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Machines

Machines. 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

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Machines

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  1. Machines Machines Machines Force Work Power Mechanical Advantage Ideal Machines 6 Simple Machines Efficiency

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

  3. 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

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

  5. 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 A figure skater lifts his partner, who weighs 450 N, 1.0 m in 3.0 s. How much power is required? F = 450 N d = 1.5 m t = 3.0 s

  6. Forces • Effort Force (Fe) • force applied to the machine • “what you do” • Resistance Force (Fr) • force applied by the machine • “what the machine does”

  7. Work • Work Input (Win) • work done on a machine Win = Fe × de • Work Output (Wout) • work done by a machine Wout = Fr × dr

  8. Ideal Machine Equation • Conservation of Energy • can never get more work out than you put in • trade-off between force and distance Win = Wout Fe × de = Fr × dr

  9. 0.3m 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? Fe × de = Fr × dr (15 N) de = (150 N)(0.3m) de = (150 N)(0.3m) 15N de = 3.0 m

  10. Practice Problem (a) A 500 N student sits 1.5 m away from the fulcrum on one side of a seesaw. A second student is sitting 2.0 m away on the other side of the fulcrum. If the students are perfectly balanced on the seesaw, what is the weight of the 2nd student (in Newtons)?

  11. Practice Problems (a) A 500 N student sits 1.5 m away from the fulcrum on one side of a seesaw. A second student is sitting 2.0 m away on the other side of the fulcrum. If the students are perfectly balanced on the seesaw, what is the weight of the 2nd student (in Newtons)? Fe × de = Fr × dr (500 N) (1.5m)= Fr(2.0m) Fr = (500 N)(1.5m) 2.0 m Fr = 375 N

  12. Practice (b) Draw and label a lever that requires an effort force of 50N to lift 200N of resistance force. Label distances.

  13. Practice (b) Draw and label a lever that requires an effort force of 50N to lift 200N of resistance force. Label distances. 200 N 50N 4.0 m 1.0 m

  14. Work • In an ideal machine... Win = Wout • But in the real world… • some energy is lost as friction Win > Wout

  15. 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

  16. Fr Fe MA 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: Fe = 20 N Fr = 500 N MA = ? WORK: MA = Fr ÷ Fe MA = (500 N) ÷ (20 N) MA = 25

  17. Fr Fe MA Mechanical Advantage • Find the effort force needed to lift a 2000 N rock using a jack with a mechanical advantage of 10. GIVEN: Fe = ? Fr = 2000 N MA = 10 WORK: Fe = Fr ÷ MA Fe = (2000 N) ÷ (10) Fe = 200 N

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

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

  20. Effort arm length Resistance arm length Mechanical Advantage Ideal Mechanical Advantage (IMA) frictionless machine • Le must be greater than Lr in order to multiply the force.

  21. First Class Lever • can increase force, distance, or neither • changes direction of force

  22. Second Class Lever • always increases force

  23. Third Class Lever • always increases distance

  24. Pulley Le Lr • a grooved wheel with a rope or chain running along the groove • a “flexible first-class lever”

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

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

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

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

  29. 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 = ? Lr = 20 cm Le = 140 cm IMA = Le Lr IMA = (140 cm) ÷ (20 cm) IMA = 7

  30. 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 = ? rw = 20 cm ra = 5 cm IMA = rw ÷ ra IMA = (20 cm) ÷ (5 cm) IMA = 4

  31. 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? rw = IMA · ra rw = (6)(4 cm) rw = 24 cm IMA = 6 rw = ? ra = 4 cm rw ra

  32. Inclined Plane • sloping surface used to raise objects

  33. 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? Fe = ? Fr = 450 N l = 3 m h = 1.2 m IMA = l ÷ h IMA = (3 m)÷(1.2 m) IMA = 2.5 Fe = Fr ÷ MA Fe = (450 N)÷(2.5) Fe = 180 N

  34. 4.0m • 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? Win = (500N)(4.0m) = 2000 J Wout = (1500N)(1.0m) = 1500 J E = 1500 J × 100% 2000 J E= 75% Fe = 500 N de = 4.0 m Fr = 1500 N dr = 1.0 m 500N 4.0m 1500N 1.0m

  35. Screw • inclined plane wrapped in a spiral around a cylinder

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

  37. 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.

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