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Simple Machines Math (Mechanical Advantage, Efficiency, and Energy)

Simple Machines Math (Mechanical Advantage, Efficiency, and Energy). What is an instrument that makes work easier called?. What is an instrument that makes work easier called?. a machine. What are the two types of work involved in using a machine?.

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Simple Machines Math (Mechanical Advantage, Efficiency, and Energy)

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  1. Simple MachinesMath(Mechanical Advantage, Efficiency, and Energy)

  2. What is an instrument that makes work easier called?

  3. What is an instrument that makes work easier called? a machine

  4. What are the two types of work involved in using a machine?

  5. What is an instrument that makes work easier called? Work that goes into a machine (work input) and work that come out of a machine (work output).

  6. Describe the two types of work involved in using a hammer.

  7. Describe the two types of work involved in using scissors.

  8. Describe the two types of work involved in using a rolling pin.

  9. Can a machine increase the work you put into it?

  10. Can a machine increase the work you put into it? No, machines can only change the factors that determine work. work = force x distance Either the force will be multiplied or the distance will be multiplied but never both at the same time.

  11. Mechanical Advantage Mechanical Advantage – a quantity that measures how much a machine multiplies force or distance.

  12. Mechanical Advantage The mechanical advantage tells you how much the force will increase by using a particular machine. The more times a machine multiplies the input or effort force, the better the machine is.

  13. Mechanical Advantage When the mechanical advantage is greater than 1, the machine increases or multiplies the force you apply.

  14. Mechanical Advantage Machines do not increase the work you put into them.The work that goes into a machine can never be greater than the work that comes out of the machine.

  15. Mechanical Advantage Equation mechanical advantage = output force = input distance input force output distance M.A. = Fo = di Fi domechanical advantage = resistance force = effort distance effort force resistance distance M.A. = FR = dE FE dRThe resistance force can be just the weight of the object you are trying to move. (Weight is a force of gravity.) Mechanical advantage has no units.

  16. M.A. Problem 1 What is the mechanical advantage of a crowbar that allows you to put 25 newtons of force into lifting a 250 newton crate?

  17. M.A. Problem 1 M.A. = Fo Fi M.A. = 250 N = 10 25 N M.A. = FR FE M.A. = 250 N = 10 25 N What is the mechanical advantage of a crowbar that allows you to put 25 newtons of force into lifting a 250 newton crate? How many times does the crowbar multiply the force that wasput into it? (Hint: Look at the answer.)

  18. M.A. Problem 2 What is the mechanical advantage of ramp that is 10 m long and 3 m high?

  19. M.A. Problem 2 M.A. = di do M.A. = 10 m = 3.3 3 m M.A. = dE dR M.A. = 10 m = 3.3 3 m What is the mechanical advantage of ramp that is 10 m long and 3 m high?

  20. M.A. Problem 3 A pulley system has a mechanical advantage of 10. a. If a mover uses this pulley to lift a piano with a weigh of 1450 N a distance of 4 m, how much force must the mover use?b. How far will the mover pull the rope?

  21. M.A. Problem 3 a. M.A. = Fo Fi 10 = 1450 N FiFi= 1450 N 10 Fi = 145 N A pulley system has a mechanical advantage of 10. a. If a mover uses this pulley to lift a piano with a weigh of 1450 N a distance of 4 m, how much force must the mover use?b. How far will the mover pull the rope? b. M.A. = di do 10 = di 4 m (10)(4m) = di di = 40 m

  22. Can the work that comes out of a machine be greater than the work that goes into the machine?

  23. Can the work that comes out of a machine be greater than the work that goes into the machine? No, because every machine has some type of friction.

  24. Are any actual machines 100% efficient?

  25. Are any actual machines 100% efficient? There are no machines that are 100% efficient. Every machine deals with friction…some more than others. Friction is a force that opposes motion.

