1. Simple Machines
My name is CJ and I would like to welcome you to this lesson on Simple Machines part 1. This lesson will cover 3 simple machines - the lever, wheel and axle and the pulley. More simple machines are discussed in the lesson Simple Machines part 2.

2. AIM: How can students distinguish between the six simple machines, their attributes, and components

3. Focus Questions 1. What are simple machines and what are their main purposes? 2.     What are some current applications of simple machines? 3. Are gears, pulleys, and sprockets simple machines? Why? 4. Can you identify simple machines around your home or classroom? 5. What are some strategies that can be used to make everyday mechanisms more efficient?

4. Six Simple Machines Lever Wheel & Axle Pulley Inclined Plane Wedge
Screw
Remember, there are six simple machines in all: ** The lever, ** the Wheel and Axle, ** the Pulley, ** the Inclined plane, ** the Wedge and ** the Screw.
** We are going to focus our attention on the first three this lesson and ** examine the last three in the lesson entitled Simple Machines Part 2.

5. Simple Machines are used to:
1. Transfer kinetic energy (the energy of motion)
2. Reduce the effort needed to move a heavy load
3. Change the direction or amount of motion
4. Change the type of motion (rotary to straight line)
All simple machines are used to do at least one of the following:
** To transfer Kinetic energy, the energy of motion
** To reduce the effort needed to move a heavy load
** To change the direction or the amount of motion
** To change the type of motion, from a rotary motion to a straight line motion or visa versa.

6. Key Term: Effort, Load
Effort (E) is the input force which must be supplied by the user or an engine of some kind.
Load (R) is the output force. It is also the force resisting motion.
When a simple machine is used, two forces are always involved. ** The force applied to the machine is called the effort force. We usually assign the letter E to this force.
** The force acting in resistance or in opposition to the effort is the load. The letter R is commonly used whenever resistance or load is specified.

7. Key Term: Mechanical Advantage
Mechanical Advantage (MA) is a measure of how much the effort is decreased by the simple machine.
** Mechanical Advantage, abbreviated MA is a measure of how much the effort is decreased by the use of a simple machine. ** Mathematically, mechanical advantage is described as the Load divided by the Effort, ** or R divided by E.

8. Mechanical Advantage Actual Mechanical Advantage
Ideal Mechanical Advantage
** Mechanical Advantage, as defined by the ratio of forces, is also referred to as Actual Mechanical Advantage. This is because the mechanical advantage can be directly measured.
** Mechanical Advantage can also be defined by the geometry or dimensions of the various simple machines. This method is referred to as “Ideal Mechanical Advantage” because it does not include the effects of friction.
Actual and Ideal Mechanical Advantage are equal if, and only if, the friction is zero, which of course is practically impossible in the real world.
Defined by the geometry or dimensions of the various simple machines

9. Key Terms: Work
Work : The force applied on an object times the distance traveled by the object.
Work = Force * Distance = F*d
** In physics, Work is defined as the force applied on an object times the distance traveled by the object.
** Mathematically that means that work is equal to the F times D.
** To bring up diagram,,,,
Simple machines are used to do work by applying an effort to move a load. The amount of work done is the same, regardless of how much mechanical advantage a simple machine provides.
In other words, the product of the effort times the distance traveled will be the same no matter how much mechanical advantage one gets from the simple machine.

10. Levers
The lever is a rigid bar which pivots at a point called the ** fulcrum. The forces on the lever are the ** Effort (E) and the ** load (R).
In order for the lever to be “balanced” or in equilibrium, the turning effect of each force must be equal. The turning effect of a force is called a Moment or Torque.
To be “balanced” or in equilibrium, the turning effect of each force must be equal.

11. Key Term: Moment Moment = Force x distance to fulcrum CW (-) CCW (+)
The moment is defined as being equal to the Force x distance to fulcrum. The distance must be measured perpendicular to the direction of the force.
Moments or torques can be either positive or negative based on the direction they are turned. ** Negative values are assigned to those that turn clockwise while ** positive values are those that are turned in a counter clockwise direction. Let’s look at an example of a lever in equilibrium.

