Rotational Equilibrium and Dynamics Simple Machines

Simple Machines Machines multiply and redirect force Simple machines – one of the six basic types of machines of which all other machines are composed Two families of simple machines: Levers and Inclined planes

The Lever Family Three groups of machines in the lever family Levers Pulleys Wheel and Axle

Levers "Give me a place to stand and I will move the earth.” Archimedes On the lever in Pappus Synagoge Levers have a rigid arm that turns around a fulcrum Force is transmitted from one part of the arm to another

Levers Three classes of lever Based on the location of the fulcrum and input and output forces First-class lever – has the fulcrum between the input and output forces Examples: claw hammer, see-saw A pair of pliers is made of two first-class levers

Levers

Levers Second class-levers – the output force is in the middle between the fulcrum and the input force Examples: Wheelbarrow, nutcrackers, hinged doors

Levers

Levers Third-class levers – the input force is between the fulcrum and the output force Example: human forearm

Levers

Pulleys Pulleys are modified levers Used to lift objects The point in the middle of the pulley is like the fulcrum in a lever The rest of the pulley is like the arm Multiple pulleys are sometimes called a block-and-tackle

Pulleys

Pulleys

Pulleys

Wheel and Axle Wheel and Axle – a lever or pulley (the wheel) connected to a shaft (the axle) Examples: steering wheel, screwdrivers

Inclined Plane Family Three types of machines in the inclined plane family Inclined plane Wedge Screw

Inclined Planes Inclined planes – the input force is directed parallel to the ramp The output force is directed up

Wedge Wedge – acts like two inclined planes back-to-back Turns a single downward force into two forces directed out to the sides Example: axe head, nails

Screw Screw – an inclined plane wrapped around a cylinder Steeper threads require more force to tighten Examples: jar lids, wood screws, spiral staircases

Compound Machines Compound machine – a machine made up of more than one simple machine Scissors – two first class levers joined at a common fulcrum with each arm having a wedge Car jack – lever with a screw

Machines and Torque Input torque equals output torque τin = τout

Machines and Mechanical Advantage Machines multiply and redirect force Changes the direction of an input force Increases the output force by changing the distance over which the force is applied Does not change the amount of work done

Machines and Mechanical Advantage Mechanical advantage – a quantity that measures how much a machine multiplies force or distance Mechanical advantage = output force input force Mechanical advantage = input distance output distance MA = Fo = di Fi = do

Machines and Mechanical Advantage Mechanical advantage greater than one multiplies the input force Mechanical advantage less than one increases distance and speed Mechanical advantage does not have any units

Efficiency of Machines Not all work done by a machine is useful work Some of the energy is lost to sound or heat No machine is perfect There are no perpetual motion machines

Efficiency of Machines Efficiency – a quality, usually expressed as a percentage, that measures the ratio of useful work output to work input Efficiency = (useful work output)/(work input)*100% Eff = Wo/WI*100%