**Principles of energy and work **

(From *The Sciences*, 6th ed., by Trefil and Hazen)

**Introduction: ***Work*

Scientists say that **work **is done whenever a force is exerted over a distance. Pick up this book and raise it a foot. Your muscles applied a force equal to the weight of the book over a distance of a foot. You did work.

This definition of work differs considerably from everyday usage. From a physicist’s point of view, if you accidentally drive into a tree and smash your fender, work has been done because a force deformed the car’s metal a measurable distance. On the other hand, a physicist would say that you haven’t done any work if you spend an hour in a futile effort to move a large boulder, no matter how tired you get. Even though you have exerted a considerable force, the distance over which you exerted it is negligible. Physicists provide an exact mathematical definition of their notion of work.

**In words: **Work is equal to the force that is exerted times the distance over which it is exerted.

**In equation form:** work (joules) = force (newtons) x distance (meters),

where a joule is the unit of work, as defined in the following paragraph.

**In symbols:** *W *= *F *x *d*

In practical terms, even a small force can do a lot of work if it is exerted over a long distance.

As you might expect from this equation, units of work are equal to a force unit times a distance unit. In the metric system of units, where force is measured in *newtons *(abbreviated N), work is measured in newton-meters (N-m). For reference, a newton is roughly equal to the force exerted on your hand by a baseball.

This unit is given the special name “joule,” after the English scientist James Prescott Joule (1818–1889), one of the first people to understand the properties of energy. One *joule *is defined as the amount of work done when a force of one newton is exerted through a distance of one meter.

**1 joule of work = 1 N of force x 1 m of distance **

In the English system of units, where force is measured in pounds, work is measured in a unit called the foot-pound (usually abbreviated ft-lb).

**Example: Working Against Gravity**

How much work do you do when you carry a 20-kg television set up a flight of stairs (about 4 meters)?

** Reasoning: **We must first calculate the force exerted by a 20-kg mass before we can determine work. We know that to lift a 20-kg mass against the acceleration of gravity (9.8 m/s

^{2}) requires a force given by

force = mass x *g*

= 20 kg x 9.8 m/s^{2}

= 196 newtons

** Solution: **Then, from the equation for work,

work = force x distance

= 196 N x 4m

= 784 joules

*Energy*

**Energy **is defined as the ability to do work. If a system is capable of exerting a force over a distance, then that system possesses energy. The amount of a system’s energy, which can be recorded in joules or foot-pounds (the same units used for work), is a measure of how much work the system might do. When a system runs out of energy, it simply can’t do any more work.

*Power*

**Power **provides a measure of both the amount of work done (or, equivalently, the amount of energy expended) and the time it takes to do that work. In order to complete a physical task quickly, you must generate more power than if you do the same task slowly. If you run up a flight of stairs, your muscles need to generate more power than they would if you walked up the same flight, even though you expend the same amount of energy in either case. A power hitter in baseball swings the bat faster, converting the chemical energy in his muscles to kinetic energy more quickly than most other players.
Scientists define power as the rate at which work is done, or the rate at which energy is expended.

**In words: **Power is the amount of work done divided by the time it takes to do that work.

**In equation form:**

where the watt is the unit of power, as defined in the following paragraph.

power (watts) = work (joules)/time (seconds)

**In symbols: **P = W/t

If you do more work in a given span of time, or do a task in a shorter time, you use more power.

In the metric system, power is measured in **watts, **after James Watt (1736–1819), the Scottish inventor who developed the modern steam engine that powered the Industrial Revolution. The watt, a unit of measurement that you probably encounter every day, is defined as the expenditure of 1 joule of energy in 1 second: **1 watt of power = (1 joule of energy) / (1 second of time)**

The unit of 1000 watts (corresponding to an expenditure of 1000 joules per second) is called a **kilowatt **and is a commonly used measurement of electrical power. The English system, on the other hand, uses the more colorful unit *horsepower, *which is defined as 550 foot-pounds per second.

The familiar rating of a light bulb (60 watts or 100 watts, for example) is a measure of the rate of energy that the light bulb consumes when it is operating. As another familiar example, most electric hand tools or appliances in your home will be labeled with a power rating in watts.

The equation we have introduced defining power as energy divided by time may be rewritten as follows:** energy (joules) = power (watts) x time (seconds)**

This important equation allows you (and the electric company) to calculate how much energy you consume (and how much you have to pay for). Note from this equation that, while the joule is the standard scientific unit for energy, energy can also be measured in units of power x time, such as the familiar kilowatt-hour (often abbreviated kwh) that appears on your electric bill.

*James Watt and the Horsepower*

The horsepower, a unit of power with a colorful history, was devised by James Watt so that he could sell his steam engines. Watt knew that the main use of his engines would be in mines, where owners traditionally used horses to drive pumps that removed water. The easiest way to promote his new engines was to tell the mining engineers how many horses each engine would replace. Consequently, he did a series of experiments to determine how much energy a horse could generate over a given amount of time. Watt found that an average, healthy horse can do 550 ft-lb of work every second over an average working day—a unit he defined to be the horsepower (hp), and so he rated his engines accordingly. We still use this unit (the engines of virtually all cars and trucks are rated in horsepower), although we seldom build engines to replace horses these days.