Work = force × distance
or
W = F × D
W = 100 × 4 = 400 ft.-lb. of work
If a force moves in a circular direction to give a twisting action, this rotating force is termed torque. For example, a belt which exerts a force to turn a pulley and thus transmits power through a shaft gives the shaft a twisting action or a torque force. The pull on the belt in pounds multiplied by the radius of the pulley equals the torque in foot-pounds or, rather, pound-feet.
A force which produces the same effect upon a body as two or more forces acting together is called their resultant. The separate forces which can be so combined are called components. The finding of the resultant of two or more forces is called the composition of forces. The finding of two or more components of a given force is called the resolution of the force.
The moment of a force with respect to a point is the product of the force multiplied by the perpendicular distance from the given point to the direction of the force. In Fig. 3–1, the moment of the force P with relation to the point A is P times AB. The perpendicular distance is called the lever arm of the force. The moment is a measure of the tendency of the force to produce rotation about the given point, which is termed the center of moments. If the force is measured in pounds and the distance in inches, the moment is expressed in pound-inches; if measured in pounds and feet, the expression would be pound-feet. If P is a force of 10 pounds and 20 inches from A, its moment about A is 200 pound-inches.
Power. Power is the rate of doing work. To determine the power used or transmitted by a machine, the force must be measured, also the distance through which the force acts, and the length of time required for the force to act through this distance. The units of power ordinarily used in America are the foot-pound per second, the foot-pound per minute, and the horsepower.
FIG. 3–1. The moment of forces.
If a body is moved 1 foot per second against a force of 1-pound weight, the rate of work is 1 foot-pound per second. If it moves 1 foot per minute against the same force the rate is 1 foot-pound per minute. If it moves so that 33,000 foot-pounds are done each minute, the rate is 1 horsepower. The horsepower is based on the rate at which a 1,500-pound horse can do work. If such a horse pulls 150 pounds, 10 per cent of its weight, and moves at the rate of 220 feet per minute, or 2 1/2 m.p.h., it would do 33,000 foot-pounds of work per minute, this being equal to 150 times 220, or 33,000 foot-pounds, or 1 horsepower.
Energy. Energy is defined as the capacity for doing work. When a 1-pound weight has been raised 1 foot, it is said to have 1 foot-pound of work greater potential energy than it had in its original position. The energy possessed by a body, such as a tractor, due to its motion, is termed kinetic energy. Inertia is the property of a body which causes it to tend to continue in its present state of rest or motion, unless acted upon by some force such as a brake.
Simple Machines. A machine is a device that gives a mechanical advantage which facilitates the doing of work. The term is usually associated with such tools as grain binders, threshing machines, mowing machines, and so forth. But really, such machines are made up of many simple machines. There are six simple machines, namely:
1. The lever
2. The wheel and axle
3. The pulley
4. The inclined plane
5. The screw
6. The wedge
Any simple machine is capable of transmitting work done upon it to some other body. The mechanical advantage of a machine is the ratio of the force delivered by the machine to the force applied. The force which operates the machine is called the applied force. The efficiency of the machine is the ratio of the work accomplished by the machine to the work applied to the machine. If the efficiency of a machine could be 100 per cent, perpetual motion would exist. Since there is always a loss due to friction, the efficiency of the machine falls below 100 per cent.
FIG. 3–2. The three classes of levers.
Lever. The lever is a rigid bar, straight or curved, which rotates about a fixed point called the fulcrum. It has an applied force and a resisting force that are well defined by their names. The lever arms for a straight bar are the parts or ends on each side of the fulcrum, if the forces act perpendicular to the bar. The mechanical advantage of the lever is the ratio of the length of the lever arm of the applied force to the length of the arm of the resistance force, or
Weight × weight arm = applied force × force arm
Levers are of three classes (Fig. 3–2). In the lever of the first class, the applied force is at one end and the resisting force, or force exerted by the object to be moved, at the other. The fulcrum, or fixed point, is placed between the applied and the resisting forces. Such a lever may have a mechanical advantage of any value, depending directly upon the length of the lever arm between the fulcrum and the point of applied force as compared with the length of the lever arm between the fulcrum and the point of resisting force. The majority of levers found on farm machinery will fall in this class.
Levers of the second class have the applied force at one end, the fulcrum at the other, and the resisting force between them. This class of levers will have a mechanical advantage that will always be greater than unity. As in the case of the lever of the first class, a lever of the second class sacrifices speed and distance for a gain in pull or force.
A lever of the third class has the resisting force at one end, the fulcrum at the other, and the applied force between them. The mechanical advantage of this kind of lever is always less than unity, and, unlike the two previous classes, work is sacrificed for a gain in speed and distance. An ordinary crane is a lever of this kind.
Wheel and Axle. This is a modification of the lever and acts on the same principle, only the forces operate constantly (Fig. 3–3). The center of the axle corresponds to the fulcrum, the radius of the axle to the short arm, and the radius of the wheel to the long arm. The mechanical advantage is expressed by the equation
F × R = W × r
where W = weight
F = force applied
R = radius of wheel
r = radius of axle
FIG. 3–3. Wheel and axle.
Pulley. A pulley consists of a grooved wheel turning freely in a frame called a block; it is a lever of the first or second class. There are several different applications of pulleys, depending on their arrangement. A single fixed pulley affords no mechanical