Work in a Mechanical System

1. Unit 6 Work in a Mechanical System

2. Unit VocabularyPg 1 - 14 Force applied Mechanical work Work done Joule Efficiency Ratio Radian

3. Unit ReviewPg 15-16 # 1-18

4. Work involves forces that cause movement

5. “Work is getting something done. You can spend a lot of time and effort on something, but if nothing is accomplished, then no work has been done.”

6. When is work done? • When a force or force like quantity causes something to move or change • It can be as big as a crane lifting tons of steel or as small as a tiny charge moving in computer memory

7. Mechanical Work • An applied force must act on an object • The object must move when the force is applied

8. Mechanical Work • Work is also done when a torque causes something to rotate

9. Mechanical Work Fluid • A constant pressure causes a fluid to flow from one place to another

10. Mechanical Work Electrical • Voltage causes charge to move from one place to another

11. Mechanical Work Unified • We can write ONE equation for work that serves as a pattern for the previous four equations

12. Mechanical Work • When a force or torque moves an object • Mechanical systems use force and torque to cause movement and, thus, to do useful work

13. Mechanical Work • Using symbols the equation can be shortened to: Units = Force x distance = foot-pound or Newton-meters

14. Work Lifting a Barbell • Given: A weight lifter applies a vertical force to raise a 200-lb barbell 5 ft. • Find: The amount of mechanical work done in lifting the barbell

15. Work Lifting a Barbell Solution • Work = Force x Distance • = (200lb)(5ft) • = 1000 ft-lb

16. Football Work • Given: A football player pushes a pile of 4 lineman 6 yards. Each lineman weighs 200 pounds. • Find: The amount of mechanical work done pushing the pile.

17. Football Solution Work = Force x Distance Force = (4 lineman x 200lbs) Distance = 6 yards = 18 feet Work = Force x Distance Work = (800lb)(18ft) = 14400 ft-lb

18. Work Done Pulling a Cart • Given: An electric truck is used to pull a loaded cart a distance of 100 meters. A force of 900 newtons is required to keep the cart moving at a constant speed. • Find: The amount of mechanical work done on the cart.

19. Work Done Pulling a Cart • Work = Force x Distance • = (900N)(100m) • = 90,000 N-m

20. Joule (J) • A common SI unit for work or energy • 1 N-m = 1 Joule • 90,000 N-m = 90,000 J • 55 N-m = 55 J

21. Work • Given: 75 Joules are acted on a tennis ball that is thrown • If the tennis ball is thrown with a force of 15 Newtons • Find: How far did the ball travel while the work was applied?

22. Work • 75 J = 75 N-m • Work = (F) x (D) • 75 N-m = (15 N) x (D) • 5 m = D

23. It is important to know that work is only done while the force is applied • Examples: Throwing a ball or a vehicle coasting to a stop • No work is done when the force is no longer applied (even if something is still moving)

24. Work and Efficiency • When work is done it can be rated by efficiency • Comparison of the output work by the input work • A pulley system = block and tackle

25. Work and Efficiency • Pull with force • (F) • Moves a distance • (D) • Load of weight • (w) • Raised a distance • (y)

26. Work and Efficiency • Input work = (F) x (D) • Output work = (w) x (y) • Efficiency is equal to a ratio of the output work to the input work

27. Work and Efficiency % Efficiency = Output Work Input Work x 100%

28. Work and Efficiency • Given: The block and tackle shown is used to lift a 600 lb engine. It is raised 0.9 ft as the operator pulls with a force of 100lb over a distance of 6 ft. • Find: • Input work • Output work • Efficiency

29. Input work • Input work = F x D • F = 100 lb • D = 6 ft • Input work = 100 lb x 6 ft • Input work = 600 ft-lb

30. Output work • Output work = w x y • w = 600 lb • y = 0.9 ft • Output work = 600 lb x 0.9 ft • Output work = 540 ft-lb

31. Efficiency • Efficiency = (Output/Input) x 100% • Output = 540 ft-lb • Input = 600 ft-lb • Efficiency = (540 ft-lb)/(600ft-lb) x 100% • Efficiency = 0.9 x 100% • Efficiency = 90%

