Mechanical Comprehension
The six simple machines
Lever, pulley, wheel and axle, inclined plane, wedge, and screw. Mechanical advantage is output force divided by input force; it multiplies force at the cost of distance.
- Levers: first class has the fulcrum between load and effort (seesaw); second class has the load between (wheelbarrow); third class has the effort between (rake). Balance: effort times effort arm equals load times load arm.
- Pulleys: a fixed pulley changes direction only and has a mechanical advantage of 1. Each additional rope segment supporting a movable pulley adds 1, so count the ropes pulling up on the moving block.
- Gears: meshing gears turn in opposite directions, and the gear ratio equals the ratio of teeth.
- Pressure equals force divided by area, so a small area creates high pressure, which is why a sharp knife cuts.
Other concepts
Friction opposes motion and lowers real mechanical advantage. Hydraulic systems transmit pressure equally in all directions, so a larger output piston gives a force advantage. An object floats when it displaces its own weight in fluid, and stability depends on the center of gravity.
Traps
- Counting the rope you pull instead of the ropes holding the load.
- Assuming connected gears turn the same way.
- Confusing pressure with force when area changes.
- Forgetting that friction makes real machines less efficient than the ideal calculation.
Worked example
A 10 lb weight sits 2 ft from a fulcrum. To balance it with an effort 4 ft from the fulcrum: 10 times 2 = effort times 4, so effort = 5 lb.