What is mechanical advantage?
Well, as the name suggests, it’s the ratio indicating the advantage a given mechanism produces via a multiplied force or torque. Typical mechanisms that produce mechanical advantages include pulleys, screws, and levers. We probably know of these “mechanisms” in a casual sense, and even utilize them on occasion. But let’s dig a little deeper and find out how all this actually works.
Mechanical advantage is often abbreviated MA, and equals the output force divided by the input force. Looking at the equation MA=output force/input force seems simple enough doesn’t it? Mechanical advantage has been around since ancient times, as is evident by the work of Greek philosopher Archimedes and the 6 “simple machines” that utilize this phenomenon – the lever, wheel and axle, pulley, inclined plane, wedge, and screw.
Let’s have a look at the image displaying the pulleys. The relationship between pulleys and their mechanical advantage can be a little tricky to understand at first, but with the help of this diagram and a little explanation, you should have no problem. An MA of 1 has no advantage or disadvantage, regardless of the position of the person doing the work.
Say there’s a 50 kilogram weight that needs to be lifted via pulley to the second floor of a warehouse from the first floor. You will use a fixed pulley attached to the ceiling of the warehouse directly above the weight. Now if you were to do what’s shown in “1” on the image diagram, although you’d have the advantage of being able to use your body weight, you won’t have any actual mechanical advantage.
Why? Because you’re still pulling the exact same distance as the weight is being lifted. There is no division of weight. In other words, with a mechanical advantage present, the distance you pull the rope should be at least double the distance the weight moves. – This signifies the mechanical advantage!
By looking at the following examples on the image diagram you will see that by each increase of MA, the distance you must pull the rope increases. On “2“, whether you are standing on the same level as the weight (with ceiling pulley) or on the second floor pulling upwards (no ceiling pulley), the mechanical advantage is the same – it’s still 2.
You might be wondering what the difference is between “1” and “2” if “2” doesn’t have the ceiling pulley. Well, the difference is that on “2“, the pulley is on the weight and on “1“, the pulley is fixed to the ceiling. If you look carefully, you’ll notice that on “2“, the weight is being divided by the fixed attachment to the ceiling and the person pulling.
You’ll also notice that it passes the acid test of needing double the rope pulled for the same distance the weight is lifted. “1” does not pass this test. So if you’re ever having a hard time remembering how all this mechanical advantage stuff works, just remember: For an MA of 2, the distance the weight is lifted is HALF that of the distance the rope is pulled by the one doing the work! But the force needed to do this is half of what’s otherwise required – thus the advantage.