32. Work and Efficiency • Given: The block and tackle shown is used to lift a 1 kg mass. It is raised 15 cm as it is pulled with a force of 5.5 N over a distance of 34 cm. • Find: • Input work • Output work • Efficiency 1 kg = 9.8 N 100 cm = 1 m

33. 1 kg = 9.8 N 100 cm = 1 m Input work • Input work = F x D • F = 5.5 N • D = 34 cm = 0.34 m • Input work = F x D • F = 5.5 N • D = 34 cm Input work = 5.5 N x 0.34 m Input work = 1.87 N-m Input work = 1.87 Joules

34. 1 kg = 9.8 N 100 cm = 1 m Output work • Output work = (w) x (y) • w = 1 kg = 9.8 N • y = 15 cm = 0.15 m • Output work = (w) x (y) • w = 1 kg • y = 15 cm Output work = 9.8 N x 0.15 m Output work = 1.47 N-m Output work = 1.47 Joules

35. Efficiency • Efficiency = (Output/Input) x 100% • Output = 1.47 N-m = 1.47 J • Input = 1.87 N-m = 1.87 J • Efficiency = (1.47 J)/(1.87 J) x 100% • Efficiency = 0.786 x 100% • Efficiency = 78.6%

36. How do you measure angles in radians? • Rotational work occurs when torque causes a mass to rotate through an angle • The size of angles is commonly measured in degrees • It can also be measured in radians “rad” • For this we must know π= 3.1416 • And Circumference = 2π r

37. How do you measure angles in radians? Circumference = 360o = 2π r = 6.28 rad

38. How do you measure angles in radians? Circumference = 360o = 2π r = 6.28 rad½ Circumference = 180o = π r = 3.14 rad

39. How do you measure angles in radians? Circumference = 360o = 2π r = 6.28 rad¼ Circumference = 90o = ½ π r = 1.57 rad

40. How do you measure angles in radians? Circumference = 360o = 2π r = 6.28 rad1/8 Circumference = 45o = ¼ π r = 0.785 rad

41. How do you measure angles in radians? • This figure shows 1 radian is equal to 57.3 degrees Circumference = 2 π r Therefore a full circle must equal 2π r = (2)(3.14)(r) = 6.28 rad

42. How do you measure angles in radians? 1 Revolution = 6.28 radians1 Radian = 57.3 degrees

43. How do you measure angles in radians? 1 Revolution = 6.28 radians1 Radian = 57.3 degrees • 7 revolutions • 435 degrees • ¾ revolutions • 14 revolutions • 26 degrees

44. Work Done by Torque • Note: The angle θmust be measured in radians

45. Work Done to operate a pump Given: An electric motor is used to drive a water pump. The motor provides a torque of 150 N-m. Find: How much work is done while the motor turns 40 revolutions? Torque = Force x Lever arm Work = Torque x Angle 1 revolution = 6.28 rad

46. Work Done to turn a crank Torque (is given)= 150 N-m Torque = Force x Lever arm 1 revolution = 6.28rad 40 revolutions = 251.2 rad Θ = 251.2 rad Work = Torque x Angle Work = (150 N-m)(40 revolutions?) Work = (150 N-m) (251.2 rad) Work = 37,680 N-m or … 37,680 Joules

47. Work Done to turn a crank • Given: A simple mechanical winch has a crank handle 1 foot long. A force of 20 pounds is required to turn the crank. • Find: How much work is done in turning the crank 5 revolutions. • Hint: First we must find torque and the angle in radians in order to find work Torque = Force x Lever arm Work = Torque x Angle

48. Work Done to turn a crank Torque = Force x Lever arm • Torque = (20 lb) (1 ft) • Torque = 20 lb-ft 1 revolution = 2π rad Work = Torque x Angle Work = (20 lb-ft)(5 revolutions?) Work = (20 lb-ft) (31.4 rad) Work = 628 ft-lb Θ = (10)(3.14) Θ = 31.4 rad

49. 4 Types of Mechanical Work ? Linear Angular Electrical Thermal

50. Work Done by a Winch Activity