1. Mechanical Advantage
Simple Machines

2. Objectives for today Discuss simple machines
Know the 6 types
Discuss mechanical advantage
Know the difference between ideal and actual
Be able to compute mechanical advantage for levers
By being able to solve various problems mechanical advantage of levers
Show comprehension of levers and their mechanical advantages by solving equations

3. Machines A machine is a device that does work.
All machines, no matter how complex, are made up of some type of simple machines.
These simple machines include: the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.
Work in = Work out. (there are no shortcuts)
Basically, a simple machine trades distance for force.

4. Simple Machines
A machine transmits mechanical work from one part of a device to another.
It produces force and controls the direction and the motion of the force, but it cannot create energy.
A machines ability to do work is measured by two factors:
Mechanical advantage
efficiency

5. Mechanical Advantage
Mechanical advantage – the ratio of the output force to the input force
Ideal – does not take into account friction or other resistances
Actual – does take into account friction and other resistances.
Ideal Mechanical advantage 𝑰𝑴𝑨= 𝑭 𝒐 𝑭 𝒊
Actual Mechanical advantage 𝑨𝑴𝑨=𝑰𝑴𝑨−𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆𝒔
𝑨𝑴𝑨= 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒐𝒖𝒕𝒑𝒖𝒕 𝒇𝒐𝒓𝒄𝒆 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒊𝒏𝒑𝒖𝒕 𝒇𝒐𝒓𝒄𝒆
Although machines can have a mechanical advantage greater than 1, no machine can do more work than was put into it.

6. Ideal Mechanical Advantage
Ma= Ideal Mechanical advantage
Fo = output force (N)
Fi = input force (N)
di = input distance (m)
do = output distance (height) (m)

7. Efficiency and energy conservation
Efficiency, as we have discussed before, is the ratio of output work to input work. 𝑜𝑢𝑡𝑝𝑢𝑡 𝑤𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡 𝑤𝑜𝑟𝑘
It will never be more than 100% efficient. (This would mean more work goes out than comes in)
Ideal mechanical advantage is 100% efficient (no friction, resistances, or other things that would mean a loss of work)
If work in = work out, then it is 100% efficient
Actual mechanical advantage is always less than 100% (it includes all friction, resistances, or other things that would mean a loss of work)
Some machines can have high efficiencies, some do not.

8. Lever A lever is a bar that rests on a pivot point (fulcrum)
A force (effort) is applied at one point which is transmitted across the fulcrum to another point where the load is located.
This should remind you of a torque problem.
𝑇=𝐹∗𝐿𝑒𝑣𝑒𝑟 𝑎𝑟𝑚 (where the lever arm is the distance from the force to the fulcrum)
When calculating IMA for a lever the torque for the effort and the torque for the load should be equal.
The IMA means that for every N of force on the effort side can move the IMA* the effort on the load side

10. Classes of Levers There are three classes of levers:
1st class - the fulcrum is between the effort and the load
The IMA could be lesser than, equal to, or greater than 1
2nd class – the load is between the effort and the fulcrum
The IMA is always greater than 1
3rd class – the effort is between the load and the fulcrum
The IMA is always less than 1

11. Objectives for today
Be able to recognize the 3 classes of levers based upon identification of fulcrum, load, and effort (worksheet)
Compare wheel and axle to the lever (class 2 or class 3)
Show comprehension of wheels and axles and their mechanical advantages by solving equations
If Time, start discussion on Pulley systems and how the mechanical advantage is tied to their supports.

12. Classes of Levers There are three classes of levers:
1st class - the fulcrum is between the effort and the load
The IMA could be lesser than, equal to, or greater than 1
2nd class – the load is between the effort and the fulcrum
The IMA is always greater than 1
3rd class – the effort is between the load and the fulcrum
The IMA is always less than 1

13. Wheel and Axle
The wheel and axle is basically a modified lever (class 2 or class 3), but it can move a load farther than a lever can.
The center of the axle serves as a fulcrum
𝐼𝑀𝐴= 𝑅 𝑒𝑓𝑓𝑜𝑟𝑡 𝑅 𝑙𝑜𝑎𝑑
In 2nd class levers and similar wheel and axles, the IMA >1
In 3rd class levers and similar wheel and axles, the IMA <1

14. 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.

15. 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).

16. 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.

17. Wheel & Axle: Problem 3
You have the choice of putting a 26 inch diameter tire or a 30 inch diameter tire on your bicycle.
Which tire will increase the top speed of the bike?
How much will the speed change in percent?
Rotary to linear motion problems are ones that students find particularly interesting. Here is an example of what I mean:
You have the choice of putting a 26” diameter tire or a 30” diameter tire on your bicycle? Which tire will increase the top speed of the bike? How much will the speed change in percent?

18. Wheel & Axle: Problem 3, answer.
S = * 26 in. = in.
S = * 30 in. = in.
% Change = (94.23 in in.) * 100
in.
= 15.4 % speed increase
It makes sense that the larger the wheel, the farther distance one would go with each tire revolution.
** With a 26 inch diameter wheel, one would travel a distance of for each revolution of the wheel.
** On a 30 inch diameter wheel, one would travel a distance of inches.
Since linear speed is equal to the distance traveled divided by the time - the larger the wheel, the farther the distance one is able to travel, the faster ones speed will be. Therefore, the 30 inch tire causes the bike to travel faster than a 26 inch tire.
** Calculations show that by increasing the tire size, one can achieve a 15.4% increase in speed.

19. Pulley (Block & Tackle)
A pulley is basically a wheel over which a rope or belt is passed.
It is a form of the wheel and axle
The IMA of a pulley is directly dependent on the number of support strings
𝐼𝑀𝐴=𝑁 where N= the number of support strings
IMA=n-1 if the effort string is being pulled down

20. Basically, every extra support does the same amount of force as the original effort, but it requires more distance moved.
This can be easily explained, each support needs to move the same distance.
The number of supports = the amount the distance is multiplied by.

29. Inclined Plane The inclined plane is a ramp.
The mechanical advantage increases as the slope decreases.
This means the load has further to move, but it is easier to move.
𝐼𝑀𝐴= 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 ℎ𝑒𝑖𝑔ℎ𝑡 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑

31. Wedge The wedge is an adaptation of the inclined plane.
It is normally used to split something apart or change the direction of a force.
The smaller the angle, the higher the mechanical advantage, but less separation.

36. SCrew The screw is an inclined plane wrapped around a shaft.
A screw converts rotational motion to linear motion.
The pitch of a screw is the distance between its threads; this is the distance the screw will advance during one complete rotation.
𝐼𝑀𝐴= 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑒𝑓𝑓𝑜𝑟𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑓𝑡𝑒𝑟 1 𝑡𝑢𝑟𝑛
1 thread = 1turn
Or 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑟𝑒𝑎𝑑 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑐𝑟𝑒𝑤

38. What is the ideal mechanical advantage of a 3
What is the ideal mechanical advantage of a 3.5-cm screw of which the threads measure 9.5 cm in length?

39. What is the ideal mechanical advantage of a 2-cm screw of which the threads measure 10 cm in length?

40. How long is the screw when it has a mechanical advantage of 10 when thread length is 10 inches?