Simple Machines

Explore how levers, inclined planes, pulleys, and wheels trade force for distance to make work easier.

What is a Machine?

A simple machine is a device that changes the direction or magnitude of a force. It does not reduce the amount of work needed, but it can make tasks easier by reducing the required force.

Work

W = F \times d

F = force (N), d = distance moved in the direction of the force (m), W = work (J).

The Lever

A lever multiplies force about a fulcrum.

A lever: effort × effort arm = load × load arm.

Lever Balance

F_e \times d_e = F_l \times d_l

F_e = effort, d_e = effort arm length, F_l = load force, d_l = load arm length.

Classes of levers:

Class 1 — fulcrum between effort and load (see-saw)
Class 2 — load between fulcrum and effort (wheelbarrow)
Class 3 — effort between fulcrum and load (tweezers)

The Inclined Plane

A ramp lets you move a heavy object to a height using less force over a longer distance.

Inclined Plane — Ideal Effort

F = \frac{m g h}{l}

m = mass, g ≈ 9.8 m/s², h = height, l = length of ramp.

Mechanical Advantage

MA = \frac{F_{\text{load}}}{F_{\text{effort}}}

MA > 1 means the machine multiplies force.

Note Pulleys, wheels and axles, screws, and wedges are all variations of these two fundamental machines.

1
Identify the machine type
Lever, ramp, pulley, wheel, screw, or wedge?
2
Set up the equation
Use the balance or work equation for that machine.
3
Solve for the unknown
Usually effort force or distance.

A lever has an effort arm of 2 m and a load arm of 0.5 m. A load of 400 N is placed on the load side. What effort is needed?

$F_e \times 2 = 400 \times 0.5 \implies F_e = \frac{200}{2} = 100 \text{ N}$

Real world: construction crane (class 1 lever)

A tower crane lifts a 2000 N load at 10 m from the pivot. To balance, a counterweight is placed 5 m on the other side. Required counterweight: $F_c \times 5 = 2000 \times 10 \Rightarrow F_c = 4000\text{ N}$ . Every crane is an application of lever balance equations.

Real world: bicycle gears

A bicycle's gear system is a wheel-and-axle machine. In a low gear (small chain-ring, large rear sprocket) a small rotational effort at the pedals produces a large rear-wheel torque — easier climbing. In a high gear the arrangement is reversed for speed on flat roads. Mechanical advantage is traded for speed.

Real world: wheelchair ramp (inclined plane)

A wheelchair user needs to descend a 0.6 m step. A ramp 4 m long reduces the force needed: $F = \frac{60 \times 9.8 \times 0.6}{4} = 88.2\text{ N}$ instead of lifting the full $60 \times 9.8 = 588\text{ N}$ weight. Building codes specify ramp ratios precisely based on this inclined plane calculation.

Tip Machines trade force for distance. A machine that halves the required force will require you to move your effort twice as far. Total work input always equals total work output (in an ideal machine).

Practice Problems

A ramp is 5 m long and 1 m high. What force is needed to push a 200 kg box up the ramp? (g = 9.8 m/s²)

Show answer

F = (200 × 9.8 × 1) / 5 = 392 N.

A lever has MA = 4. If the load is 800 N, what effort is needed?

Show answer

F_effort = 800 / 4 = 200 N.

You push a 50 N box 3 m along a flat surface. How much work do you do?

Show answer

W = 50 × 3 = 150 J.