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Simple machines are the most basic mechanical devices that change the direction or magnitude of a force. They form the foundation of complex machinery and make work easier by trading force for distance (or vice versa).
This lesson covers definitions, the 6 classical types, mechanical advantage (MA), velocity ratio (VR) and efficiency, with worked examples and a CBT quiz.
Types of Simple Machines
Lever — rigid bar rotating about a fulcrum.
Pulley — wheel and rope to change direction and mechanical advantage.
Inclined Plane — raise loads using less force over a longer distance.
Wedge — converts force to lateral forces to split objects.
Screw — inclined plane around a cylinder converting rotation to linear motion.
Wheel & Axle — two radii rotating together to multiply force or distance.
Mechanical Advantage (MA)
MA is the factor by which a machine multiplies an input force:
MA = Output Force / Input Force
Higher MA means less effort for the same load (ignoring losses).
Velocity Ratio (VR)
VR is the ratio of distances moved by effort and load (ideal, lossless):
VR = Distance moved by effort / Distance moved by load
In an ideal machine (no friction), MA = VR.
Efficiency
Efficiency measures how well input work is converted to useful output work:
Efficiency (%) = (MA / VR) × 100
Real machines have <100% efficiency due to friction and losses.
Summary & Applications
Simple machines trade force for distance to make work easier. Understanding MA, VR, and efficiency helps analyze or design devices ranging from hand tools to mechanical lifting systems.
10 Worked Examples (solutions hidden)
Example 1 — Lever MA
Q: Fulcrum 2 m from load and 6 m from effort. Effort = 50 N. Find output force.
Solution:
MA = Effort arm / Load arm = 6 / 2 = 3 → Output = 3 × 50 N = 150 N.
Example 2 — Pulley (block & tackle)
Q: VR = 4, effort = 30 N. Ideal output force?
MA = VR = 4 → Output = 4 × 30 N = 120 N.
Example 3 — Inclined plane
Q: Ramp length 5 m, height 1 m. Effort 100 N. Find ideal output force (MA).
VR = 5/1 = 5 → Ideal MA = 5 → Output = 5 × 100 N = 500 N.
Example 4 — Wedge
Q: Effort 200 N produces output 600 N. Find MA.
MA = Output / Effort = 600 / 200 = 3.
Example 5 — Screw
Q: How does pitch affect screw MA?
A smaller pitch (threads closer) advances less per turn → larger MA (less force per turn) but more turns needed.
Example 6 — Wheel & Axle VR
Q: Wheel radius 0.5 m, axle radius 0.1 m. Find VR.
VR = R_wheel / R_axle = 0.5 / 0.1 = 5.
Example 7 — Efficiency
Q: MA = 4, VR = 5. Find efficiency.
Efficiency = (MA/VR)×100 = (4/5)×100 = 80%.
Example 8 — Compound machine
Q: Lever (MA=3) attached to pulley (MA=4). Overall MA?
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