Re: virus: simple machines

Eric Boyd (6ceb3@qlink.queensu.ca)
Mon, 7 Jun 1999 13:07:25 -0400

Sorry virians,

It appears that somehow I sent the wrong thing in this email -- sorry. (I can't actually figure out what went wrong, since my "sent" folder contains the proper message, but I don't mind posting again)

Here's the real message for the above header:

Wade T.Smith <wade_smith@harvard.edu> writes: <<
And, one of the Virian lessons should be the physics of simple machines.
>>

That's a good idea. I'll start off such a discussion with the basics from my digital encyclopedia:

Simple Machines and Machine Principles

Machines date back to antiquity. Some of the simplest machines are the lever, the wheel and axle, the inclined plane, and the screw. The screw is actually an inclined plane wrapped around a cylinder or cone. Modifications of simple machines are wedges, pulleys, hoists, cranks, and gears. All of these devices are used to redirect forces or motion to perform specific tasks



Excerpted from Compton's Interactive Encyclopedia Copyright 1994, 1995, 1996, 1997 The Learning Company, Inc. All Rights Reserved.

Simple Machines

Many principles of mechanics are clearly demonstrated in devices called simple machines. A number of these machines have been known since antiquity and have come to form the basis of many components in modern machinery. Among these devices are the lever, the wheel and axle, the inclined plane, the screw, and the rope-and-pulley system. All are designed to amplify the effect of forces or to do work--that is, to exert forces over certain distances in order to move weights or to overcome resistances.

A lever allows a small force applied at one end to lift a large weight at the other. It is a stiff bar that rotates about a fixed point, known as a fulcrum (F). Force is applied at some point (often called E for effort) along the bar. As a result, at some other point (often called R for resistance), the bar exerts force to move a weight or overcome a resistance. The distance between the point of effort and the fulcrum (E-F) is called the effort, or input, arm, and the distance between the fulcrum and the resistance (F-R) is called the resistance, or output, arm.

What the lever will do depends first of all upon where the effort, fulcrum, and resistance may be along the bar. In the first-class lever, the fulcrum is between the effort and resistance. Examples include a crowbar and a pair of scissors. In second- and third-class levers the effort and resistance are on the same side of the fulcrum. In the second class, the resistance is between the fulcrum and the effort, as in a wheelbarrow. In the third class, the effort is between the fulcrum and the resistance, as in an arm bending at the elbow in order to lift a weight.

The amount of weight that a person can move or the amount of resistance that can be overcome depends upon the distance through which points E and R move in turning around the fulcrum. This principle is known as the law of ideal machines: the applied force multiplied by the distance through which it acts equals the output force multiplied by the distance through which it moves. The actual movements in lever actions are portions of circles, made as a lever turns around its fulcrum, but the relative distances through which the forces move can be calculated from the lengths of the input and output arms.

The law of levers can be applied in various ways. For first- and second-class levers, the law implies that favorable ratios for lifting weights can be obtained depending on the relative lengths of the input and output arms. For example, for a given force applied at E, E x EF = R x RF, where EF is the length of the input arm and RF is the length of the output arm. If the input arm EF is four times as long as the output arm RF, the input force will be amplified fourfold--that is, the output force will be four times the applied force. Whenever the input arm is longer than the output arm, the lever allows a small input force moving through a certain distance to lift a large weight through a smaller distance. The ratio of the output force divided by the applied force, R/E, is known as the mechanical advantage of the lever.

A different mechanical advantage is given by a third-class lever, such as a person's arm. Here the muscles can lift the forearm at the fulcrum or point of attachment, the elbow, only a short distance, whereas the full length of the forearm can lift a weight held in the hand a much greater distance. There is also an advantage in speed of movement, since the weight is moved a greater distance than the point where the force is applied. To gain this double advantage, however, the muscles must exert a force correspondingly greater than the weight held in the hand. The same sort of advantage can be gained from a first-class lever by making the input arm shorter than the output arm.

Special forms of levers are used in many common machine parts. A windlass, for example, can be used to hoist a heavy weight with minimum effort, but many turns of the crank are required. Cranks and cams are often used to transform one type of motion into another.

The law of ideal machines may also be stated in terms of work and energy: in the absence of resistances, the work done by the applied force E must equal the energy put into R. Thus while a machine can be used to increase forces, it cannot be used to create energy. A machine can only transform an input of work or energy into an output exactly equal in amount. Only the characteristics, such as distances moved and forces applied and delivered, can be changed. Actually, because of friction, the work done on R is likely to be less than the work expended by E.

A rope-and-pulley system is another simple machine that amplifies the effect of an applied force. Pulling a rope over a single fixed pulley merely changes the direction of the force; the mechanical advantage is unity--that is, the pull must equal the weight. On the other hand, a series of pulleys connected with a single rope replaces lever arms with wheels. Pulling on the free end of the cord amounts to operating the input arm of a lever, and the number of strands running through the moving pulleys determines the advantage obtained. Each strand of rope supports a fraction of the weight: for instance, two strands of rope each support one half of the weight, and a pull of only one half the weight will lift it. However, the pull must be exerted over twice the distance the weight is lifted because each strand of rope must be shortened by the amount of the lift.

One method of determining the mechanical advantage of a pulley system is to isolate the pulley to which the weight is attached. Simply counting the number of strands of rope (excluding the one to which the weight is directly attached) that lead to that pulley yields the mechanical advantage.

Another simple machine is the inclined plane. When a locomotive pushes freight cars up an incline of height H along a track of length L, the force required by the locomotive will be less than if the cars had to be hoisted straight up to a height H. An inclined plane provides a mechanical advantage equal to the ratio of the length of the plane to its height, L/H. Two inclined planes can be set back-to-back to form a wedge. A wedge can be used to overcome resistance other than weight, as in splitting a log: a moderate downward force applied at the end provides increased sideways forces.

A screw can be viewed as an inclined plane wrapped around a cylinder. It can be used to lift weights and also to overcome resistances. It can draw together the jaws of a vise and hold material tightly.

Gears are a variation of the screw. If they are of different sizes, they provide a mechanical advantage. Other types of gears, such as bevel gears and worm gears, are used to turn corners.



Excerpted from Compton's Interactive Encyclopedia Copyright 1994, 1995, 1996, 1997 The Learning Company, Inc. All Rights Reserved.

What do we want to say about simple machines?

ERiC