12. Force 1 x distance 1 = Force 2 x distance 2
Lever in Equilibrium
Moment 1 = Moment 2
Force 1 x distance 1 = Force 2 x distance 2
300 lb x 4 ft = 1200 lb x 1 ft
1200 ft-lb = 1200 ft-lb
Added units; no audio changes needed
** The moment from the ** left side of the fulcrum which we will call moment 1 must ** equal the moment on the right side of the fulcrum, moment 2 for this lever to be in equilibrium. This means that ** Force 1 times distance 1 must equal force 2 times distance 2.
** 300 pounds times 4 feet, must be equal to 1200 pounds times 1 foot.
** Each side of the equation simplifies to be 1200 foot pounds. This example IS in equilibrium.

13. Lever – Mechanical Advantage
For this example, the ** mechanical advantage is the Load divided by the Effort. The load is 1200 pounds divided by the effort of 300 pounds which yields a mechanical advantage of 4.
Notice that the unit of pounds is on the top and bottom. This means that they cancel each other out. The result is that mechanical advantage has no units.

14. Lever – General Terms E = Effort R = Load
LE = Length (distance) from fulcrum to Effort
LR = Length (distance) from fulcrum to Load (R)
In general terms, the Lever can be described as follows:
** E is equal to the effort
** R is equal to the load
** LE is the length or distance from the fulcrum to the Effort
** and LR is equal to the length or distance from the fulcrum to the Load or resistance.

15. For All Simple Machines
The formula we have been using to define Mechanical Advantage: ** Load divided by Effort, is a key formula which will be used with all simple machines. However, how mechanical advantage is defined will change from one simple machine to the next.

16. MA for Levers =
As we saw earlier, the mechanical advantage for levers can be thought of as the ** length to the Effort divided by the length to the Load or ** LE divided by LR. =

17. MA For Levers – 2 =
If we take that thought process one step further and combine both equations we have seen to this point: ** Mechanical Advantage being equal to LE divided by LR and ** Mechanical Advantage equaling the Load divided by effort, we can establish another ** mathematical relationship: ** LE divided by LR is equal to ** L divided by R.
Last, we can re-arrange terms algebraically to yield ** the distance from the fulcrum to the effort, LE, times the effort E is equal to the distance from the fulcrum to the Load, LR, times the Load or resistance. It is time to start to apply what we have been thinking about to this point.

18. Lever Problem 1 MA Increases
Suppose you were given a 6’ board and a log to use as a fulcrum and you wanted to lift a heavy object a short distance. Where would you place the log? Why?
Locate the log as close as possible to the load
LE becomes very large.
Suppose you were given a 6’ board and a log to use as a fulcrum and you wanted to lift a heavy object a short distance. Where would you place the log? Why?
This type of problem is very important to give to your students. Knowing how to manipulate mathematical formulas is important, knowing HOW and WHY are just as important.
So what do you think? Where would you place the log? Why would you place it there?
(pause)
** To maximize mechanical advantage, locate the log as close as is humanly possible to the load. In this way, you will create a situation where the distance from the Effort to the fulcrum is very large when compared to the distance from the load to the fulcrum. The mechanical advantage will increase.
LR becomes
very small.
MA Increases

19. STOP
STOP

20. Simple Machines ****** Levers Wheel and axle Pulleys
My name is CJ and I would like to welcome you to this lesson on Simple Machines part 1. This lesson will cover 3 simple machines - the lever, wheel and axle and the pulley. More simple machines are discussed in the lesson Simple Machines part 2.

21. There are three
Classes of
Levers

22. Lever
A rigid bar used to exert a pressure or sustain a weight at one point of its length by the application of a force at a second and turning at a third on a fulcrum.

23. Classes of Levers : 1st Class
If LE > LR, then MA >1
If LE<LR, then MA<1
** First class levers are those that have the fulcrum located in the center of the lever arm, and the effort and load at opposite ends. 1st Class levers can have a mechanical advantage greater than or less than one depending on the values of LE and LR.
** If LE > LR then MA >1. ** An example would be a pair of pliers.
** If LE<LR then MA<1. ** Salad Tongs would be an example of this state.

