Machines - Ch. 9 I. Introduction to Machines Machines Force Work Mechanical Advantage

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

B. Force 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

C. 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

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

D. 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

D. 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 crowbars 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

D. 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

C. Work 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

Classwork

Homework Page 290: 5-7

Machines - Ch. 9 II. The Simple Machines Lever Pulley Wheel & Axle Inclined Plane Screw Wedge

A. Lever 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 Effort arm Resistance arm Fulcrum

A. Lever 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.

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

B. Pulley Ideal Mechanical Advantage (IMA) equal to the number of supporting ropes IMA = 0IMA = 1IMA = 2

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

B. Pulley Movable Pulley IMA = 2 increases force doesnt change direction

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

C. Wheel and Axle Wheel and Axle two wheels of different sizes that rotate together a pair of rotating levers Wheel Axle

C. Wheel and Axle Ideal Mechanical Advantage (IMA) effort force is usu. applied to wheel axle moves less distance but with greater force effort radius resistance radius

Problems You use a 160 cm plank to lift a large rock. If the rock is 20 cm from the fulcrum, what is the planks IMA? GIVEN: L r = 20 cm L e = 140 cm IMA = ? WORK : IMA = L e ÷ L r IMA = (140 cm) ÷ (20 cm) IMA = 7 IMA LeLe LrLr 20cm 160cm

Problems 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? GIVEN: r e = 20 cm r r = 5 cm IMA = ? WORK : IMA = r e ÷ r r IMA = (20 cm) ÷ (5 cm) IMA = 4 IMA rere r 5 cm 20 cm

Problems 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? GIVEN: IMA = 6 r e = ? r r = 4 cm WORK : r e = IMA · r r r e = (6)(4 cm) r e = 24 cm IMA rere r r rere

Problems 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? GIVEN: F r = 150 N F e = 15 N L r = 0.3 m L e = ? MA = 10 WORK : L e = IMA · L r L e = (10)(0.3) L e = 3 m Total length = L e + L r Total length = 3.3 m IMA LeLe LrLr 0.3m ? 150N 15N

D. Inclined Plane Inclined Plane sloping surface used to raise objects h l

E. Screw Screw inclined plane wrapped in a spiral around a cylinder

F. Wedge Wedge a moving inclined plane with 1 or 2 sloping sides

F. Wedge Zipper 2 lower wedges push teeth together 1 upper wedge pushes teeth apart

Mechanical Advantage MA l ___ h L e ___ L r # of support- ing ropes N/A r e ___ r r MA = F r / F e

Problems 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? GIVEN: F e = ? F r = 450 N l = 3 m h = 1.2 m WORK : IMA = l ÷ h IMA = (3 m)÷(1.2 m) IMA = 2.5 IMA l h MA FrFr FeFe F e = F r ÷ MA F e = (450 N)÷(2.5) F e = 180 N

Machines - Ch. 9 III. Using Machines Compound Machines Efficiency Power

A. Compound Machines Compound Machine combination of 2 or more simple machines

A. 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.

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

B. Efficiency 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 ramps efficiency? GIVEN: F e = 500 N d e = 4.0 m F r = 1500 N d r = 1.0 m WORK : W in = (500N)(4.0m) = 2000 J W out = (1500N)(1.0m) = 1500 J E = 1500 J × 100% 2000 J E = 75% 1.0m 1500N 4.0m 500N

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

C. Power 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