⚙️ Simple Machines & Mechanical Advantage
Simple machines reduce the effort needed to move a load. Mechanical advantage tells you how many times a machine multiplies your force — the foundation of levers, pulleys, gearboxes and inclined ramps in every workshop.
2Topics
8Examples
4Calculators
12Practice Qs
⚙️ Engineering context: A crowbar is a Class 1 lever — the pivot sits between effort and load. A wheelbarrow is Class 2 — load between pivot and effort. Understanding which class a machine is determines how much mechanical advantage you get.
🔨Levers & MAClasses 1, 2 & 3
🔄Pulleys & Inclined PlanesVR & efficiency
⚙️Applications4 workshop calculators
🎮Game12 randomised questions
📝Practice12 graded questions
🔨
Levers & Mechanical Advantage
A lever is a rigid bar that turns about a pivot (fulcrum). By choosing where to apply your effort and where the load sits, you multiply or redirect force.
🎮Live explorer — drag the sliders to see the lever balanceUpdates instantly
💡 MA > 1 means the lever multiplies your effort — the longer the effort arm, the greater the advantage
📋Try it — Lever CalculatorUpdates as you type
Select what to find and enter values above.
📚 Key vocabulary
- Mechanical advantage (MA)
- load divided by effort — how many times the machine multiplies the input force.
- Fulcrum (pivot)
- the fixed point about which a lever rotates.
- Effort arm
- the perpendicular distance from the fulcrum to the point where effort is applied.
- Load arm
- the perpendicular distance from the fulcrum to the point where the load acts.
- Moment
- turning effect of a force = force × perpendicular distance from pivot. Unit: N m.
- Principle of moments
- for equilibrium, total clockwise moments = total anticlockwise moments about any pivot.
👁️ Visual aid — three lever classes: where the pivot, effort and load sit determines the class and MA
✍️Worked example 1 — crowbar (Class 1 lever) step through it
QuestionA crowbar has an effort arm of 1.5 m and a load arm of 0.3 m. A load of 900 N needs to be moved. Find the effort required and the MA.
Formula
Effort × dₑ = Load × dₗRearrange
Effort = Load × dₗ ÷ dₑ = 900 × 0.3 ÷ 1.5Calculate
900 × 0.3 = 270 → 270 ÷ 1.5 = 180MA
MA = 900 ÷ 180 = 5AnswerEffort = 180 N MA = 5 ✓
Step 1 of 6
✍️Worked example 2 — wheelbarrow (Class 2 lever)
QuestionA wheelbarrow wheel is the pivot. The load of 400 N acts 0.4 m from the pivot. Handles are 1.2 m from pivot. Find the effort and MA.
Effort
Effort = 400 × 0.4 ÷ 1.2 = 160 ÷ 1.2 = 133.3 NMA
MA = 400 ÷ 133.3 = 3.0AnswerEffort = 133.3 N MA = 3.0
✍️Worked example 3 — finding MA from force measurements
QuestionA machine lifts a 1200 N load using an effort of 300 N. Calculate the MA.
Formula
MA = Load ÷ EffortSubstitute
MA = 1200 ÷ 300 = 4AnswerMA = 4
✍️Worked example 4 — finding load arm length
QuestionA lever has an effort arm of 2.4 m. An effort of 250 N just balances a load of 1000 N. Find the load arm length.
Formula
dₗ = Effort × dₑ ÷ LoadSubstitute
dₗ = 250 × 2.4 ÷ 1000 = 600 ÷ 1000Answerdₗ = 0.6 m
🔄
Pulleys & Inclined Planes
A pulley changes the direction or magnitude of a force. An inclined plane spreads a load over a longer distance, reducing the effort needed.
🔄Live explorer — pulley systemDrag sliders to explore MA, VR and efficiency
VR (velocity ratio)
4
Actual MA
3.0
Effort needed
267N
Efficiency
75%
💡 VR = number of rope sections going up from the load block. Each section shares the load equally in a perfect system.
