The T Method - Calculate Mechanical Advantage

Video Caption File/Transcript by Arborist Industry Expert Taylor Hamel.

[Music] Taylor Hamel here from DMM on the TreeStuff Channel. This is the T Method for calculating a simple mechanical advantage.

Here's the basic definition of a simple mechanical advantage system: we have the load, which is being lifted or moved, and that is our moving block. We have the anchor point, which is not moving, so there's one stationary block and one moving block in a simple mechanical advantage. We also have various forces here. We've got an input force, which is the force or the tension that I'm placing into the system. We have an output force, which is at the load or the moving block, and we have a reaction force, which is at the anchor point.

Now, to calculate these forces, we can use a method called the T Method. Before we get into the T Method, though, we need to talk about friction in the system. An ideal mechanical advantage assumes that there is no friction in the system, so when we do this T Method here, we're assuming that there's no friction. But in real life, you're going to have friction losses in the system, so you need to consider that to determine the actual mechanical advantage.

So, the T Method: I am inputting some force here. We're going to call that one T. When this rope travels around the moving block, we end up with one T on this leg of rope and one T on that leg of rope. We total that up: 2T. We only have one T, however, at the anchor point. So we've got an input force of one T, an output force of two T, and a reaction force of one T. The ratio between input and output—that is our ideal mechanical advantage. In this case, a two-to-one.

A little late on the snap. Am I doing another cold thing?

All right, let's look at this same system with the redirect at the anchor point. So, using the T Method: one T on this leg of rope, one T this leg, one T that leg. Now we sum them where they make a bend, so we have 2T at that point. We have 2T at the output, one T at this point. So we have an input force of one T, we have a reaction force of 3T, an output of 2T. So we have the same mechanical advantage; we just have a change of direction in the rope to change our pulling angle—two-to-one.

I should probably redo—All right, let's look at the nested—okay, let's look at the next—

Okay, let's look at the next example. Can you guess what the mechanical advantage is here? Well, let's use the T Method and find out. We've got one T input force here, one T on this leg of rope, one T on that leg of rope, 2T at this portion, 2T at the anchor, and another one T here. We sum those for 3T at the moving block. Our input force is one, our output force is three—that's a three-to-one mechanical advantage.

All right, continuing on.

Here's our final example. Can you guess the mechanical advantage? Let's use the T Method and find out. Input force: one T, one T, one T, one T, and one T. We've got 2T here, 2T, 2, 2, and one. So if we count the T's at the load, at the moving block, we get four. Input force of one, four T at the moving block—that's a four-to-one mechanical advantage. We have five T at the anchor—that's a reaction force of five.

Check out our next video when we describe the difference between ideal mechanical advantage and actual mechanical advantage and talk about friction in the system.