Mechanical Advantage Simple Machines - Lever-Wheel Axle-Inclined Plane-Wedge-Pully-Screw

Welcome to MooMooMath and Science. In this video, let's go over how to calculate the mechanical advantage of a lever, wheel and axle, incline plane, wedge, pulley, and a screw. Let's get started. In this video, let's figure out how to calculate the mechanical advantage of a lever, and at first I will use calculate the mechanical advantage using output and input force, and then one more specifically for the lever. Let's get started. It says a mechanic applies an input force of 30N on a lever and it produces an output force of 90N. What is the mechanical advantage of the lever? Let's go ahead and draw a lever. We have the fulcrum here, and we have an input force of 30N, and an output force of 90N, and we want the MA mechanical advantage. Basically all we do is take the output force, divide it by the input force, and that gives us the MA mechanical advantage. Notice that the 90 divided by 30 is 3, so the MA is 3. Let's look at another example. With this example, it says how much force needs to be applied to a lever with a MA of 4 to lift a 1,200N object. Remember, MA equals output force over input. Let's look at this. We have a lever, and we want to know what the input is, how much effort you have to apply, so we will call that x. We need an output of 1,200N, and we have a MA of 4. Let's just plug in what we have. We know that the MA is 4. We do not know where the output is 1,200N, and we don't know what input. We don't know how much effort we need to apply. We can place 4 over 1, and cross multiply. 4x equals 1,200N. We will divide by 4. These cancel, so x equals 1,200 divided by 4 is 300, and remember your unit of measure is Newtons. We have to apply 300N with a MA of 4 to lift an object 1,200N. Let's work one more. With a lever, you can also calculate the MA using the length of the effort arm divided by the length of the load arm. What is the MA of a lever with an effort arm of 180 cm and a load arm of 60 cm? If we have our lever here, and the effort is applied here, the length of this is the effort arm, and the length here is the load arm. In this, let's just see what we have. We have a MA equals, the effort arm is 180 cm, and the load arm is 60 cm. Centimeters will cancel, and 180 divided by 60 equals 3. The MA equals 3. In this video, let's go over how to calculate the MA of a wheel and axle. We will do two types of problems. One where you calculate the MA, and another one in which we will calculate the size of the wheel. Let's get started. What is the MA of a wheel and axle of a wheel radius of 25 and has an axle radius of 5? The formula you use is wheel radius divided by axle radius. Here is what I am talking about. Here would be a wheel and axle. The gray is the wheel, the dark is the axle. The radius of the wheel is from the center out, and it says it is 25 inches in from. The dark section is the axle, like right here, and it is 5 inches. So we are just going to plug this into the formula. We have 25 inches divided by 5 inches. Remember the units will cancel, and that gives you a mechanical advantage of 5. Let's work another style problem. This problem says, what size wheel radius do you need if you have an axle with a radius of 6 inches if you want a mechanical advantage of 3? Let's go ahead and plug it into the formula. Let's see what we have. We have a wheel radius, that is what we are trying to find. That would be x. The axle radius is 6 inches, and it has a mechanical advantage of 3. I am just going to 3 over 1. I am going to cross multiply x equals 18 inches. Actually, that would be 1x. So we know that if you want a mechanical advantage of 3, the wheel radius needs to be 18 inches. In this video, let's go over how to calculate the mechanical advantage of an inclined plane. You can use one of two formulas. The mechanical advantage is the slant length, which is L over the rise. The slant length is this length right here, and the rise is there. A second way you can use is the angle I am talking about. This angle right here is called the inclined angle. You take 1 over the sine of the angle in radians. Let's work two examples that use both of these formulas. The first problem is what is the mechanical advantage of an inclined plane with a height of 6 inches and a slant length of 12 inches. Remember that the formula is L over V, so the slant length is 12 inches, and the rise is 6 inches. When you divide 12 by 6, you get 2. The mechanical advantage is 2. Now let's work an example where we use an angle. Let's get started with this one. It is a little bit more involved. It says, what is the mechanical advantage of an inclined plane that has an angle and inclination of 20 degrees. The first thing we need to do is convert the degrees to radians. We can do this by multiplying 20 times pi, and I am just going to use 3.16 over 180. When you multiply this out, you get 35 hundredths. Let me give you more detail. When you divide 3.16 or pi by 180, you get 175 ten thousandths. When you multiply 20 times 0.0175, you get 35 hundredths. Now we are going to take this and plug it into the other formula. We are going to go 1, and we are going to divide it by the sine of 35 hundredths. You will use the calculator for this, and when you do that, you get 2.9. Let's go back to our original question. You have an inclined plane that has an angle and inclination of 20 degrees. You get a mechanical advantage of 2.9.10. Let's go over how to find the mechanical advantage of a wedge, and also a pulley system. Let's get started. For a wedge, the mechanical advantage is you just divide the length, which is shown here, by the width, which is shown here. Here is an example. What is the width of 3 and the length of 6 inches? The length is 6 inches, the width is 3 inches, these cancel, 6 divided by 3 is 2, so your mechanical advantage of this wedge would be 2. Now let's look at a system of pulleys. With pulleys, assuming that they are all the same size, you just use, for the mechanical advantage, 2 times n, and n just equals the number of pulleys. Here is an example. What is the mechanical advantage of a pulley system that has 4 pulleys that are all the same size? We are going to go 2, and we are going to plug 4 in for n, and 2 times 4 is 8. That is the mechanical advantage. In this video, let's talk about how to find the mechanical advantage of a screw. This will be a fairly basic video, so we won't be converting between different units. First, let's look at the equation we are going to use. We are going to take pi times the diameter over the pitch. Now, pi times the diameter will give you the circumference. If you look at this picture, the diameter is the length across the screw, and the pitch is the length between the threads. Let's look at our problem, and I will explain this a little bit more. What is the mechanical advantage of a screw that has a diameter of 25 hundredths of an inch and a pitch of 20 threads per inch? Let's go ahead and see what we have and set it up so we can find an answer. First, let's just use 3.14 for pi, and we are going to multiply it by the diameter, and the diameter is given of 25 hundredths of an inch. Then we are going to place that over the pitch, but what we need to do is we need to convert the pitch into the distance between two individual threads. The way we are going to do that is we are going to take one inch and we are going to divide it by 20. When you take one divided by 20, that gives you five hundredths of an inch. I am going to use this number. Now we have the formula set up, and then all we do is multiply and divide. We are going to take 3.14 times 0.25, and that gives you 785 thousandths of an inch, and we are going to divide that. That is the circumference, and we are going to divide that by the pitch of five hundredths of an inch. When you divide these, notice that the units of measure cancel, and that is going to give you a mechanical advantage of 15.7. In summary, all you need is the diameter of the screw and the pitch of the screw, and you can calculate the mechanical advantage. Thanks for watching, and remember, kindness multiplies kindness. Kind someone today.