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?
Which statement correctly identifies a third-class lever and its characteristic effect?
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?
A ramp raises a load 0.5 m using a 2.5 m slope. What is the ideal mechanical advantage of the ramp?