Unit 3 – Work, Power, and Machines

Work Transfer of energy through motion Force exerted through a distance Requires two conditions The force must make the object move The movement must be in the same direction as the force!

Does it do work? Lifting a box Pushing against a wall Floor pushing up (normal force) on a box as it slides Moves in direction of force – up Yes Doesn’t move No Moves in a different direction than force

W = Fd Work d W F Equals force times distance Measured in Joules W: work (Joules) F: force (Newton) d: distance (meters) 1 J = 1 N·m Distance must be in direction of force!

Work Brett’s backpack weighs 30 N. How much work is done on the backpack when he lifts it 1.5 m from the floor to his back? GIVEN: F = 30 N d = 1.5 m W = ? WORK: W = F·d W = (30 N)(1.5 m) W = 45 J F W d

Work d W F GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after W = ? A dancer lifts a 40 kg ballerina 1.4 m in the air and walks forward 2.2 m. How much work is done on the ballerina during and after the lift? GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after W = ? WORK: W = F·d F = m·a F =(40kg)(9.8m/s2)=392 N W = (392 N)(1.4 m) W = 549 J during lift No work after lift. “d” is not in the direction of the force. F W d

Power P: power (W) W: work (J) t: time (s) rate at which work is done More power is doing more work in less time measured in watts (W) P: power (W) W: work (J) t: time (s)

Power P W t F = 450 N P = W ÷ t d = 1.0 m W = F·d t = 3.0 s A figure skater lifts his partner, who weighs 450 N, 1.0 m in 3.0 s. How much power is required? GIVEN: F = 450 N d = 1.0 m t = 3.0 s WORK: P = W ÷ t W = F·d W = (450 N)(1.0 m) = 450 J P = 450 J ÷ 3.0 s P = 150 W P W t

Power P W t F = 450 N P = W ÷ t d = 1.5 m W = F·d t = 3.0 s A figure skater lifts his partner, who weighs 450 N, 1.0 m in 3.0 s. How much power is required? GIVEN: F = 450 N d = 1.5 m t = 3.0 s WORK: P = W ÷ t W = F·d W = (450 N)(1.5 m) = 675 J P = 675 J ÷ 3.0 s P = 225 W P W t

Machines A device that makes work easier It changes the size and/or direction of the exerted force

Mechanical Advantage Used to measure these changes in force from using the machine Large mechanical advantage means: Smaller force needed Work done more easily

Ideal Mechanical Advantage (IMA) Ratio of input (effort) distance to output (resistance) distance IMA > 1 : machine requires larger input distance, means smaller input force (easier) IMA < 1 : machine outputs larger distance, means greater input force (harder) IMA = 1 : only direction is changed

Example Consider the work done to lift a 4,500 lb (20,000 N) car to a height over your head. W=Fd W = 20,000 N x 2 m = 40,000 J How could this be done more easily?

Example - Continued Use a ramp! If ramp is 100 m long: F=W/d = 40,000 J / 100 m = 400 N Only about 90 pounds of force! Effort distance was 100 m, resistance distance was 2 m IMA = 100/2 = 50 This made it 50x easier to do the same amount of work

Real Machines Machines in the real world always have to overcome FRICTION!!! This requires a larger effort force Conservation of energy Work done because of friction is lost to heat Input work > output work

Actual Mechanical Advantage (AMA) Ratio of output force (resistance) to input force (effort) This is because the input force takes into account friction overcome Same as with IMA: AMA > 1 : easier – requires less force AMA < 1 : harder – requires more force AMA = 1 : only direction is changed

Efficiency Efficiency measure of how completely work input is converted to work output always less than 100% due to friction

Types of Machines

Simple Machines: Inclined Plane sloping surface used to raise objects Example: ramp h l

Simple Machines: Lever a bar that is free to pivot about a fixed point, or fulcrum “Give me a place to stand and I will move the Earth.” – Archimedes Engraving from Mechanics Magazine, London, 1824 Resistance arm Effort arm Fulcrum

Simple Machines: Levers Examples:

Simple Machines: Pulley grooved wheel with a rope or chain running along the groove F Le Lr

Simple Machines: Pulley Fixed Pulley does not increase force changes direction of force Example: flagpole

Simple Machines: Pulley Movable Pulley Moves the object Example: Construction crane

Simple Machines: Pulley Block & Tackle Combines a Fixed and a Movable Pulley Cranes use block & tackle pulleys to lift and move heavy loads

Simple Machines: Wheel and Axle two wheels of different sizes that rotate together a pair of “rotating levers” Example: screwdriver Wheel Axle

Simple Machines: Screw inclined plane wrapped in a spiral around a cylinder

Simple Machines: Wedge a moving inclined plane with 1 or 2 sloping sides Examples: fork, knife, axe, teeth

Simple Machines: Wedge Zipper 2 lower wedges push teeth together 1 upper wedge pushes teeth apart

Compound Machines combination of 2 or more simple machines

Compound Machines Engine A machine for converting energy into mechanical force and motion

A Car uses the wheel and axle method for the steering wheel and the axle, or other wise known as the Dry Shift. It also uses lever for things like the gas/brake pedals, and emergency brake. Screws are found anywhere in the interior and the hood, and car also have pulleys in the engine drive belt, for the water pump, and the alternator.

Compound Machines Rube Goldberg Machine Rube Goldberg walks in his sleep, strolls through a cactus field in his bare feet, and screams out an idea for self-operating napkin: As you raise spoon of soup (A) to your mouth it pulls string (B), thereby jerking ladle (C) which throws cracker (D) past parrot (E). Parrot jumps after cracker and perch (F) tilts, upsetting seeds (G) into pail (H). Extra weight in pail pulls cord (I), which opens and lights automatic cigar lighter (J), setting off sky-rocket (K) which causes sickle (L) to cut string (M) and allow pendulum with attached napkin to swing back and forth thereby wiping off your chin. After the meal, substitute a harmonica for the napkin and you'll be able to entertain the guests with a little music.

Ok Go Video – “This Too Shall Pass” http://www.youtube.com/watch?v=qybUFnY7Y8w While watching the video, write down 5 of the simple or compound machines that you see at work. If they are compound machines, list some of the simple machines that they are made of.