Simple Machines

Levers, pulleys, inclined planes, and mechanical advantage in elementary devices.

General idea of the topic

A simple machine is a device that changes the magnitude or the direction of a force to make a task easier. It does not create energy: in the ideal case the work applied equals the work obtained, so what is gained in force is lost in distance traveled.

The topic goes through the five classic ones: the lever, the pulley, the inclined plane, the wheel and axle and the screw. For each one the mechanical advantage, the ratio between the output force and the applied one, is computed, and friction and real efficiency are discussed.

What you will truly understand

By the end you will be able to compute the ideal and real mechanical advantage of each machine, relate the applied force to the load and explain why friction reduces the efficiency.

You will also be able to recognize several simple machines combined in everyday tools.

Recommended learning route

  1. Lever: balance of moments about the fulcrum and relation between the arms.
  2. Types of Levers: first-, second- and third-class levers according to the position of fulcrum, effort and load.
  3. Pulley: fixed and movable pulleys, number of ropes supporting the load and required force.
  4. Inclined Plane: resolution of weight, advantage according to the ratio of length to height and effect of friction.
  5. Wheel and Axle: advantage as the ratio between the wheel radius and the axle radius, and transmission of moments.
  6. Screw: wound inclined plane, thread pitch and large mechanical advantage with significant friction.
  7. Mechanical Advantage: ideal and real advantage of all of them, relation to efficiency and the rule that force is gained at the cost of distance.

Physical criterion you must acquire

The essential criterion is that mechanical advantage does not mean gaining energy: W_in = W_out + losses. An advantage of 4 means traveling four times the distance with the applied force. Efficiency is the ratio between useful work and applied work, and is always less than 1.

Connection with real problems

  • scissors, wheelbarrows and tool levers.
  • cranes, pulleys and hoists.
  • ramps, wedges and axes.
  • screwdrivers, jacks and vises.

Final goal of the topic

The final goal is to analyze any simple machine, compute its mechanical advantage and efficiency and explain clearly what is gained and what is paid.

Topics in this section

  • Types of Levers

    Classifies levers by the order of fulcrum, effort, and load. Theory, formulas, worked examples and interactive graphs.

  • Mechanical Advantage

    Compares the ideal and real help that a machine provides to reduce the required force.

  • Lever

    Analysis of torque balance in simple machines to amplify force or displacement.

  • Pulley

    Fixed and movable pulleys; mechanical advantage, efficiency and the golden rule.

  • Inclined Plane

    Vectorial analysis of the inclined plane: mechanical advantage, force components, friction, and energy balances in simple machines.

  • Wheel and Axle

    Coaxial wheel and axle; mechanical advantage, torque, efficiency and the golden rule.

  • Screw

    Analysis of the screw as a helical inclined plane, mechanical advantage and efficiency.