4dSimple Machines
Explore the six simple machines, learn how mechanical advantage multiplies force, and discover why real machines are never perfectly efficient.
Simple machines are the building blocks of all complex machinery. Understanding mechanical advantage and efficiency helps you analyze everything from bicycle gears to construction cranes.
Lesson Overview
Simple machines are devices that make work easier by changing the magnitude or direction of a force. The six classical simple machines are the lever, pulley, wheel-and-axle, inclined plane, wedge, and screw. Mechanical advantage (MA) describes how much a machine multiplies force. Efficiency compares useful output energy to total input energy, and is always less than 100% in real machines due to friction.
Key Concepts
Six Simple Machines
Lever, pulley, wheel-and-axle, inclined plane, wedge, screw
Mechanical Advantage
MA = output force / input force (no units)
Ideal MA (IMA)
Calculated from geometry; assumes no friction
Actual MA (AMA)
Calculated from measured forces; always < IMA due to friction
Efficiency
η = (useful output work / total input work) × 100%
Work In = Work Out (ideal)
F_in × d_in = F_out × d_out for an ideal machine
A lever has an input force of 50 N and produces an output force of 200 N. What is its mechanical advantage?
An inclined plane is 5 m long and 1 m high. What is its ideal mechanical advantage?
A pulley system requires 30 N of input force to lift a 90 N load. What is the actual mechanical advantage and efficiency if the ideal MA is 4?
A machine has an efficiency of 80% and an input work of 500 J. How much useful output work does it produce?
A wheel-and-axle has a wheel radius of 0.4 m and an axle radius of 0.05 m. What is its ideal mechanical advantage?
A lever requires 40 N of input force to lift a 160 N load. Calculate the mechanical advantage.
Hint: MA = output force ÷ input force. Identify which force is the output (the load being lifted).
An inclined plane is 8 m long and 2 m high. What is its ideal mechanical advantage?
Hint: IMA for an inclined plane = slope length ÷ vertical height.
A machine does 600 J of useful work from 800 J of input work. What is its efficiency?
Hint: Efficiency = (useful output / total input) × 100%. Divide and multiply by 100.
A pulley system has an IMA of 6 and an efficiency of 70%. What input force is needed to lift a 420 N load?
Hint: First find AMA = efficiency × IMA / 100. Then use AMA = output force / input force.
Why is the actual mechanical advantage of a real machine always less than its ideal mechanical advantage?
Hint: Think about what happens to some of the input energy in a real machine.
Key Vocabulary
Mechanical Advantage
The ratio of output force to input force for a machine; indicates how much the machine multiplies force.
Example: A crowbar with MA = 5 means you apply 10 N to lift a 50 N rock.
Efficiency
The ratio of useful output work to total input work, expressed as a percentage. Always ≤ 100% due to friction.
Example: A ramp with 80% efficiency converts 80% of your input work into lifting the load; 20% is lost to friction.
Ideal Mechanical Advantage (IMA)
The theoretical mechanical advantage of a machine calculated from its geometry, assuming no friction.
Example: A pulley system with 4 supporting rope segments has an IMA of 4.
Inclined Plane
A flat surface set at an angle to the horizontal; one of the six simple machines. It reduces the force needed to raise an object by increasing the distance over which the force acts.
Example: A ramp into a moving truck is an inclined plane — it lets movers push heavy boxes up instead of lifting them straight up.
Interactive Practice — 5 Questions
A machine has an input force of 25 N and an output force of 100 N. What is its mechanical advantage?
Which simple machine consists of a grooved wheel with a rope running through it?
A machine does 300 J of useful work from 400 J of input work. What is its efficiency?
Why can no real machine have 100% efficiency?
An inclined plane is 10 m long and 2 m high. What is its ideal mechanical advantage?
Independent Practice
List the six simple machines and give one real-world example of each.
A lever requires 60 N of input force to lift a 300 N load. Calculate (a) the mechanical advantage and (b) the efficiency if the IMA is 6.
A ramp is 12 m long and 3 m high. A 90% efficient machine is used to push a 600 N box up the ramp. What input force is required?
Explain why a screw is considered a type of inclined plane wrapped around a cylinder.
★ A compound pulley system has 5 rope segments supporting the load. The system is 65% efficient. What input force is needed to lift a 1,300 N engine block? How far must you pull the rope to raise the engine 0.5 m?
ChallengeCommon Mistakes
Thinking a machine with high mechanical advantage also has high efficiency.
MA and efficiency are independent. A machine can have high MA but low efficiency if there is a lot of friction.
Assuming a machine creates energy because the output force is greater than the input force.
A machine never creates energy. When output force > input force, the output moves a shorter distance, so work in = work out (ideally).
Confusing IMA and AMA — using geometry to calculate AMA or measured forces to calculate IMA.
IMA comes from geometry (distances or radii). AMA comes from measured forces (F_out / F_in).
Math Tips
MA = F_out / F_in. Efficiency = (AMA / IMA) × 100% = (W_out / W_in) × 100%. For inclined plane: IMA = length / height. For wheel-and-axle: IMA = R_wheel / R_axle.
To find input force with a known efficiency: F_in = F_out / (IMA × efficiency). Always convert efficiency to a decimal before calculating.