The illustration shows what is called a lever of the first class. The power and weight are on opposite sides of the fulcrum F, and act in the same direction. A poker between the bars of a grate, raising the coals, a spade, a pair of scissors, a common balance or scales, are examples of levers of this class.

POWER

LEVER

W

LEVER OF SECOND CLASS.

Here we have an illustration of a lever of the second class. The power and weight are applied on the same side of the fulcrum, and act in opposite directions, the power being applied at a greater distance from the fulcrum than the weight is. A wheelbarrow is an illustration, the point where the wheel touches the ground being the fulcrum; an oar of a boat is another example, the blade of the oar in the water being the fulcrum.

In levers of the third class the power and weight are applied on the same side of the fulcrum, and act in opposite directions, the power being nearer to the fulcrum than the weight is.

GENERAL RULE: The power or force multiplied by its distance from the fulcrum is equal to the weight multiplied by its distance from the fulcrum.

ILLUSTRATIVE EXERCISES

1. In a lever of the first class the weight is 9 in. and the power is 12 in. from the fulcrum. If the weight is 4 lb., what is the power?

2. In a lever of the second class what power 15 ft. from the fulcrum will lift a weight of 600 lb. 3 ft. from the fulcrum ?

1. If 480 lb. be applied to the end of a lever of the first class 135 in. from the fulcrum, what weight will it lift 45 in. from the fulcrum ?

2. In a lever of the second class what power 14 ft. from the fulcrum will lift a weight of 441 lb. 4 ft. from the fulcrum?

W

3. If AF is 3 ft. and AB is 13 ft., a pressure of 528 lb. (at right angles) at B will exert an upward pressure of how many pounds (at right angles) at A?

in.

18 lbs

4. AF is 18 in.; BF is 6 in.; FC is 15 in.; FD is 36 What upward power at D will keep the lever in equilibrium?

NOTE. The difference between the products of the weights and arms at one side should equal the difference of the products of the weights and arms at the other.

B

W 4800

5. A weight of 4800 lb. is suspended from a point A of a beam AC, 35 ft. long. AC rests on a cross beam at B, and the end C is under another cross beam. If BC is 14 ft., find the upward pressure in pounds at C. (Weight of AC and breadth of cross beams not considered.)

Lesson No. 38. Simple Mechanics - The Wheel and Axle

The wheel and axle may be described as a continuous lever. It consists of a wheel, to the outer edge of which the power is applied, and of the axle, to which the wheel is fastened and to the circumference of which the weight is attached by means of a cord.

The above illustration shows the machine in its most elementary form. P and W represent the power and the weight. In practice, as you have frequently seen, the wheel disappears, and you simply have the crank left; as, however, this is turned around, it describes the same path as a continuous wheel would do; therefore its principle is the same.

Note the drawing of a cross-section of the wheel and axle. AB is the lever with the fulcrum at C. From the fact that when the power and the weight act as shown in the diagram, there is always a lever in the position AB, the machine is called a "continuous lever." The radius of the wheel forms the long arm of the lever, and the radius of the axle the short arm. If the radius of the wheel is five times the radius of the axle, the relation of P to W will be as 1 to 5; that is, a weight of 1 lb. at the circumference of the wheel will balance a weight of 5 lb. at the circumference of the axle.

You can also readily see that for one complete turn of the wheel we have a complete turn of the axle; so that a weight running down a distance equal to the circumference of the wheel will lift a weight through a distance equal to the circumference of the axle.

As the circumference of wheel and axle bear the same proportions as their radii, it is clear that for every inch through which the weight is raised the power will have to run down 5 in., and the rate at which the weight is raised is only one-fifth that at which the power runs down. Here we have the law of virtual velocities - what we gain in power we lose in speed.

DIFFERENTIAL WHEEL AND AXLE.