5.3 Simple Machines, Work Input, and Mechanical Advantage
Key Takeaways
A machine changes the size or direction of a force but never creates energy: work output can never exceed work input, so any reduction in required force is paid for with a proportional increase in distance.
Ideal mechanical advantage is a geometric ratio (effort arm ÷ load arm, slope length ÷ height, wheel radius ÷ axle radius), while actual mechanical advantage is load force ÷ effort force and is always smaller because of friction.
Efficiency = (work output ÷ work input) × 100%, and it is always below 100% in a real machine because friction converts part of the input work into thermal energy.
The three lever classes are set by what sits in the middle: fulcrum in the middle (first class, seesaw), load in the middle (second class, wheelbarrow), effort in the middle (third class, tweezers and the human forearm).
A pulley system's ideal mechanical advantage equals the number of rope segments actually supporting the movable load, so a single fixed pulley has an MA of 1 and only redirects the force.
Machines as an Application of Force and Work
Competency 006 closes with a descriptive statement about analyzing force-motion relationships in real situations, and simple machines are the framework's named example. This is also where Domain II connects to the energy competencies: a simple machine is the cleanest classroom demonstration that energy is conserved while force is not.
The Core Trade-Off
Work is force times distance: W = F × d. A machine cannot create work, so ignoring friction:
Work input = Work output, that is, F_effort × d_effort = F_load × d_load
If a ramp lets you push a 600 N barrel up with only 200 N of force, you must push it through three times the distance. Cut the force by a factor of three, multiply the distance by three. This is why the answer to "does a machine reduce the work required?" is no — it reduces the force required.
Mechanical Advantage
Ideal mechanical advantage (IMA) comes from the machine's geometry and assumes no friction. Actual mechanical advantage (AMA) comes from measured forces:
AMA = load force ÷ effort force | IMA = effort distance ÷ load distance
AMA is always less than IMA in a real device because friction requires extra effort force. Efficiency compares them:
Efficiency = (work output ÷ work input) × 100% = (AMA ÷ IMA) × 100%
Worked example. A ramp is 6.0 m long and 1.5 m high. IMA = 6.0 ÷ 1.5 = 4.0. A student measures that pushing a 400 N crate up the ramp actually takes 125 N. AMA = 400 ÷ 125 = 3.2. Efficiency = (3.2 ÷ 4.0) × 100 = 80%. The missing 20% became thermal energy through friction between the crate and the ramp surface.
The Six Simple Machines
| Machine | How it works | Ideal mechanical advantage | Everyday example |
|---|---|---|---|
| Lever | Rigid bar rotating on a fulcrum | effort arm ÷ load arm | Crowbar, seesaw, bottle opener |
| Pulley | Grooved wheel with a rope | number of rope segments supporting the load | Flagpole, block and tackle, window blinds |
| Inclined plane | Sloped surface raising a load over a longer path | slope length ÷ vertical height | Wheelchair ramp, loading ramp |
| Wedge | Two inclined planes back to back; converts a downward force into sideways forces | slope length ÷ thickness | Axe, chisel, knife, doorstop |
| Screw | Inclined plane wrapped around a cylinder | circumference ÷ thread pitch | Jar lid, bolt, auger, spiral staircase |
| Wheel and axle | Two connected cylinders of different radius | wheel radius ÷ axle radius | Doorknob, steering wheel, screwdriver handle |
The Three Lever Classes
The class is determined by which of the three components — fulcrum, load, effort — sits between the other two.
| Class | Middle component | Force effect | Examples |
|---|---|---|---|
| First | Fulcrum | Can increase force or distance; always reverses direction | Seesaw, crowbar, scissors, pliers |
| Second | Load | Always increases force; MA > 1 | Wheelbarrow, nutcracker, bottle opener, door |
| Third | Effort | Always increases distance and speed; MA < 1 | Tweezers, broom, fishing rod, human forearm |
The third-class lever is the one students find counterintuitive: it requires more force than the load, and its payoff is range of motion and speed. The biceps attaches close to the elbow, so a modest weight in the hand demands a large muscle force — but a small muscle contraction sweeps the hand through a wide, fast arc. That biomechanical example is a strong Domain II–Domain III bridge and appears in framework language as applying force-motion relationships to systems such as blood flow and body movement.
Lever calculation. A 1.8 m plank rests on a fulcrum 0.3 m from a 900 N rock. The effort arm is 1.8 − 0.3 = 1.5 m, so IMA = 1.5 ÷ 0.3 = 5.0, and the ideal effort force is 900 ÷ 5.0 = 180 N.
Pulleys
A fixed pulley attached to a ceiling changes only the direction of the effort: pull down to raise a load. Its IMA is 1, which is genuinely useful (pulling down lets you add body weight) but multiplies no force. A movable pulley attached to the load itself has an IMA of 2, because two rope segments share the load — at the cost of pulling twice as much rope. A block and tackle combining both can reach an IMA of 4, 5, or more; count the rope segments that actually support the movable block, not the number of wheels.
Compound Machines and Efficiency in Practice
A compound machine links simple machines so their mechanical advantages multiply. A bicycle combines wheel-and-axle pairs (pedal crank and gears), levers (brake handles), and screws (fasteners). A pair of scissors is two first-class levers joined at a fulcrum, each blade also acting as a wedge.
Real efficiency figures are worth knowing as plausibility anchors: a well-lubricated bicycle drivetrain runs above 95% efficient, a typical lever or pulley system 70-90%, a screw jack often under 30% because thread friction is large. No machine reaches 100%, and any exam option claiming an efficiency of 100% or above is wrong — a machine cannot output more work than it receives, which is the conservation of energy stated in mechanical terms.
Movers use a 9.0 m ramp to raise a 750 N crate to a loading dock 1.5 m high. Ignoring friction, what effort force is required, and how does the work compare with lifting the crate straight up?
125 N, and the work is the same as lifting it straight up
125 N, and the work is one-sixth of lifting it straight up
4,500 N, and the work is six times lifting it straight up
750 N, and the work is the same because the ramp changes only direction
Which statement correctly identifies a third-class lever and its characteristic effect?
A wheelbarrow, because the load sits between the fulcrum and the effort, multiplying force
A seesaw, because the fulcrum sits between the load and the effort, reversing direction
A pair of tweezers, because the load sits in the middle and the mechanical advantage exceeds one
The human forearm, because the effort of the biceps is applied between the elbow fulcrum and the load in the hand, trading force for speed and range of motion
A student measures that a pulley system lifts a 240 N load with 80 N of effort, and counts four rope segments supporting the movable block. What is the system's efficiency?
75%
100%
133%
33%
A ramp raises a load 0.5 m using a 2.5 m slope. What is the ideal mechanical advantage of the ramp?
0.2
2
5
12.5
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