24. 1st Class Lever
Fulcrum is located between the effort and the resistance force
Effort and resistance forces are applied to the lever arm in the same direction
Only class of lever that can have a MA greater than or less than 1
MA =1
Effort
Resistance
Resistance
Effort
MA <1
Effort
Resistance
MA >1

25. Classes of Levers: 2nd Class
Since LE > LR, then MA >1
Second class levers are those that have the weight, or the load, in between the fulcrum and the effort. ** Second class levers must have a mechanical advantage greater than one because LE, the length from the Effort to the fulcrum is always larger than LR, the distance between the load and the fulcrum as the picture illustrates. ** A wheelbarrow is an example of a second class lever. Can you think of another one?

26. 2nd Class Lever Fulcrum is located at one end of the lever
Resistance force is located between the fulcrum and the effort force
Resistance force and effort force are in opposing directions
Always has a mechanical advantage >1
Resistance
Effort

27. Classes of Levers: 3rd Class
If LE < LR, then MA <1
** The third and class of levers are those where the effort is applied at the middle of the arm, and the weight or load is held at one end while the fulcrum is at the other. Take a moment and think about the mechanical advantage for the 3rd class lever.
** Since the distance from the effort to the fulcrum is shorter than the distance from the fulcrum to the load, the mechanical advantage is less than one.
** Anyone who has dug a hole or shoveled snow, would recognize a shovel as being a 3rd class lever.

28. 3rd Class Lever Fulcrum is located at one end of the lever
Effort force is located between the fulcrum and the resistance
Resistance force and effort force are in opposing directions
Always has a mechanical advantage < 1
Resistance
Effort

29. Lever Problem 2 Given: LR = 2 ft , LE = 6 ft , E = 1 lb Find R.
Solution:
Please grab a piece of scrap paper and a pencil to try a couple of problems about Levers before we move onto the Wheel and Axle.
Here is the first one:
** Given that the length from the load to the fulcrum is 2 feet, the distance from the effort to the fulcrum is 6 feet, and the effort being used is one pound, what is the resistance or load?
Pause the lesson, jot down your solution, and restart the lesson when you have the answer.
Lets start with the equation that LE divided by LR is equal to the Load divided by the Effort.
** Substituting the knowns into the equation: 6 feet divided by 2 feet is equal to R divided by 1 pound and algebraically solving the problem tells me ** that the Resistance or load is equal to 3 pounds.

30. Lever Problem 3 Given: R = 8 lb , LE = 4 ft , E = 4 lb Find LR.
Solution:
Let’s use the same diagram. This time find the distance from the load to the fulcrum if the load is 8 pounds, the distance from the fulcrum to the effort is 4 feet and the effort needed to lift the load is 4 pounds. Once again, please take a moment to work on this problem. Pause the lesson, and rejoin me when you have an answer.
** My solution, using the ** same formula as I did in the previous problem was 2 feet. What did you get?

31. Lever Moment Calculation
Effort
Resistance
5.5 in. ?
36 2/3 lb
15 lb
15 lbs
Using what you know regarding static equilibrium, calculate the unknown distance from the fulcrum to the resistance force.
Static equilibrium:
Effort Moment = Resistance Moment
82.5 in.-lb = 36 2/3 lb x DR
82.5 in.-lb /36.66 lb = DR
DR = 2.25 in.

32. Lever IMA ______________________ Resistance Effort
Both effort and resistance forces will travel in a circle if unopposed.
Circumference is the distance around the perimeter of a circle.
Circumference = 2 π r
DE = 2 π (effort arm length)
DR = 2 π (resistance arm length)
______________________
2 π (effort arm length)
IMA =
2 π (resistance arm length)

33. Lever AMA
The ratio of applied resistance force to applied effort force
2.25 in.
5.5 in.
32 lb
16 lb
Effort
Resistance
What is the AMA of the lever above?
AMA = 2:1
Why is the IMA larger than the AMA?
IMA = 2.44:1
What is the IMA of the lever above?

34. Efficiency The ratio of AMA to IMA No machine is 100% efficient.
In a machine, the ratio of useful energy output to the total energy input, or the percentage of the work input that is converted to work output
The ratio of AMA to IMA
What is the efficiency of the lever on the previous slide? Click to return to previous slide
AMA = 2:1
Efficiency
= .82 or 82.00%
IMA = 2.44:1
No machine is 100% efficient.

