**Pulleys**

Calculating pulley forces is very simple. A pulley is a simple moment arm. The force being applied on the rope multiplied by the pulley radius is the torque being applied. But now notice that there are two forces countering each other. This is like two opposite moments, so you would subtract them. Remember, don't be confused by the device itself. Even if the pulley were square, the calculation would still be exactly the same. Can you see the moment arm in this example?

**Moment = Torque = Force_A * Pulley_Radius - Force_B * Pulley_Radius**

**or** **Torque = Pulley_Radius * (Force_A - Force_B)**

You should also note Force C, the force required to hold the pulley up.

**Force C** is always **Force_A + Force_B + pulley_weight**.

**Crowbar - Mechanical Advantage Moment Balancing**

Another example of a moment would be a crow bar. What you have is a beam, a pivot point in the center, and a weight on each end. Now suppose you have two exact same weights. Now move one of those weights real close to the pivot point. What will happen? The weight that did not move would go down. Although the force remained the same, the distance decreased, therefore resulting in a smaller moment. Although this example looks very different from the rest, it is actually exactly the same.

Both sides of the crowbar create a moment about the **pivot point** (the triangle tip). So your equation is this:

**Moment Side A = Moment Side B**

**Force_A * Length_2 = Force_B * Length_1**

Now if you knew any three variables out of the four, you can use simple algebra to calculate the fourth one.

For example, suppose this was a see-saw at a childrens' playground. Now you have a 40 pound child sitting on one end, and you plan to catapult him into the next playground. Now this child is sitting exactly 4 feet from the pivot point. Your plan is to jump on it with your weight of 200 pounds. What is the closest distance to the pivot point you can stand on the see-saw and still lift the child into the air?

filling in the equation:

**40 lbs * 4 ft = 200 lbs * distance**

solving:

**40 * 4 / 200 = distance = .8 feet**

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