Mechanical advantage is the ratio of force exerted by a machine to the force exerted on it. The most canonical example of an inclined plane is a sloped surface; for example a roadway to bridge a height difference.
One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m. IMA also equals the distance over which the effort is applied, de, divided by the distance the load travels, dr.
Example: Calculate the mechanical advantage if N force is needed to overcome the load of N. An ordinary pulley has an MA of 1; it only changes the direction of the force and not its magnitude. Combinations of pulleys, such as those illustrated in Figure 4, are used to multiply force. This is referred to as a 2 to 1 mechanical advantage, or MA. We can calculate it by simply counting how many parts, or legs, of rope are acting on the pulley: in this case there are 2, so we calculate a advantage.
You can see that his pulling power is doubled, but you might not have realized that the trade-off for his newfound strength is that he must pull twice as much rope to move the load. In other words, if the rope were tied directly to the load, you would need to pull the full weight yourself, but for every foot of rope that you pulled, the load would advance by a foot.
With this MA setup, you only need to pull half as much weight, but to move the load 1 foot up the hill, you must pull 2 feet of rope. Mechanical advantage always involves a trade-off: pulling distance for pulling power. The block and tackle system was reportedly invented by Archimedes himself and has been used for centuries for lifting and pulling jobs of all sorts. The block and tackle system builds on the general concepts that we have been talking about, but it goes one step further. A block and tackle uses two pulleys to multiply the forces in the system.
One pulley is attached to the load and is referred to as the moving pulley. The other is attached to an anchor point. The simplest form of a block and tackle system is a mechanical advantage setup called a Gun Tackle:.
The bottom pulley is functioning exactly the same as our last example, serving to double the pull on the load. The top, or anchor pulley, serves as a re-direct, allowing us to stand on the ground to pull down on the rope. Without the re-direct up top, we would have to stand on the ceiling and pull upwards to get the 2 to 1 advantage, exactly as we did in our previous example where stickman was at the top of the hill and pulling upwards. So, to hold the weight suspended in the air, we pull 50 lb downwards, which gets re-directed by the anchor pulley up top, and then gets doubled by the moving pulley attached to the load, allowing a lb weight to be held with only 50 lb of input force.
The next example is where things really start to get interesting. What if we used multiple pulleys? Here is a simple example of that, and then I will show the equivalent setup with block and tackle:.
Pretty amazing, right? Keep in mind that for stickman to hoist the load upwards, he would have to haul 3 feet worth of rope to make the load move 1 foot. Remember, every mechanical advantage system involves a trade-off, pulling distance for pulling power. The above example can be set up using block and tackle, but instead of requiring two separate pulleys at the anchor, those pulleys are combined into a double pulley. This example is technically referred to as a Luff or Watch Tackle:.
Hopefully by this point, you get the concept. We use pulleys and double pulleys to amplify forces. We require an anchor point and a moving pulley attached to the load, and we require an input force. We can calculate the mechanical advantage by counting the number of legs of rope that are acting on the moving pulley, which is the same as calculating the trade-off of pulling distance for pulling power. There are many definitive sources out there that will dig deeper.
Instead, I want to now focus our attention on the most common applications of mechanical advantage used in tree work. However, for our purposes here, we will need to agree on some assumptions just so we can do some basic math.
These assumptions allow us to use nice, easy numbers. In reality of course, no pulley has perfectly zero friction and pulling angles are not always degrees. So, realistically, when we say that a system is or , it never actually is.
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