Fig. 101.—An inclined plane.
Or while the weight is being lifted the vertical height BC, the effort has to move the length of the plane AC. Since by the law of machines the effort times its distance equals the weight times its distance, or the weight is to the effort as the effort distance is to the weight distance, therefore the mechanical advantage of the inclined plane is the ratio of the length to the height of the inclined plane.
Inclined planes are used to raise heavy objects short distances, as barrels into a wagon, and iron safes into a building. Stairways are inclined planes with steps cut into them.
128. The Wedge.—Wedges are used to separate objects, as in splitting wood (see Fig. 102), cutting wood, and where great force is to be exerted for short distances. An axe is a wedge, so is a knife. A fork consists of several round wedges set in a handle. The edge of any cutting tool is either an inclined plane or a wedge. Our front teeth are wedges. Numerous examples of inclined planes may be seen about us.
No definite statement as to the mechanical advantage of the wedge can be given as the work done depends largely on friction. The force used is generally applied by blows on the thick end. In general, the longer the wedge for a given thickness the greater the mechanical advantage.
Fig. 102.—One use of the wedge.
129. The Screw.—The screw is a cylinder around whose circumference winds a spiral groove. (See Fig. 103.) The raised part between the two adjacent grooves is the thread of the screw. The screw turns in a block called a nut, within which is a spiral groove and thread exactly corresponding to those of the screw. The distance between two consecutive threads measured parallel to the axis is called the pitch of the screw. (See Fig. 104.) If the thread winds around the cylinder ten times in the space of 1 in., the screw is said to have ten threads to the inch, the pitch being {1/10} in. The screw usually is turned by a lever or wheel with the effort applied at the end of the lever, or at the circumference of the wheel. While the effort moves once about the circumference of the wheel the weight is pushed forward a distance equal to the distance between two threads (the pitch of the screw). The work done by the effort therefore equals F × 2πr, r being the radius of the wheel, and the work done on the weight equals W × s, s being the pitch of the screw. By the law of machines F × 2πr = W × s or W / F = (2πr) / s. Therefore the mechanical advantage of the screw equals (2πr) / s. Since the distance the weight moves is small compared to that the power travels, there is a great gain in force. The screw is usually employed where great force is to be exerted through small distances as in the vise (Fig. 105) the jack screw (Fig. 106), screw clamps, to accurately measure small distances as in the micrometer (Fig. 107) and spherometer, and to lessen the motion in speed-reducing devices. The worm gear (Fig. 108) is a modification of the screw that is sometimes used where a considerable amount of speed reduction is required.
