A demonstration of the law of the inclined plane can be made with an apparatus like that shown in Fig. 85. The cylinder is the weight and the pull of the power is made parallel to the plane by means of the cord running over the fixed pulley at the top.

116. The Wedge is nothing more than a modified inclined plane. It is generally made with its base (which corresponds to the height of an inclined plane) perpen

dicular to a line drawn from the edge to the middle of the base. This means that it is made of two inclined planes placed base to base. The power is usually applied by the blow of a heavy body. Wedges are used in splitting logs and stone, raising heavy weights a short distance, launching ships, and similar operations.

FIG. 86

117. The Screw consists of a cylinder of wood or metal about which is a thread. If the cross section of this thread is square, the thread is called a square thread; if triangular, it is called a V-thread. A good model of a square-thread screw can be made by winding a long strip of leather in a spiral around a wooden cylinder, and tacking it fast.

Square Thread

V-thread

That the screw is a modified inclined plane may be seen by cutting a right-angled triangle out of paper and winding it about a pencil as in Fig. 88. It will be seen that the hypotenuse, which represents the length of an inclined plane, forms the spiral thread of the screw. If

CB is taken equal to the circumference of the
pencil, then AB will be equal to the distance
between the threads DE. This distance is called
the pitch, and determines how far the screw (or
the resistance) moves at each revolution.
power is generally applied to a

screw at the end of a lever,
as the handle of a wrench. It

is applied either to the screw or to the nut, as in bolting two pieces of wood together.

FIG. 88

118. The Law of the Screw. The mechanical advantage of a screw cannot be determined unless we know at what point the power is applied. From the gen

FIG. 89.-Lifting
Jack

eral law of machines, the formula can be written PX 2 TR = Wp, or

in which p is the pitch of the screw, and R is the radius of the circle through which the power moves.

119. Application of the Screw. - Lifting jacks, cotton and hay presses, the screw pro

peller of ships, and air fans are familiar examples of the prac

crometer screw are examples of its use in scientific work. The speed counter shown in Fig. 90 shows how an endless screw, meshing into teeth on the circumference of a wheel, can be used to determine the rotation of an axle, the pointed end of the screw being thrust into a hole in the end of the axle and rotating with it.

120. Friction. Whenever any body is put in motion by sliding or rolling it over another, and the body is then left to itself, its velocity will gradually diminish, and it will come to rest. This is due to friction, which is the resistance that is encountered in moving (or trying to move) one body over another under pressure. Friction arises from inequalities in the surfaces in contact. If any means is taken to reduce these inequalities, either by making the surfaces smoother, or by filling up the depressions with some form of lubricating material, the friction is diminished.

121. Laws of Sliding Friction. - Experiment has established the following law for sliding friction - both for friction of motion and for friction of rest:

Sliding friction is proportional to the pressure, and independent of the extent of the surfaces in contact. It varies with the character of the surfaces.

Within certain limits friction of motion is also independent of the velocity of the motion.

122. Coefficient of Friction. The coefficient, or measure, of sliding friction - either of rest or of motion--is expressed by the equation.

in which P is the force necessary to overcome the friction, and W is the pressure normal (perpendicular) to the surfaces

FIG. 91

in contact. A simple method of determining this, for friction of rest, is to place a block of known weight, W, upon a level board, and set it in motion by putting weights in a scale pan

suspended as in Fig. 91. In measuring friction of motion care must be taken that the speed is uniform.

123. Rolling Friction. - If two equal masses of iron are drawn over a smooth iron surface, one being in the form of a block with a flat base and the other in the form of a cylinder so arranged as to roll, it will be found that the cylinder offers much less resistance to the motion than the block does. Rolling friction depends upon the hardness and smoothness. of the surfaces in contact. When these are very hard and smooth, rolling friction is much less in amount than sliding friction as in the case of a car wheel running on a steel track. If, however, the surface over which a wheel rolls is soft and yielding,

as in the case of a wagon in deep sand, rolling friction may be even greater than sliding friction. In such a case the

wheel has to be constantly climbing the hill caused by the sinking of the wheel in the sand. If the wheel is yielding,

as in the case of an automobile tire that is not well filled with air, the wheel is flattened at the point of contact, thus increasing the rolling friction.

The efficiency of machines is increased by changing sliding friction to rolling friction, by the use of hardened steel cylinders or balls placed between the axle and the bearing. In roller bearings, the contacts are line contacts, while in ball bearings, they are point contacts.

124. Advantages of Friction. While all possible means are taken to reduce the friction between the parts of a machine that move over each other, friction has many advantages. The difficulty of walking on an icy pavement illustrates the decrease of stability that comes with a decrease of friction. The stability of the ceiling of a room is dependent upon the friction between the lath nails and the joists. Horses that easily draw a heavy load over a dry pavement will fall when the pavement is wet. The ability of a locomotive engine to haul its train is due to the friction between the driving wheels and the rails. If the rails are wet, the wheels slip until sand is sifted over the rails.

Questions

1. Is a perpetual motion machine possible? Why?

2. What effect upon the efficiency of a machine does it have to reduce its friction?

3. State the general laws of machines. (And,

4. Name three machines in which the mechanical advantage is one of speed. Which is greater in each case, the power used or the resistance overcome?

5. What point is the center of moments in a lever?

6. Draw a figure of a lever of the first class, in which the moment of the power and the moment of the weight shall each be 80.