Mechanical Advantage: Definition, Calculations & Equations

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  • 0:02 Mechanical Advantage
  • 0:52 Lever
  • 3:34 Pulley
  • 5:30 Lesson Summary
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Lesson Transcript
Instructor: Rebecca Gillaspy

Dr. Gillaspy has taught health science at University of Phoenix and Ashford University and has a degree from Palmer College of Chiropractic.

If you need to move a heavy object, a simple machine can be used to make your job easier. Learn how simple machines, like levers and pulleys, can be used to gain a mechanical advantage. See mechanical advantage equations and calculations.

Mechanical Advantage

Welcome to the Caveman Olympics! Today's event is rock lifting. Let's meet our two contestants. Caveman A is big and strong, but not the smartest caveman in the clan. Caveman B is a little guy, but what he lacks in muscle, he more than makes up for in brains.

Caveman B understands the concept of mechanical advantage, and he plans on using it to help him win gold. What's mechanical advantage? It is a measure of how much a simple machine multiplies the input force. In other words, Caveman B is going to use a couple of simple machines to make the job of lifting the rocks easier. We will learn more about mechanical advantage and how it is calculated by watching today's event.

Lever

Caveman A will be leading off the competition. He confidently strides over to the rock pile and stands in front of the first rock. He gives the rock a bear hug, and, with a tremendous amount of effort, he lifts the rock off the ground.

Now it's Caveman B's turn. He walks over to the same rock and stands in front of it. He gives the rock a bear hug, but the rock doesn't budge. But Caveman B has a trick up his sleeve. He grabs an 11-foot-long board and a triangle-shaped rock. He is going to make a lever. A lever is a simple machine that involves a rigid bar positioned on a pivot. The pivot, in this case - the triangle-shaped rock - is called a fulcrum. Levers are used to make moving or lifting heavy objects easier.

lever diagram

Let's take a look at how this works. Here we have a bar with a fulcrum placed directly in the middle. You can apply a force on one end of the lever; this is called the input force. The input force produces a force on the other end known as the output force. The output force can be used to lift a heavy load, such as a rock.

With the fulcrum placed in the middle, there is not much of an advantage because the force needed to lift the rock is equal to the amount of force you need to push down. But notice what happens if we move the fulcrum closer to the load.

Lever with adjusted fulcrum

Here we see that the resistance arm, which is the length from the load to the fulcrum is shorter than the effort arm, which is the length from the input force to the fulcrum. This gives us a mechanical advantage, and allows Caveman B to lift the same rock as Caveman A with less force.

We can calculate just how much of a mechanical advantage the lever provides by doing a simple calculation.

mechanical advantage for a lever = length of the effort arm / the length of the resistance arm

For example, when the fulcrum was in the middle, the length of the effort arm and resistance arm were both five and a half feet. The mechanical advantage was 1, which is really no advantage. So, if the rock weighs 100 pounds, it would take 100 pounds of force to lift it. But, if the fulcrum is moved so the resistance arm is only 1 foot long, then the effort arm would be 10 feet long. The mechanical advantage would be 10. Therefore, it would only take Caveman B one-tenth, or 10 pounds of input force, to move the rock.

Pulley

We are ready for round two of our competition. This time the rock weighs 200 pounds. Caveman A walks up to the rock, gives it a bear hug and lifts with all of his might, but the rock does not budge.

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