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ScotlandEngineering ScienceSyllabus dot point

How much does a machine multiply force, and how efficient is it?

Mechanical advantage, velocity ratio and efficiency of a mechanism, including calculating each and relating efficiency to wasted energy.

An SQA National 5 Engineering Science answer on mechanical advantage, velocity ratio and efficiency, covering mechanical advantage as load over effort, velocity ratio, the percentage efficiency relationship, and why a real machine's efficiency is always below 100% because of friction.

Generated by Claude Opus 4.810 min answer

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

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  1. What this key area is asking
  2. Mechanical advantage
  3. Velocity ratio
  4. Efficiency
  5. Why this matters
  6. Try this

What this key area is asking

The SQA wants you to calculate the mechanical advantage, velocity ratio and efficiency of a mechanism, and explain why a real machine's efficiency is always less than 100%.

Mechanical advantage

Velocity ratio

A machine that multiplies force always does so at the cost of distance or speed: the effort has to move further than the load moves. This is why MA and VR are so closely linked. A block-and-tackle pulley with four supporting ropes, for example, has a velocity ratio of 4 - you must pull four metres of rope to raise the load one metre - and in an ideal frictionless case it would give a mechanical advantage of 4 as well.

The velocity ratio is fixed by the geometry of the machine (the number of teeth, the pulley diameters or the number of supporting ropes), so it does not change with the load. The mechanical advantage, by contrast, depends on the actual forces and is reduced by friction, which is why comparing the two reveals the efficiency.

Efficiency

If a machine were perfect, the mechanical advantage would equal the velocity ratio and the efficiency would be 100%. In reality the MA is always less than the VR because some input effort is used to overcome friction, which is transformed into wasted heat. The bigger the friction, the lower the efficiency.

Why this matters

These three quantities let an engineer judge a mechanism: how much it multiplies force (MA), the speed-distance trade involved (VR) and how much energy it wastes (efficiency). They tie together levers, gears and pulleys and connect directly to the work and energy ideas in the next key area. Improving efficiency - usually by reducing friction with lubrication or bearings - is a common design goal.

Try this

Q1. A machine lifts a 900 N900 \text{ N} load with a 300 N300 \text{ N} effort. Calculate the mechanical advantage. [2 marks]

  • Cue. MA=900/300=3\text{MA} = 900/300 = 3.

Q2. A machine has MA =2= 2 and VR =2.5= 2.5. Calculate the efficiency. [2 marks]

  • Cue. efficiency=(2/2.5)×100=80%\text{efficiency} = (2/2.5)\times 100 = 80\%.

Q3. State why a real machine can never be 100% efficient. [1 mark]

  • Cue. Friction always transforms some of the input energy into wasted heat.

Exam-style practice questions

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

SQA N5 style3 marksA pulley system lifts a load of 600 N using an effort of 150 N. Calculate the mechanical advantage.
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Use the mechanical advantage relationship.

Relationship: MA=loadeffort\text{MA} = \dfrac{\text{load}}{\text{effort}}.

Substitution: MA=600150=4\text{MA} = \dfrac{600}{150} = 4.

The mechanical advantage is 4 (no unit): the machine multiplies the effort four times. Markers reward load over effort, correct substitution, and stating that MA has no unit.

SQA N5 style4 marksA machine has a mechanical advantage of 3 and a velocity ratio of 4. Calculate its efficiency as a percentage.
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Efficiency compares the mechanical advantage with the velocity ratio.

Relationship: efficiency=MAVR×100%\text{efficiency} = \dfrac{\text{MA}}{\text{VR}} \times 100\%.

Substitution: efficiency=34×100=75%\text{efficiency} = \dfrac{3}{4} \times 100 = 75\%.

Markers reward selecting MA over VR times 100, correct substitution, and a percentage answer. The 25% shortfall is energy wasted as heat through friction; no real machine reaches 100%.

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