Energy and Power
Energy and power are fundamental concepts in physics that are often used interchangeably, yet they have distinct meanings. Energy refers to the capacity of an object to perform work, while power is the rate at which that work is performed or energy is transferred. The unit of energy is the joule, and power is measured in watts, where one watt equals one joule per second. The relationship between work, power, and time can be expressed mathematically, illustrating that power is the total work done divided by the time it takes to do that work.
When lifting an object, for example, a person does work against gravitational forces, increasing the object's potential energy. The amount of power required to lift the object varies with the speed of the lift; thus, lifting the same weight more slowly results in lower power usage. In practical terms, understanding these concepts is crucial for measuring energy consumption in appliances, machines, and vehicles. For example, household electricity usage is often expressed in kilowatt-hours, reflecting energy consumption over time, while devices like dynamometers measure the power produced by engines. Recognizing the differences between energy and power can lead to more informed choices regarding energy use and efficiency in everyday life.
Energy and Power
FIELDS OF STUDY: Classical Mechanics; Electronics; Electromagnetism
ABSTRACT: There are many different ways to measure the amount of energy used to perform a task. Some involve knowing the force used and the resulting velocity. Others use the work done and the time it took to do that work. When dealing with circuits, there is a third way of calculating the energy used and the power expended.
Principal Terms
- displacement: the difference between the initial position of an object and its final position, regardless of its path.
- force: the result of an interaction between two objects that changes the pattern of motion of the objects. A force can be a pull or a push.
- joule: the base unit of energy, equal to one kilogram-meter squared per second squared (kg·m2/s2).
- kilowatt-hour: a unit for measuring electricity consumption, equal to one thousand watts of power consumed over one hour, or 3.6 × 106 joules.
- newton: the base unit of force, equal to one kilogram-meter per second squared (kg·m/s2).
- potential energy: the energy that is stored in objects and can be converted to other forms of energy, such as kinetic energy.
- watt: the base unit of power, equal to one joule per second (J/s).
- work: the energy used by a force to move an object over a given distance.
From Energy to Power
As a person lifts an object, he or she is increasing the object’s gravitational potential energy. That energy is being transferred to the object at different amounts per second, as the force a person expends when lifting an object is not constant. When the object is lifted, work is being done on the object. The work done on the object, like the force expended, is also not constant. The amount of work done per unit of time is what physicists call "power." Whether it takes a person three seconds or ten minutes to lift a box one meter above the ground, the amount of work done is the same; it is the power that is different. In terms of the amount of energy spent per second in each case, the person who took ten minutes to lift the box spent energy at a much lower pace. The person developed less power, which is why it took the person longer to lift the box. The power spent by an object is equal to the total work done divided by the time it took to do that work.
Because work is a measurement of the difference in energy, in the International System of Units (SI), it is measured in joules (J). This means that power is measured in units of joules per second (J/s), or watts (W). Named after Scottish engineer James Watt (1736–1819), one watt represents the amount of work done in joules over a period of time measured in seconds. Power is also the amount of radiant energy produced by a light source. For instance, a hundred-watt light bulb produces one hundred joules of energy each second.
Calculating Power
Power (P) is a function of work done (W) over a given period of time (t):
Therefore, if a washing machine does 9 × 105 joules of work per load, and one load takes 1,800 seconds to complete, then the power spent by the washing machine in one load is calculated as follows:
This definition can be mathematically expanded by considering the definitions of work and energy themselves. Work is the difference in energy between a starting point and an end point. It depends on the force (F) acting on an object and the displacement (d) of the object. This relationship is given by the equation
W = Fd
Substituting this value into the original equation for power produces the equation
Remembering that velocity (v) is equal to distance over time, this equation can be simplified:
P = Fv
The SI unit of force is the newton (N). The energy spent to exert one newton of force over a distance of one meter is equal to one joule.
There are many ways to calculate power; which method to use depends on the type of problem. For example, imagine a hundred-kilogram man walking into an elevator. The elevator takes the man up to the second floor, a displacement of ten meters. It takes the elevator five seconds to do this. The force the elevator has to overcome is the weight of the man himself. Force is equal to the product of mass (m) and acceleration (a):
F = ma
Therefore, the weight of an object is also equal to its mass times its acceleration—specifically, the acceleration due to gravity (g), which on Earth is 9.8 meters per second squared (m/s2). This is the rate at which the velocity of an object in freefall will increase. Given this information, the power required for the elevator to lift the man is calculated as follows:
As seen in this example, power depends directly on the distance the object moves, the time it takes to do so, and the force, which itself depends on the mass of the object. Thus, accurate measurements of these quantities must be taken in order to obtain correct measurements of power.
These examples deal with the power spent against a specific kind of potential energy, known as gravitational potential energy. Other forms of potential energy exist, such as electric potential energy. To calculate electric potential energy, one must use a different equation of power. The power provided by batteries for circuits is the product of the current (I) that flows from the batteries, measured in amperes (A), and the voltage (V) supplied by the batteries:
P = IV
Note that one volt (V), the base unit of electric potential difference, is equal to one watt per ampere. If a six-volt battery supplies a current of 0.002 ampere into a circuit, then the power provided by the battery is calculated as follows:
P = (0.002 A)(6 V)
P = (0.002 A)(6 W/A)
P = 0.012 W
Measurements of Power
Knowing the amount of energy used by appliances, machines, and other devices in homes is of great importance to people and companies. Power companies install wattmeters in their customers’ homes to measure the amount of energy consumed by a household. This amount can then be quoted to the consumer in units of kilowatt-hours (kWh). A kilowatt-hour is used to measure energy consumption per unit time, such as the total energy used during a last billing cycle. One kilowatt-hour is equal to 3.6 × 106 joules..
Other types of measuring devices are employed when measuring the power produced by machines. Dynamometers are used to measure the power produced by engines. These devices measure the rotational speed and the torque produced by the engine to calculate the power the engine can achieve.
Sample Problem
A 1,500 kg plane starts moving down the runway in order to take off. The engines are running at a power of 3.5 × 105 W. It takes the plane 35 s to travel from the starting position to the takeoff point, a distance of 2 km.What is the speed of the plane as it takes off? To calculate acceleration (a), use the distance formula 
.
Answer:
The equation for power is calculated as the force producing the motion multiplied by the velocity of the object. Because the acceleration of the plane is proportional to the force applied, as stated in Newton’s second law of motion, the force can be calculated. First, find the acceleration of the plane by rearranging the distance formula to solve for a:
Next, use the rate of acceleration to calculate the force the engines must produce in order to achieve that acceleration, based on the mass of the plane:
F = ma
F = (1,500 kg)(3.27 m/s2)
F = 4,905 kg·m/s2 = 4,905 N
Finally, solve the power equation for the speed of the plane, using the force exerted on the plane and the given engine power:
The plane is traveling at 71.4 m/s at takeoff.
Energy versus Power
The words "energy" and "power" are commonly used to mean the same thing. People quote the energy of light bulbs they buy by incorrectly quoting the power. These quantities are very much related, yet they represent different things. While energy is the ability of an object to perform work, power is the rate of energy use. Energy consumption is a subject that affects every society. When buying compact fluorescent light bulbs (CFLs), for instance, people have noticed that they have lower power ratings. A CFL with a power rating of sixty watts can be as bright as a hundred-watt incandescent light bulb because the CFL uses most of this power to produce visible light rather than heat. Hundred-watt incandescent bulbs use a smaller proportion of that power to produce visible light; the rest is used to heat the element. Accurately measuring the energy spent and how fast it is being spent affects everything from the amount of power produced by utility companies to horsepower in cars.
Bibliography
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