Upon completion of this chapter, you should be able to do the following:

Have you ever tried to open a door when the knob was missing? If you have, you know that trying to twist that small four-sided shaft with your fingers is tough work. That gives you some appreciation of the advantage you get by using a knob. The doorknob is an example of a simple machine called a wheel and axle.

The steering wheel on an automobile, the handle of an ice cream freezer, and a brace and bit are all examples of a simple machine. All of these devices use the wheel and axle to multiply the force you exert. If you try to turn a screw with a screwdriver and it doesnt turn, stick a screwdriver bit in the chuck of a brace. The screw will probably go in with little difficulty.

Theres something youll want to get straight right at the beginning. The wheel-and-axle machine consists of a wheel or crank rigidly attached to the axle, which turns with the wheel. Thus, the front wheel of an automobile is not a wheel-and-axle machine because the axle does not turn with the wheel.

How does the wheel-and-axle arrangement help to magnify the force you exert? Suppose you use a screwdriver bit in a brace to drive a stubborn screw. Look at figure 3-1, view A. You apply effort on the handle that moves in a circular path, the radius of which is 5 inches. If you apply a 10-pound force on the handle, how much force will you exert against the resistance at the screw? Assume the radius of the screwdriver blade is 1/4 inch. You are really using the brace as a second-class leversee figure 3-1, view B. You can find the size of the resistance by using the formula

In that

1 = one-half the width of the edge of the screwdriver blade,

Substituting in the formula and solving:

This means that the screwdriver blade will turn the screw with a force of 200 pounds. The relationship between the radius of the diameters or the circumferences of the wheel and axle tells you how much mechanical advantage you can get.

Take another situation. You raise the old oaken bucket, figure 3-2, using a wheel-and-axle arrangement. If the distance from the center of the axle to the handle is 8 inches and the radius of the drum around which the rope is wound is 2 inches, then you have a theoretical mechanical advantage of 4. Thats why these rigs were used.