📋Try it — Pulley & Efficiency CalculatorUpdates as you type
Select what to find and enter values above.
📚 Key vocabulary
- Velocity ratio (VR)
- the distance effort moves divided by the distance the load moves — equals number of rope sections in a pulley system.
- Efficiency (η)
- MA ÷ VR × 100%. Always less than 100% in real systems due to friction and weight of moving parts.
- Single fixed pulley
- VR = 1 — only changes direction of force, no mechanical advantage (but convenient).
- Block and tackle
- multiple pulleys giving VR = number of rope sections; used in cranes and hoists.
- Inclined plane
- a ramp that trades a smaller effort for a longer travel distance.
- sinθ
- for an inclined plane: sinθ = height ÷ length = ideal effort ÷ weight.
👁️ Visual aid — inclined plane: a 500 N crate on a 30° ramp requires only 250 N effort (ideal, no friction)
✍️Worked example 5 — pulley system: MA, VR and efficiency step through it
QuestionA 4-rope pulley system lifts a 600 N load. The actual effort is 180 N. Find MA, VR and efficiency.
VR
VR = number of rope sections = 4MA
MA = Load ÷ Effort = 600 ÷ 180 = 3.33Efficiency
η = MA ÷ VR × 100 = 3.33 ÷ 4 × 100Calculate
3.33 ÷ 4 = 0.833 → 0.833 × 100 = 83.3%AnswerVR = 4 MA = 3.33 Efficiency = 83.3% ✓
Step 1 of 6
✍️Worked example 6 — inclined plane effort
QuestionA 500 N crate is pushed up a ramp inclined at 30° to the horizontal (ideal — no friction). Find the effort.
Formula
E = W × sinθSubstitute
E = 500 × sin 30° = 500 × 0.5AnswerE = 250 N
✍️Worked example 7 — finding effort from efficiency
QuestionA 3-rope pulley lifts 450 N. System efficiency is 80%. Find the actual effort.
Ideal effort
E𝒊𝒊𝒅 = 450 ÷ 3 = 150 NActual effort
E𝑎𝑐𝑡 = E𝒊𝒊𝒅 ÷ η = 150 ÷ 0.80 = 187.5AnswerActual effort = 187.5 N
✍️Worked example 8 — inclined plane VR and efficiency
QuestionA ramp is 8 m long and 2 m high. A 600 N crate is pushed up using 200 N. Find VR, ideal MA and efficiency.
VR
VR = L ÷ h = 8 ÷ 2 = 4Ideal MA
MA𝒊𝒅𝒆𝑎𝑙 = 600 ÷ (600÷4) = 4 (ideal effort = 150 N)Actual MA
MA𝑎𝑐𝑡 = 600 ÷ 200 = 3Efficiency
η = 3 ÷ 4 × 100 = 75%AnswerVR = 4 Efficiency = 75%
⚙️
Engineering Applications
Four live calculators for practical workshop and plant scenarios.
🔨 Lever — find effort or load
Use the principle of moments to find the effort needed to lift a workshop load with a bar or crowbar.
Effort = Load × dₗ ÷ dₑ
🧮 Calculator
Enter load and arm lengths.
🔄 Pulley — efficiency and actual effort
Find the actual effort needed when a pulley system has a known efficiency — real-world friction always reduces MA below VR.
Actual effort = Load ÷ (VR × η)
🧮 Calculator
Enter load, VR and efficiency.
🔋 Inclined plane — ramp effort
Find the push needed to slide a load up a ramp at a given angle (ideal, frictionless case).
E = W × sin θ
🧮 Calculator
Enter weight and ramp angle.
📈 Efficiency from test data
Calculate the mechanical efficiency of any lifting machine from measured load, effort and VR.
η = (Load ÷ Effort) ÷ VR × 100%
🧮 Calculator
Enter load, effort and VR.
🎮
Machines Challenge
12 randomised questions per round. New numbers every time.
