Pulleys

Pulleys - Mechanical Advantage of Simple Machines

Mechanical Comprehension Tests often address pulleys, so it’s important to understand the advantages of pulleys and how they work.

First, let’s talk about a simple fixed pulley. A fixed pulley is when a rope or chain or something similar is wrapped around a wheel, or axle in order to raise or move a weight. Like the image to the left. In this case, the wheel (axle) simply changes the direction of the force exerted to move the weight.

This all changes when a double pulley (or block and tackle) system is used. When multiple pulleys are used, their mechanical advantages increase and the weight becomes easier to move. Let’s look at some examples.

Here we have a block and tackle, or moveable pulley system. One pulley is still fixed (in this case, to the ceiling) while the other moves with the object itself. Here we can see the force exerted by someone pulling is 50 newtons. That force goes around the pulley and acts on the weight, but then it goes around the second pulley, once again acting upon the weight, because that original 50 newtons of force acts toward raising the weight every time it circles a pulley. This provides a significant advantage, as you can see here, since the person pulling can raise a 100 newton weight with only 50 newtons of force. (Of course, in these examples, and likely many of the problems you will see, friction is neglected.)

The mechanical advantage of a four legged (that’s what the lines between pulleys are called) pulley is equal to four times the effort initially expended toward moving the object.

The equation to find out how many times the rope or should wrap between the fixed block pulley and the moveable pulley is the same equation used to find the mechanical advantage:

Here, MA = mechanical advantage
W = weight
T = tension or force used to pull
n = number of legs, or times the rope travels between the two pulleys.

Let’s try an example problem:

The man on the right is trying to lift this large package. The package weighs 200lbs. How much force does the man have to exert in order to move the package upward?

ANSWER – First, let’s find the mechanical advantage for this pulley system. Using our equation,
it looks like if we have a mechanical advantage of two, because in this case.

n = 2.

So, that means the force of the man’s pull will be doubled… yet even that won’t be enough to lift the 200lb package.

Thanks for watching this video tutorial.

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by Mometrix Test Preparation | Last Updated: December 10, 2021