  26. Ideal Machines Ideal Machines are 100% efficient. Ideal Machines do not exist.

  27. What form of energy does friction produce?

  28. What form of energy does friction produce? heat Why? Friction opposes motion.

  29. Efficiency The efficiency of a machine is defined as the ratio of the output work to the input work. efficiency = work output x 100% work input eff = Wo x 100% Wi

  30. Efficiency In an ideal machine… - work output equals work input. - the efficiency is 100%. In real machines… - the efficiency is less than 100%. - work output is less than work input. - loss due to friction and heat.

  31. Efficiency Problem 1 A man uses 419 J of work in removing a nail from a piece of wood with a hammer. The hammer has a work output of 305 J. What is the efficiency of the hammer?

  32. Efficiency Problem 1 A man uses 419 J of work in removing a nail from a piece of wood with a hammer. The hammer has a work output of 305 J. What is the efficiency of the hammer? eff = Wo x 100% Wieff = 305 J x 100 419 J eff = 72.8 %

  33. Efficiency Problem 2 John uses 39 J of energy to move four boxes with the handcart. The work output from the handcart is 32.4 J. What is the efficiency of the handcart?

  34. Efficiency Problem 2 John uses 39 J of energy to move four boxes with the handcart. The work output from the handcart is 32.4 J. What is the efficiency of the handcart? eff = Wo x 100% Wieff = 32.4 J x 100 39 J eff = 83 %

  35. Moment Problems Moment = length  massmomentresistance = momenteffort(length  mass)resistance = (length mass)effort

  36. Moment Problems resistance arm5 m effort arm? m 45 g 22.3 g Solve for the missing quantity.

  37. Moment Problems resistance arm5 m effort arm? m (length  mass)resistance = (length mass)effort(45 g  5 m) = (22.3 g  X)X = 10.09 m 45 g 22.3 g

  38. Moment Problems resistance arm3 m effort arm? m 38 g 13.5 g Solve for the missing quantity.

  39. Moment Problems resistance arm3 m effort arm? m 38 g 13.5 g (length  mass)resistance = (length mass)effort(38 g  3 m) = (13.5 g  X)X = 8.4 m

  40. Energy Energy is the ability to do work.Potential Energy – energy at rest due to position, composition, or compression.Kinetic Energy – energy of motion

  41. Potential Energy potential energy = mass  free fall acceleration  heightPE = m  g  hJ = kg  m/sec2  m1 joule = 1 kg  m2sec 2g = 9.8 m/sec2

  42. Potential Energy Problem 1 A rock climber climbs 63 m to the top of a cliff. If the rock climber has a mass of 85 kg, what is the potential energy of the climber?

  43. Potential Energy Problem 1 A rock climber climbs 63 m to the top of a cliff. If the rock climber has a mass of 85 kg, what is the potential energy of the climber?PE = m  g  hPE = (85 kg)(9.8 m/sec2)( 63 m)PE = 52,479 J

  44. Potential Energy Problem 2 A 1.8 kg book sits on top of a 2.8 m shelf. What is the potential energy of the book?

  45. Potential Energy Problem 2 A 1.8 kg book sits on top of a 2.8 m shelf. What is the potential energy of the book?PE = m  g  hPE = (1.8 kg)(9.8 m/sec2)( 2.8 m)PE = 49.39 J

  46. Kinetic Energy Kinetic energy = ½  mass  speed squaredKE = ½  m  v2J = ½  kg  m2/sec21 joule = 1 kg  m2sec 2

  47. Kinetic Energy Problem 1 What is the kinetic energy of a 35 kg dog running at 2.8 m/sec?

  48. Kinetic Energy Problem 1 What is the kinetic energy of a 35 kg dog running at 2.8 m/sec? KE = ½  m  v2KE = ½  35 kg  (2.8 m/sec)2KE =137.2 J

  49. Kinetic Energy Problem 2 What is the kinetic energy of a 1635 kg car traveling at 29 m/sec?

  50. Kinetic Energy Problem 2 What is the kinetic energy of a 1635 kg car traveling at 29 m/sec? KE = ½  m  v2KE = ½  1635 kg  (29 m/sec)2KE =687,517.5 J

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