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Math of Simple Machines

Math of Simple Machines. Tuesday July 24, 2007. Ratio and Proportion. Ratio is a fraction. Proportion is the relationship between two quantities with constant ratios or fractions. Work. Anything that pushes or pulls to move an object across a distance. Work (W) = force (F) × distance (d)

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Math of Simple Machines

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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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