14. If it takes 14 hours to raise a weight of 20 tons 100 ft., what H. P. engine will be required?

15. If a workman carries 5 tons of pig iron up a flight of steps 14 ft. high in 10 hours, how much work does he accomplish expressed in ft.-lbs.?

per

16. A rope turns a pulley 48 in. dia. with a pull of 10 lbs. at the rim at the rate of 2500 ft. minute. How many ft.-lbs. of work are done in 5 hours consecutive movement? 17. A 12 lb. ball falls 2500 ft. What is its velocity when it strikes and what is its kinetic energy?

18. A 500 volt electric motor runs 50 machines using 22 amperes of current. What is its H. P.?

19. What is the H. P. of a dynamo which will run 300 110-volt incandescent lamps if each lamp consumes ampere of current?

20. An electric motor has a voltage of 250 and supplies 30 amperes to run a certain set of machines. Find the

H. P. of motor.

21. What H. P. will be required to run a 250 lamp circuit, the lamps being the same as in problem 19?

22. A direct connected dynamo delivers power at 110 volts to a 1400 electric light circuit, also to 9 motors with normal amperage as follows: 1 at 144, 1 at 110, 1 at 80, 3 at 76, 1 at 57 and 2 at 20 amperes. What H. P. will be required to run the above equipment?

MECHANICAL POWERS

An appliance by which force can be used to do useful work is called a machine.

The mechanical powers or elements of machines are six in number, as follows:

The mechanical advantage of all kinds of machines, whether simple or compound, may be computed in accordance with the following

GENERAL LAW

The force multiplied by the distance through which it moves is equal to the resistance or weight multiplied by the distance through which it moves, or PXdP=WxdW.

Each class of machines permits of a special statement of this law by substituting for the general terms the special terms used with that class of machines.

1. THE LEVER

The lever is an inflexible bar or rod supported at some point, the bar being free to move about that point as a pivot. This pivotal point is the fulcrum, usually represented by F. The force applied to the lever is represented by P.

The weight lifted, or the resistance to the force is represented by W.

The lever is classed according to the position of the three

The machinists' and the tinsmiths' pliers are examples of levers of the first class.

The nut cracker and lemon squeezer, are levers of the second class.

The sheep shears and firm joint calipers are good examples of levers of the third class.

The three classes of levers are operated and controlled by the following:

LAW FOR LEVERS. The force multiplied by its distance from the fulcrum is equal to the weight multiplied by its distance from the fulcrum.

Let P= force

W = weight or resistance.

=

Pa distance from fulcrum to point where force is

applied.

Wa-distance from fulcrum to point where weight is applied.

Then the law of Levers becomes PX Pa=WXWa.

From this equation the following are readily derived.

Example. What force 18 in. from fulcrum will balance a weight of 870 lbs. 3 in. from the fulcrum?

The law for bent levers is the same as for straight levers but the lengths of arms are computed on lines from the

positions. The case of pulling out a nail with the common claw hammer is a good illustration of the bent lever, Fig. 4.

The moving strut in Fig. 5 is a bent lever with one arm

not the weight, W, but its resistance to being moved. The ratio between force and resistance changes as the angle A changes.

separately by the formula for single levers. These separate operations, however, are usually condensed into one, in accordance with the following: