1. Six Simple Machines Lever Wheel & Axle Pulley Inclined Plane Wedge
Screw
Part 2
In Part 1, we focused our attention on vocabulary, formulas and applications for three of the simple machines: ** the Lever, the Wheel and Axle and the Pulley. ** In this lesson, we will continue our discussion of Simple Machines by talking about the Inclined Plane, the Wedge and the Screw.

2. Mechanical Advantage (MA)
Key Terms
Effort (E)
Load (R)
In Part 1, we talked about three important terms associated with simple machines.
** Effort is the input force which must be applied by the user or an engine of some type.
** Load or resistance is the output force resisting motion.
** Mechanical Advantage is a measure of how much the effort is decreased by using a simple machine. We defined Mechanical Advantage as Load divided by Effort.
If any of these terms seem unfamiliar, we invite you to stop this lesson, and review the material from Simple Machines Part 1. If you are comfortable, let’s begin with the simple machine known as the inclined plane.
Mechanical Advantage (MA)

3. The Inclined Plane ** To start animation of objects
An inclined plane is a flat sloping surface along which an object can be pushed or pulled. It is used to reduce the amount of effort needed to lift a load.

4. Geometry and DefinitionsB H L R E 
If we look at a diagram of an inclined plane, notice how the plane ** makes an angle theta with the ground (a horizontal line).
** A load R is being raised from point A to point B. ** The height from A to B is H. ** The length of the inclined surface is L. **The effort, E, is applied in a direction parallel to the inclined surface.

5. Formulas for Inclined PlanesB H L R E 
MA =
I am sure that you remember this ** formula for Mechanical Advantage from Part 1 on Simple Machines. For the inclined plane, as well as all other simple machines, the mechanical advantage is defined as the Load divided by the Effort.
** There is another formula which applies to this case, and ** that is the mechanical advantage for an inclined plane can also be calculated by taking the ** length of the incline, what we call the hypotenuse in a right triangle, and dividing that by ** the length of the vertical edge. Please note: this formula for mechanical advantage, L divided by H, is only valid if we assume NO friction. Do you remember what we called this in Part 1?
This is the Ideal Mechanical Advantage.

6. Inclined Plane Problem 1
Given the diagram as shown, if L equals 12 inches, H equals 3 inches and the effort is 30 pounds, find the mechanical advantage and the maximum load that can be moved. What is the tradeoff for reducing the effort? A B H L R E 
Let’s look at an inclined plane problem together. I invite you to grab a piece of scrap paper and work along with me. Suppose I am given the diagram as shown. L equals 12 inches, H equals 3 inches and the effort is 30 pounds. Find the mechanical advantage and the maximum load that can be moved. What would be the tradeoff for reducing the effort?

7. Inclined Plane Problem 1, solutionH L R E 
The best place to begin this problem is by calculating the ideal mechanical advantage for the inclined plane, where we assume that the plane is frictionless. ** The ideal mechanical advantage is the length of the incline, divided by the height the object is being lifted, H. ** 12 inches divided by 3 inches, ** gives us an ideal mechanical advantage of 4.
** Now we will use the general formula for mechanical advantage; mechanical advantage is equal to the load divided by the effort.
** 4 is equal to the load, divided by the effort to move the load, 30 pounds.
** Solving this equation algebraically tells us that we are moving a 120 pound load up the inclined plane with a force of 30 pounds.
What is the trade off?
In order to move the 120 pounds 3 inches off the ground, we need to travel a distance of 12 inches along the incline.

8. Wedge ** To start the animation of objects
The wedge is a modification of the inclined plane. It is used to either separate or to hold devices or objects together. There are two major differences between an inclined plane and a wedge.

9. Inclined Plane vs. Wedge
Effort
Effort
During use, ** the inclined plane remains stationary. **The effort is applied parallel to the slope of the incline.
The ** wedge, on the other hand, moves during its use. With a wedge ** the effort is applied to the vertical edge, the height of the incline
Inclined Plane
Wedge

10. Shape of Wedges Double L H Single L H
One can see ** single wedges or ** double wedges. The only difference is the value used for the Height.

