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Understanding Simple Machines and Work: Mechanical Efficiency

Explore the fundamental concepts of simple machines, work, and mechanical advantage. Learn about ratios, conservation of energy, efficiency, and types of simple machines like levers, pulleys, and inclined planes. Discover the relationship between mechanical advantage and efficiency in machines.

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Understanding Simple Machines and Work: Mechanical Efficiency

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  1. Math of Simple Machines Tuesday July 24, 2007

  2. Ratio and Proportion • Ratio is a fraction • Proportion is the relationship between two quantities with constant ratios or fractions.

  3. Work • Anything that pushes or pulls to move an object across a distance. Work (W) = force (F) × distance (d) W = F*d • Conservation of Energy implies Work In = Work Out + Work Lost to Friction • Ideal Machine does Ideal Work with no work lost to friction

  4. Mechanical Advantage • Consider the work in and work out of a simple machine like an inclined plane : Work in = F1 x d1 Work out = F2 x d2 F2 x d2 = F1 x d1

  5. Efficiency of a Machine • An Ideal Machine has 100% efficiency • What is the relationship between mechanical advantage and efficiency?

  6. Simple Machines • The Lever • The Pulley • The Wheel and Axle • The Inclined Plan • The Wedge (single or double) • The Screw

  7. Force, F2 Load, F1(force of the object desired to move) d1 d2 Lever • A rigid bar that rotates around a fixed point called a fulcrum. • A Load or force is also the gravitational weight

  8. d1 d2 Load, F1 Force, F2 Pulley Fixed Movable ? Movable = Fixed

  9. Raxle Rwheel Wheel and Axle

  10. Load, F1 Force, F2 height, h length, l Inclined Plane

  11. l Force, F2 Load, F1 h SINGLE WEDGE l h Load, F1 Force, F2 DOUBLE WEDGE Wedge

  12. Screw • Modified version of the inclined plane.

  13. Trigonometric Functions • Sine and cosine functions • Sine function • Cosine function

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