Simple machines and MA
| Machine | Mechanical advantage | Example |
|---|---|---|
| Lever (1st class) | L_in / L_out (about fulcrum) | Seesaw, crowbar |
| Lever (2nd class) | L_in / L_out | Wheelbarrow, bottle opener |
| Lever (3rd class) | L_in / L_out (< 1) | Fishing rod, tweezers |
| Wheel & axle | R_wheel / R_axle | Car steering, doorknob |
| Fixed pulley | 1 (direction change only) | Flagpole |
| Movable pulley | 2 | Rescue pulley |
| Block & tackle (N ropes) | N | Crane, sailboat rigging |
| Inclined plane | L / h (length / height) | Ramp, road grade |
| Wedge | L / t (length / thickness) | Knife, axe, door stop |
| Screw | 2π · r / pitch | Vise, bench screw |
| Gear train | N_output_teeth / N_input_teeth | Gearbox |
| Hydraulic press | A_output / A_input | Jack, brake system |
Key principle
| Conservation | MA × velocity ratio = 1 (ideal); work in = work out |
|---|---|
| Efficiency | η = W_out / W_in — real machines lose energy to friction |
| MA trade-off | Higher force = proportionally shorter distance (lever arm longer = less force but more motion) |
Notes
- Hydraulics: pressure is uniform, so force scales with piston area (Pascal's principle).
- All simple machines can be thought of as tools to redistribute force and distance while conserving total work.
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