| Elevator down |
In a previous lesson we defined Work as
a force acting through a distance, 
symbolically. Let's consider a thought
experiment (gedunken experiment in German) because I don't
feel like doing exercise. Consider the work required to move your
body from the floor of the math wing to the floor at the media
center. W = mgx, where mg is your weight and x is the vertical
distance between floors (about 7 m in this building). For this
example, let's consider an average teenage girl (mg = 540 N) moving
7 m. Question 1. How much work does she do in climbing the stairs
in 60 seconds? How does she feel? How much work does she do in
climbing the same stairs in 10 seconds? The first trip up the
stairs was probably rather boring; the second trip, on the other
hand, was an invitation to cardiac arrest. By the formal definition
of work above, the girl did the same amount of work in each example.
But our stair runner will confirm between gasps that something
was different. It turns out that the difference in the two situations
is a manifestation of a scalar quantity called power.
The need to measure a quantity defined above as power was unnecessary until about 1765. In that year James Watt, an instrument maker working at the University of Glasgow in Scotland, introduced a significant improvement to the very primitive steam engines of the day. Early engines used steam from a boiler to build enough pressure to move a piston in a cylinder. To cause the piston to retract, cold water was dumped on the cylinder to cool it down. It then took time and more energy to raise the pressure sufficiently to move the piston again. The cycle time for such an arrangement made the contraption hardly worth the trouble. Watt added a separate condenser that was always kept cool. That meant that the cylinder and piston could maintain the high operating temperatures. With this arrangement, the piston could move back and forth very rapidly, doing much work in short time. Attach a flywheel to the piston and the reciprocating motion of the piston is converted to a rotary motion. Add a long shaft attached to the fly wheel and the mechanical energy produced by the steam engine could be distributed to machines in a factory. Thus, the improvement of the steam engine represents the event that triggers the Industrial Age
Other uses for steam engines soon followed. Mount the engine on a cart whose wheels are turned by the energy output of the engine and the locomotive is born. Put a steam engine in a boat driven by a steam-powered paddle wheel and , well you get the picture.
Watt used some of the excess steam in the boiler to heat his office by causing the steam to move through a series of pipes we would call a radiator. Thus, the notion of centralized heating system is born.
His engine moved through their cycle so rapidly that he could no longer rely on humans to perform such routine tasks such as opening and closing valves. Instead he used for the first time ever part of the engine output to regulate the operation of the machine, a phenomenon we call synergism.
When one thinks of the word power , it is usually in the context of political power or economic power. I believe that these terms come later and are related to the mechanical power managed by people who owned a Watt engine. The Watt engine was able to do da lot of work per unit time, earning a lot of money for its owner. The other forms of power come after one has money in hand.
The SI unit for power is the Watt = 1 Joule/second. This is not much energy per unit time. Central Maine Power Company will sell your family 1 kw-hr ( = 3.6 million joule/second) for under 20 cents. Maine Yankee, at peak operating times, produced energy at the rate of 1 gigawatt (10^9 W). 1 gW = 10^6 kW. Thus in one hour, MAine YAnkee produced energy that netted the owners $150,000 when 1 kw-hr costs 15 cents
The proper unit for power in British Engineering system is the foot-pound/second. While there is no derived unit for one of these, 550 ft-lb/s is renamed one horsepower (about 746 W). Watt had determined though measurement that a load of 550 lbs. attached by pulley to a draft animal , could be raised at a rate of one foot/ second. Thus one horsepower = 550 ft-lbs/s. As it turns out, 1hp is a lot of work per unit time. An adult male digging a ditch does work at the rate of about .05 hp and has to rest often.