⚙️ Quick-fire round
Question 1 / 12
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📝
Practice Questions
12 graded questions — type your answer to check it, then reveal full working.
⚙️ Show formula, substitution and every step. MA = Load ÷ Effort. Efficiency = MA ÷ VR × 100%.
Q1 · MA1 mark
A machine lifts a 900 N load using 300 N effort. Calculate the mechanical advantage.
MA = Load ÷ Effort = 900 ÷ 300 = 3
Q2 · Lever effort2 marks
A Class 1 lever has an effort arm of 1.8 m and a load arm of 0.6 m. The load is 450 N. Find the effort.
Effort = Load × dₗ ÷ dₑ
= 450 × 0.6 ÷ 1.8 = 270 ÷ 1.8 = 150 N
= 450 × 0.6 ÷ 1.8 = 270 ÷ 1.8 = 150 N
Q3 · Lever MA2 marks
A crowbar has effort arm 2.0 m and load arm 0.25 m. State the MA and identify the lever class.
MA = dₑ ÷ dₗ = 2.0 ÷ 0.25 = 8
Pivot between effort and load → Class 1 lever
Pivot between effort and load → Class 1 lever
Q4 · Lever arm2 marks
An effort of 200 N just balances a 1000 N load. The effort arm is 2.5 m. Find the load arm.
dₗ = Effort × dₑ ÷ Load = 200 × 2.5 ÷ 1000 = 500 ÷ 1000 = 0.5 m
Q5 · Pulley VR1 mark
A block-and-tackle system has 5 rope sections supporting the load. State the VR.
VR = number of rope sections supporting the load = 5
Q6 · Pulley MA2 marks
A 4-rope pulley system lifts 800 N using 240 N effort. Find the MA and efficiency.
MA = 800 ÷ 240 = 3.33
η = 3.33 ÷ 4 × 100 = 83.3%
η = 3.33 ÷ 4 × 100 = 83.3%
Q7 · Efficiency2 marks
A machine has MA = 3 and VR = 5. Calculate the efficiency.
η = MA ÷ VR × 100 = 3 ÷ 5 × 100 = 60%
Q8 · Actual effort2 marks
A 3-rope pulley system has 75% efficiency. The load is 450 N. Find the actual effort.
Ideal effort = 450 ÷ 3 = 150 N
Actual effort = 150 ÷ 0.75 = 200 N
Actual effort = 150 ÷ 0.75 = 200 N
Q9 · Inclined plane2 marks
A ramp is 6 m long and 1.5 m high. Calculate the VR.
VR = Length ÷ Height = 6 ÷ 1.5 = 4
Q10 · Inclined plane effort2 marks
A 700 N crate is pushed up a frictionless ramp at 20°. Find the effort. (sin 20° = 0.342)
E = W × sinθ = 700 × 0.342 = 239.4 N
Q11 · Combined3 marks
A lever has effort arm 3.0 m and load arm 0.5 m. Find (a) the ideal MA, (b) the effort to lift 750 N, (c) the effort if actual efficiency is 90%.
MA = 3.0 ÷ 0.5 = 6
Ideal effort = 750 ÷ 6 = 125 N
Actual effort = 125 ÷ 0.90 = 138.9 N
Ideal effort = 750 ÷ 6 = 125 N
Actual effort = 125 ÷ 0.90 = 138.9 N
Q12 · Combined3 marks
A 5-rope pulley system lifts a 1000 N load. (a) State VR. (b) If efficiency is 70%, find the actual effort. (c) Find the actual MA.
VR = 5
Actual effort = 1000 ÷ (5 × 0.70) = 1000 ÷ 3.5 = 285.7 N
Actual MA = 1000 ÷ 285.7 = 3.5
Actual effort = 1000 ÷ (5 × 0.70) = 1000 ÷ 3.5 = 285.7 N
Actual MA = 1000 ÷ 285.7 = 3.5