35. STOP
STOP

36. Wheel and Axle - 2nd Class Lever
A wheel and axle can be thought about as being created with either a rotating 2nd class lever or 3rd class lever.
** As a rotating second class lever, the effort is applied at the wheel and the load or resistance is applied at the axle. Take a moment to think: Is the mechanical advantage greater than or less than one?
(pause)
Since the distance from the effort to the fulcrum, the center of the circles, is greater than the distance from the fulcrum to the load, the mechanical advantage is greater than one.

37. Wheel and Axle – 3rd Class Lever
How about a wheel and axle which is a rotating 3rd class lever?
** In this case, the effort is applied at the axle and the resistance or load is at the wheel. What about the mechanical advantage in this scenario? Is it greater than or less than one?
(pause)
Since the distance from the fulcrum to the effort is less than the distance from the fulcrum to the load, the mechanical advantage is less than one.

38. Formulas for Wheel & Axle
Whether based on a ** 2nd class lever, or a ** third class lever, the formulas for working with wheels and axles are no different from the ones we have worked with up to this point.
** Mechanical advantage is defined as the load divided by the effort, R divided by E.
** For a wheel and axle, mechanical advantage is also described by the radius, or length of the segment from the fulcrum to the effort, divided by the radius from the fulcrum to the load: LE divided by LR. MA =

39. Wheel & Axle IMA
Ǿ6 in.
Ǿ20 in.
Both effort and resistance forces will travel in a circle if unopposed.
Circumference = 2 π r or π d
______________________
IMA =
(effort diameter)
(resistance diameter)
What is the IMA of the wheel above if the axle is driving the wheel?
6 in. / 20 in. = .3 = .3:1 = 3:10
What is the IMA of the wheel above if the wheel is driving the axle?
20 in. / 6 in. = 3.33 = 3.33:1

40. Wheel & Axle AMA
Ǿ6 in.
Ǿ20 in.
200lb
Use the wheel and axle assembly illustration to the right to solve the following.
70lb
What is the AMA if the wheel is driving the axle?
200lb/70lb = 2.86 = 2.86:1
What is the efficiency of the wheel and axle assembly?
2.86/3.33 = .859 or 85.9%

41. Example
An example of this would be a steering wheel on a car. The driver’s hands supply the effort, the steering mechanism provides the load. The larger the steering wheel diameter, the greater the mechanical advantage and the easier it is to turn the wheel. But remember our price for any mechanical advantage greater than one: the hands have to travel a longer distance as the wheel gets larger.

42. Wheel & Axle: Problem 1
Suppose a wheel with a 12 inch radius is used to turn a water valve stem of radius .5 inches. What is the mechanical advantage? MA =
Ready to try a Wheel and axle problem? Pause the lesson while you try this one:
Suppose a wheel with a 12 inch radius is used to turn a water valve stem, of radius .5 inches. What is the Mechanical Advantage?
(pause)
** This formula looks familiar, doesn’t it?
** Since the wheel is turning the water stem valve, the radius of the effort, LE, is 12 inches, while the radius of the load, LR, is .5 inches. 12 inches, divided by .5 inches is 24. That is the mechanical advantage.

43. Wheel & Axle: Problem 2
Consider an axle used to drive the wheels of a car. The wheel radius is 15 inches, while the axle radius is 1 inch. What is the mechanical advantage? MA =
How about a car problem this time?
Consider an axle used to drive the wheels of a car. The wheel radius is 15 inches, while the axle radius is 1 inch. What is the mechanical advantage?
(pause)
** This time the mechanical advance is much less than one. It is .067 (67 thousandths).

44. Wheel & Axle – Rotary to LinearS
S = Distance traveled in one revolution
= Circumference of wheel
= Pi * Wheel Diameter
= * D
The Wheel and Axle can be used to convert rotary motion to linear motion. Consider a wheel and axle rolling on the ground. As the wheel turns, the wheel and axle travel in a straight line. Rotary motion has been changed to linear motion. To calculate the distance traveled in one revolution of a wheel, we use formulas associated with circles.
** S is the distance traveled by the wheel in one revolution which is ** also known as the circumference of the wheel. The formula for circumference is ** pi times the diameter, or ** approximately times D.

