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## Notes on Machines: Inclined Planes and Pulleys

Last time we studied the concepts of work and energy. Today we will see how those concepts apply to different sorts of machines. Machines are devices that modify or redirect forces in useful ways. Machines do not save work; rather, they redirect or amplify forces in a way to assist in the process of accomplishing a goal. Today we will experiment with two simple machines in class, the inclined plane and the pulley. Both of these are machines, even though the inclined plane has no movable parts. We will see that both machines "trade off force for distance"; they do not save us any work, but they do allow us to use force more effectively.

To see how an inclined plane operates as a machine, let's imagine we want to lift a heavy weight, say 2200N (this is approx 100 lbs)to a height of five meters. Lifting this much weight requires an amount of work given by:

Work = Force x distance = Weight x distance = 2200 N x 5m = 11,000 Joules

Suppose though, we dont have the strength or equipment to lift this object straight up from the ground to a height of five meters. Is there any other way we could get this weight to a height of five meters above the ground? This is clearly where an inclined plane becomes useful. As we will see in class, we can pull an object up an inclined plane and measure the force needed to pull the weight up the ramp. Not surprisingly, we will see that the force required to pull the object up the ramp is less than the weight of the object. Thus, the inclined plane allows us to lift objects by using less force than their weight!

This might sound to some as if the inclined plane is allowing us to save work, since we can lift the object with less force than its weight. However, remember that work is the product of both force (in the direction of motion) and distance through which the force moves. While the inclined plane allows us to use less force than the weight of the object, it also requires that we travel a distance along the plane that is longer than the original five meters. In short, we need to use less force, but we have to travel a longer distance.

In fact, we can relate all these parameters:

Weight of object x height to be lifted = Force need to pull object up ramp x distance along ramp.

So lets say we had a ramp of 30 degrees, and we wanted to lift an object to a height of five meters above the ground. We would have to pull the object through 10 meters along the ramp, but we would only have to use a force equal to half the object's weight.

A second important class of simple machine is the pulley

Pulley systems can range from the simple to very complex, but at their core, all pulley systems have two essential properties:
1) Pulleys redirect the direction of force;
2) By adding ropes to the system, each rope can support the weight of the object, thereby reducing the force needed to lift the object.

The following site has some nice drawings of different pulley designs. The simplest pulley system is shown in the diagram (look for the identifier ppt#276,20 in the URL). In this simple system, the rope merely redirects the force so that you can pull down on the free end of the rope to make the object go up. But since there is only one rope supporting the weight, the force you must exert on the rope to make the weight rise is equal to the weight of the object.

If you go to the next slide (URL identifier ppt#277,21), you see a slightly different pulley. There is still just one rope and one pulley, however, in this configuration, the arrangement of the pulley creates the equivalent of two ropes supporting the weight of the pulley, so that each rope carries half the load, and you only have to exert a force of half the object's weight to lift it. However, this does not save work, since (and you will do this in class) you will see that you have to pull the rope through one meter to lift the weight by a half meter. Again, you will see that if the machine (in this case, the pulley) allows you to use less force, you have to exert that force through a longer distance.

We will experiment with various pulley systems in class.

David B. Slavsky
Loyola University Chicago
Cudahy Science Hall, Rm. 404
1032 W. Sheridan Rd.,
Chicago, IL 60660
Phone: 773-508-8352
E-mail: dslavsk@luc.edu

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