)