45. STOP
STOP

46. Pulley & Belt
Mechanism can increase torque or speed and can run in reverse
Input and output shafts are parallel and rotate in the same direction
Slipping of the belt may occur

47. Three Types of Pulleys MA = 1 MA = 2 MA = 3 E Fixed Pulley
There are three types of pulleys. There is the ** Fixed pulley. This type of pulley is attached or fixed to a strong, stationary member. When a fixed pulley is used, the effort and the load are equal. If the load is lifted one foot, then the rope needs to be pulled one foot. If the load is 50 pounds, it will take a force of 50 pounds to move it.
** The mechanical advantage for this pulley is 1. The end strand is not counted since it is pointing down.
** The second type of pulley is a moveable pulley. A moveable pulley is attached to the moving load. The effort is half the load. If the load is lifted 1 foot, the rope needs to be pulled two feet. If the load is 50 pounds, it takes 25 pounds of force to move it.
** A moveable pulley has a mechanical advantage of 2. This time the end strand is counted since it is pointing upwards.
** The third type of pulley is known as a block and tackle. It is a system of three pulleys and reverses the direction of the effort so that pulling down can lift and object up. In addition, the effort in this case is one third the load. If the load is lifted 1 foot, it took 3 feet of rope to lift it. If the load weights 75 pounds, it takes 25 pounds of force to move it.
Count the number of strands. What is the block and tackle’s mechanical advantage?
The mechanical advantage is 3.
Movable Pulley
Block & Tackle
MA = 1
MA = 2
MA = 3

48. Pulleys at work
BLOCK & TACKLE
PULLEYS 2

49. Work at Effort end = Work at Load end
Pulleys and Work E
Work at Effort end = Work at Load end
Effort * Dist. traveled by rope =
Load * Dist. moved by Load
The amount of work done at each end of the pulley system is the same. ** Said in another way, the Work done at the Effort end is equal to the word done at the Load end.
** Stated at a formula: the Effort times the distance traveled by rope is equal to the Load times the distance moved by Load.

50. TO DETERMINE THE MECHANICAL ADVANTAGE OF EACH SYSTEM:
Count the number of rope segments on each side of the pulleys, including the free end. If the free end is to be pulled down, subtract 1 from this number. This number is the mechanical advantage of the system!

51. Pulley Formulas MA = The number of strands supporting
the load. The end strand ONLY
counts when the effort is pointing
upward.
** The first formula is one you have seen and will be seeing again in the lesson Simple Machines, Part 2. Mechanical Advantage is equal to the load or resistance divided by the effort.
** For a pulley, one can also calculate the mechanical advantage by counting the total number of strands supporting the load. This only works if there is one continuous rope in the pulley system. The end strand should only be counted when the effort is pointing up.

52. Pulley Example 1
The pulley system shown is used to lift a load of 60 lbs a distance of 2’. How much effort must be applied, and how much rope do you need to pull?
The pulley system shown is used to lift a load of 60 lbs a distance of 2’. How much effort must be applied and how much rope do you need to pull? See what you can do with this problem on your own. Press the pause button and when you have an answer, please resume the lesson.

53. Pulley Example 1 MA = 6 Effort = 10 lb Distance traveled = 2 ft * 6
** This pulley system has a mechanical advantage of 6 when looking at the number of strands. It also uses the formula: mechanical advantage is equal to the Load divided by the Effort. ** Using the values that we know, ** we can solve and find that the ** Effort needed to lift 60 points is 10 pounds of force.
The distance that the rope needs to travel is ** two feet times six. In total the rope moves a distance of 12 feet.

54. Pulleys & Sprockets Pulley Sprocket Method of Transmitting Force Belt
Chain
Advantages
Quiet, no lubrication needed, inexpensive
No slip, greater strength
Disadvantages
Can slip
Higher cost, needs lubrication, noisy

55. DO NOW Given: LR = 3 ft , LE = 8 ft , R = 12 lb Find the Effort.
Sept 22, 2011
Given: LR = 3 ft , LE = 8 ft , R = 12 lb
Find the Effort.
Find the M.A.