5. What would be the kinetic energy of the train in problem 4 if it were going 60 miles per hour? If it were going 90 miles per hour? How does doubling or trebling the speed of an object affect its kinetic energy? How does it affect its momentum?
6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 ft. per second?
7. Mention as many kinds of mechanical work as you can and show how each satisfies the definition of work.
8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work is done upon it?
9. If the pile driver in problem 8 is dropped upon the head of a pile which meets an average resistance of 30,000 lbs., how far will one blow drive it?
10. A 40 kg. stone is placed upon the top of a chimney 50 meters high. Compute the work done in kilogram-meters and foot-pounds.
(2) Power and Energy
109. Horse-power.—In computing work, no account is taken of the time required to accomplish it. But since the time needed to perform an undertaking is of much importance, the rate of work, or the power or activity of an agent is an important factor. Thus if one machine can do a piece of work in one-fifth the time required by another machine, it is said to have five times the power of the other. Therefore the power of a machine is the rate at which it can do work. James Watt (1736-1819), the inventor of the steam-engine, in expressing the power of his engine, used as a unit a horse-power. He considered that a horse could do 33,000 ft.-lbs. of work a minute. This is equal to 550 ft.-lbs. per second or 76.05 kg.-m. per second. This is too high a value but it has been used ever since his time. Steam engines usually have their power rated in horse-power. That is, locomotives produce from 500 to 1500 horse-power. Some stationary and marine engines develop as high as 25,000 horse-power. The power of an average horse is about 3/4 horse-power and of a man about 1/7 horse-power when working continuously for several hours.
110. The Watt.—In the metric system, the erg as a unit of work would give as a unit of power 1 erg per second. This amount is so small, however, that a larger unit is usually employed, the practical unit being 10,000,000 ergs a second, that is, one joule per second. (See Art. 105.) This practical unit is called a Watt after James Watt. The power of dynamos is usually expressed in kilowatts, a kilowatt representing 1000 watts. Steam-engines in modern practice are often rated in kilowatts instead of horse-power. A horse-power is equivalent to 746 watts, or is nearly 3/4 of a kilowatt.