MachinesMachines Machines  Machines  Force  Work  Power  Mechanical Advantage  Ideal Machines  6 Simple Machines  Efficiency

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

Work  A force causes an object to move  The movement must be in the same direction as the applied force.  Units: N  m or Joules (J) W = F × d

Power rate at which work is done measured in watts (W) P = W t P = power (W) W = work (J) t = time (s)

Calculating Power P = W ÷ t W = F·d W = (450 N)(1.5 m) = 675 J P = 675 J ÷ 3.0 s P = 225 W F = 450 N d = 1.5 m 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?

Forces  Effort Force (F e ) force applied to the machine “what you do”  Resistance Force (F r ) force applied by the machine “what the machine does”

Work  Work Input (W in ) work done on a machine  Work Output (W out ) work done by a machine W in = F e × d e W out = F r × d r

Ideal Machine Equation  Conservation of Energy can never get more work out than you put in trade-off between force and distance W in = W out F e × d e = F r × d r

Ideal Machine Equation  You need to lift a 150 N box using only 15 N of force. How long does the lever need to be if the resistance arm is 0.3m? 0.3m F e × d e = F r × d r (15 N) d e = (150 N)(0.3m) d e = (150 N)(0.3m) 15N d e = 3.0 m

Work  In an ideal machine...  But in the real world… some energy is lost as friction W in = W out W in > W out

Mechanical Advantage  Mechanical Advantage (MA) number of times a machine increases the effort force MA > 1 : force is increased MA < 1 : distance is increased MA = 1 : only direction is changed

Mechanical Advantage  A worker applies an effort force of 20 N to open a window with a resistance force of 500 N. What is the crowbar’s MA? GIVEN: F e = 20 N F r = 500 N MA = ? WORK : MA = F r ÷ F e MA = (500 N) ÷ (20 N) MA = 25 MA FrFr FeFe

Mechanical Advantage  Find the effort force needed to lift a 2000 N rock using a jack with a mechanical advantage of 10. GIVEN: F e = ? F r = 2000 N MA = 10 WORK : F e = F r ÷ MA F e = (2000 N) ÷ (10) F e = 200 N MA FrFr FeFe

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

Lever A lever is 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

Mechanical Advantage Ideal Mechanical Advantage (IMA) frictionless machine Effort arm length Resistance arm length L e must be greater than L r in order to multiply the force.

First Class Lever a.can increase force, distance, or neither b.changes direction of force

Second Class Lever always increases force

Third Class Lever always increases distance

Pulley a.a grooved wheel with a rope or chain running along the groove b.a “flexible first-class lever” LeLe LrLr

IMA of a Pulley equal to the number of supporting ropes IMA = 0 IMA = 1 IMA = 2

Single Fixed Pulley IMA = 1 does not increase force changes direction of force

Block and Tackle combination of fixed & movable pulleys increases force (IMA = 4) may or may not change direction

Wheel and Axle a.two wheels of different sizes that rotate together b.a pair of “rotating levers” IMA = radius of wheel radius of axle

IMA Problems 1. You use a 160 cm plank to lift a large rock. If the rock is 20 cm from the fulcrum, what is the plank’s IMA? IMA = L e L r IMA = (140 cm) ÷ (20 cm) IMA = 7 IMA = ? L r = 20 cm L e = 140 cm

2. A crank on a pasta maker has a radius of 20 cm. The turning shaft has a radius of 5 cm. What is the IMA of this wheel and axle? IMA = ? r w = 20 cm r a = 5 cm IMA = r w ÷ r a IMA = (20 cm) ÷ (5 cm) IMA = 4

3. A steering wheel requires a mechanical advantage of 6. What radius does the wheel need to have if the steering column has a radius of 4 cm? r w = IMA · r a r w = (6)(4 cm) r w = 24 cm rara rwrw IMA = 6 r w = ? r a = 4 cm

Inclined Plane sloping surface used to raise objects

Inclined Plane  How much force must be exerted to push a 450 N box up a ramp that is 3 m long and 1.2 m high? IMA = l ÷ h IMA = (3 m)÷(1.2 m) IMA = 2.5 F e = F r ÷ MA F e = (450 N)÷(2.5) F e = 180 N F e = ? F r = 450 N l = 3 m h = 1.2 m

 A worker exerts a force of 500 N to push a 1500 N sofa 4.0 m along a ramp that is 1.0 m high. What is the ramp’s efficiency? F e = 500 N d e = 4.0 m F r = 1500 N d r = 1.0 m W in = (500N)(4.0m) = 2000 J W out = (1500N)(1.0m) = 1500 J E = 1500 J × 100% 2000 J E = 75% 4.0m 1.0m 500N 1500N

Screw inclined plane wrapped in a spiral around a cylinder

Wedge a moving inclined plane with 1 or 2 sloping sides

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.