Mechanical Advantage, Velocity Ratio & Efficiency Calculations

This lesson consolidates the key calculations for mechanical systems — mechanical advantage (MA), velocity ratio (VR) and efficiency. These formulae and calculation techniques are essential for AQA GCSE Design and Technology (8552), Section 3.1.5, and appear on virtually every Paper 1 exam.

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Mechanical Advantage (MA)

Mechanical advantage is the ratio of the output force (load) to the input force (effort). It tells you how much the mechanism multiplies your force.

Formula

$MA = \frac{\text{Load (N)}}{\text{Effort (N)}}$MA=Effort (N)Load (N)​

Interpreting MA

MA Value	Meaning
MA > 1	The mechanism multiplies force — the output force is greater than the input
MA = 1	No force multiplication — output force equals input
MA < 1	The mechanism multiplies speed/distance — the input force is greater than the output

MA for Different Mechanisms

Mechanism	MA Formula
Lever	MA = Effort arm ÷ Load arm
Pulley	MA = Number of rope sections supporting the load
Gear	MA = Teeth on driven ÷ Teeth on driver (for torque)
Inclined plane (ramp)	MA = Length of slope ÷ Height of slope
Screw thread	MA = Circumference of effort circle ÷ Pitch (lead) of thread

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Velocity Ratio (VR)

The velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load. It describes the trade-off between force and distance.

Formula

$VR = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$VR=Distance moved by loadDistance moved by effort​

VR for Different Mechanisms

Mechanism	VR Formula
Lever	VR = Effort arm ÷ Load arm
Pulley	VR = Number of rope sections supporting the load
Gear	VR = Teeth on driven ÷ Teeth on driver
Belt drive	VR = Driven pulley diameter ÷ Driver pulley diameter

Key Relationship: MA vs VR

In a perfect (frictionless) system:

$MA = VR$MA=VR

In a real system (with friction):

$MA < VR$MA<VR

This is because friction reduces the output force, so the actual mechanical advantage is always less than the theoretical velocity ratio.

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Efficiency

Efficiency measures how much of the input energy is usefully converted to output energy. The rest is lost to friction, heat and sound.

Formulae

$\text{Efficiency} = \frac{MA}{VR} \times 100\%$Efficiency=VRMA​×100%

$\text{Efficiency} = \frac{\text{Useful output energy (or work)}}{\text{Total input energy (or work)}} \times 100\%$Efficiency=Total input energy (or work)Useful output energy (or work)​×100%

$\text{Efficiency} = \frac{\text{Useful output power}}{\text{Total input power}} \times 100\%$Efficiency=Total input powerUseful output power​×100%

Work Done

$\text{Work done (J)} = \text{Force (N)} \times \text{Distance (m)}$Work done (J)=Force (N)×Distance (m)

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Worked Examples

Example 1: Lever Efficiency

A lever is used to lift a 300 N load. The effort arm is 1.2 m and the load arm is 0.3 m. The actual effort required is 100 N.

Step 1: Calculate VR

$VR = \frac{1.2}{0.3} = 4$VR=0.31.2​=4

Step 2: Calculate MA

$MA = \frac{300}{100} = 3$MA=100300​=3

Step 3: Calculate Efficiency

$\text{Efficiency} = \frac{3}{4} \times 100\% = 75\%$Efficiency=43​×100%=75%

Interpretation: 75% of the input energy is usefully converted. The remaining 25% is lost to friction at the fulcrum.

Example 2: Pulley System Efficiency