11. Formulas for Wedges MA = L L H H Double Single
Do you recognize these formulas? That’s Right ! They are exactly the same ones we were using for the inclined plane. Mechanical Advantage is defined as both the load divided by the effort -- and for a Wedge, the length of the incline divided by the height of the wedge. With this information in hand, let’s try another problem.
Double L H
Single L H

12. Wedge Problem 1
Find the mechanical advantage and the maximum separation load for a wedge with an incline length of 10 inches, an overall height of 4 inches, and which is exerting an effort of 100 pounds.
Find the mechanical advantage and the maximum separation load for a wedge whose incline length is 10 inches, whose overall height is 4 inches and which is exerting an effort of 100 pounds. L H

13. Wedge Problem 1, solution
Effort
MA =
Remember where the effort for ** a wedge is applied: perpendicular to the vertical edge. ** The mechanical advantage for the wedge is the length of the incline divided by the height of the wedge, ** in this case 10 inches divided by 4 inches. We now know that the ** mechanical advantage for this problem is 2.5.
** Don’t forget the general mechanical advantage equation: Mechanical advantage is equal to the load divided by the effort. We will use that equation to find the maximum separation load.
** 2.5 is equal to the load divided by the effort, 100 pounds.
** Solving the problem algebraically, gives us a maximum separation load of 250 pounds.

14. Screw ** to start transitions of pictures
The screw is a modification of the inclined plane. When used with other simple machines, such as a wheel and axle or lever, screws can be used to change rotary motion to straight line or linear motion.

15. Screw Thread Classifications
1/ UNC
1/4 is the outer diameter of the threads.
20 is the number of threads per inch of screw length.
UNC refers to Unified National Coarse thread.
For those of you who visit hardware stores, you know that all screws are not created equally. Screw threads are described with a code,
** for example ¼ - 20 UNC.
** The ¼ refers to the outside diameter of the screw threads.
** The 20 is the number of threads per inch of screw length, while
** UNC refers to Unified National Course thread. This is a standard which is used to define the details of the thread shape.

16. Screw Definitions OD 1in. Number of Threads per Inch View A View A
If we look ** at a sketch of a screw, we can see the number of threads per inch as well as the OD – the outside diameter. Taking a closer look, ** by looking at section view A, we can see that the pitch is the distance between two adjacent threads on a screw.
View A
Pitch

17. Screw Pitch Pitch = 1in. Number of Threads per Inch
The mathematical formula for pitch is that ** pitch is equal to 1 divided by the number of threads per inch of length. We are going to need that formula to calculate the mechanical advantage we get when using a screw.
1in.

18. Screw Formulas
MA =
I bet that at this point in these two lessons, you know the first formula for mechanical advantage: **mechanical advantage is equal to the load divided by the effort. In order to be used, a screw needs to be turned by another simple machine. The total mechanical advantage ** is the circumference of the simple machine that has the effort applied to it (think screw driver), divided by the pitch of the screw.

19. Screw Problem 1
A screw with 20 threads per inch is turned by a screwdriver having a handle diameter of 1 inch. What is the mechanical advantage of the screw?
MA =
Please grab that piece of scrap paper you were using earlier, and let’s look at this problem using a screw.
** A screw with 20 threads per inch is turned by a screwdriver having a handle diameter of 1”. What is the mechanical advantage of the screw?
The mechanical advantage is the ration of the circumference of the screwdriver where the effort is being applied, divided by the pitch of the screw.

20. Screw Problem 1, Solution
Circumference =
Pitch =
First we need to calculate the circumference of the screw driver handle where the effort is being applied. ** Circumference is equal to pi times the diameter, or ** times 1 inch which is inches.
** Next, the pitch. That is ** 1 divided by the number of threads per inch or 1 divided by 20. Therefore, the pitch for this screw is .05 inches per thread.
** The mechanical advantage for a driven screw is the circumference divided by the pitch, ** divided by .05. The mechanical advantage is No wonder it is easier to insert a screw using a screw driver than it is attempting to insert it using only one’s fingers!
MA =