Power – the Rate of Work Just as we were interested in the rate at which motion occurs (velocity), we are often interested in the rate at which work gets done In physics, “power” is the rate at which work gets done, or the rate at which energy gets used We use the equation: P = W/Δt power is directly proportional to work and inversely proportional to time The units of power are J/s or “Watts” (W)

Machines Machines are devices that change how work gets done by changing the input and output distances and therefore the input and output forces Machines do NOT change the amount of work that gets done – just the distribution of that work between force and distance Some machines also change the direction of input or output forces, but this is more an issue of convenience

Let’s Think Back… In the “It’s All Uphill” activity, the amount of work that got done was the same regardless of the angle of the ramp What changed with the ramp angle was the length of the ramp required to reach a height of one meter, and therefore, the force required to move the cart through that distance the longer the distance, the lower the force

Input & Output We can analyze the “It’s All Uphill” situation by looking at the input work and the output work Input work = input force x input distance Output work = output force x output distance The input work is the force applied along the ramp times the displacement along the ramp The output work is the force acting on the raised cart (its weight) times its height above the table By increasing the input distance, we decreased the input force required to get the same output

Efficiency In the absence of friction, the output work would be equal to the input work (work is energy, energy cannot be created or destroyed) In the real world there is friction, and some of the input energy is used to overcome this friction Thus (in the real world) output work is always less than input work We use the concept of “efficiency” to quantify this effect Efficiency = output work/input work x 100%

Mechanical Advantage The factor by which a machine changes an input force into an output force is called the “mechanical advantage” of the machine By using force (some of which is lost to friction), we determine an “actual mechanical advantage” AMA = output force/input force For the best-case situation (no friction), we use distances to get an “ideal mechanical advantage” IMA = input distance/output distance The State Reference Table use “resistance” (output) and “effort” (input) in these equations

The Simple Machines The Lever – a rigid bar that pivots on a “fulcrum” first-class lever: input-fulcrum-output second-class lever: input-output-fulcrum third-class lever: output-input-fulcrum IMA = the distance from input force to fulcrum/ the distance from the output force to fulcrum The Wheel-and-Axle – two connected disks or cylinders having different diameters IMA = the diameter having the input force/ the diameter having the output force

The Simple Machines The Inclined Plane – a slanted surface (ramp) IMA = the distance along the ramp/the height at the end of the ramp (vertical distance) Consider the 30˚ ramp in “It’s All Uphill” IMA = displacement/height = 2/1 = 2 Input force (14.7 N) x 2 = output force (29.4 N) The Wedge – a variation on the inclined plane IMA = the wedge length/the wedge width (at top) The Screw – another variation (an inclined plane wrapped around a cylinder)

The Simple Machines The Pulley fixed pulley – pulley attached to a fixed location; the applied force is in the opposite direction of the displacement; no mechanical advantage moveable pulley – pulley attached to the load; the applied force is in the same direction as the displacement; mechanical advantage = 2 pulley system – fixed and moveable pulleys combined; applied force in any direction relative to displacement; the mechanical advantage is the number of ropes supporting the load