What is Energy in Physics? (w/ Formula & Examples)

You probably use the word energy in your everyday life all the time, but what does it really mean? What physical quantity are you getting at when you say things like, “I just don’t have the energy today,” or, “Those kids need to burn off some energy”?

The colloquial use of the word might give you an initial sense of what energy is, but in this article you will learn how physicists define energy, learn what the different types of energy are and see some examples along the way.

Definition of Energy

Energy is the ability to do work or cause change. It is different from a force. A force is the thing that causes the change, while energy can be thought of as the impetus behind the force. It takes energy in order to apply a force, and applying a force to an object often transfers energy to it.

The SI unit of energy is the joule where 1 joule = 1 newton × 1 meter or 1 kg⋅m2/s2. Other units include calories, kilocalories and kilowatt-hours.

Types of Energy

The two most fundamental forms of energy are ​potential energy​ and ​kinetic energy​. Potential energy is stored energy while kinetic energy is the energy of motion.

Scientists usually differentiate between macroscopic and microscopic versions of these energy types. For example, potential energy that is stored due to gravity or due to a compressed spring is called ​mechanical​ potential energy. But objects can also have a different type of potential energy stored in the bonds between molecules and between nucleons in an atomic nucleus.

Mechanical kinetic energy is the energy due to the motion of a macroscopic object. But inside any object, the molecules themselves have their own kinetic energies of a different type.

The sum of an object's mechanical potential and kinetic energy is called its ​total mechanical energy​. This is not the same as the object's total energy, which would be the sum of all forms of its energy, including thermal, chemical and so on.

The type of potential energy stored in molecular bonds is a form of energy called ​chemical​ energy. Energy stored in atomic bonds or nuclear bonds is called ​atomic​ energy or ​nuclear​ energy.

Kinetic energy that exists on a molecular level due to the vibrations and motions of molecules is called ​thermal​ energy or ​heat​ energy. When you measure temperature, you are measuring the average amount of this type of energy.

Mechanical Potential Energy in More Detail

The most common types of mechanical potential energy you might learn about include:

  • Gravitational potential energy:​ The energy stored in an object based on its location in a gravitational field. For example, a ball held high above the earth has gravitational potential energy. When released, it will drop as a result.
  • Electric potential energy:​ This is the energy stored in a charged object due to its position in an electric field. For example, the electrons in a circuit will become endowed with a certain amount of electric potential energy due to the battery. When the circuit is connected, this causes the electrons to flow.
  • Magnetic potential energy:​ This is energy stored in an object with magnetic moment due to its location in a magnetic field. Consider when you hold two button magnets near each other and you feel them tugging; this is because of the magnetic potential energy.
  • Elastic potential energy:​ This is energy stored in an elastic material. For example, a stretched rubber band has stored energy, as does a compressed spring. When either are released, they will move.

Mechanical Kinetic Energy in More Detail

Mechanical kinetic energy differs from potential energy in that it is associated with motion, and it comes in just one variety. A simple equation gives the kinetic energy of any object of mass ​m​ moving with speed ​v​. That is:

KE = \frac{1}{2}mv^2

The faster an object moves or the heavier it is, the more kinetic energy it has.

When an object that has potential energy is released and allowed to move freely, it will begin to accelerate. As a result, its kinetic energy increases. At the same time, the potential energy decreases. In net, the total mechanical energy of the object remains constant (assuming no friction or similar forces act), it’s just that the energy changes form.

Equations for Energy

In the last section, the equation for mechanical kinetic energy was introduced. There are also formulas for different types of potential energies as well as equations that describe the relationship between energy and other physical quantities.

The gravitational potential energy of mass ​m​ at height ​h​ above the Earth is:

PE_{grav} = mgh

Where ​g​ = 9.8 m/s2 is the acceleration due to gravity.

The electric potential energy of a charge ​q​ at voltage ​V​ is simply:

PE_{elec} = qV
PE_{spring} = \frac{1}{2}k\Delta x^2

Where ​k​ is the spring constant (a constant that depends on the stiffness of the spring) and ​Δx​ is the amount by which the spring is compressed or stretched.

Thermal energy change (aka heat energy transferred) is given by the following equation:

Q = mc\Delta T

Where ​Q​ is the energy, ​m​ is the mass, ​c​ is the specific heat capacity and ​ΔT​ is the temperature change in units of Kelvin.

The physical quantity work (defined as the product of force and displacement) has the same units as energy (J or Nm). The two quantities, work and kinetic energy, are related via the the work-kinetic energy theorem, which states the net work on an object is equal to the change in the object's kinetic energy.

The Law of Conservation of Energy

A fundamental fact of nature is that energy can neither be created nor destroyed. This is summarized in the law of conservation of energy. This law states that the total energy of an isolated system remains constant.

While the total energy remains constant, it can and often does change form. Potential might change into kinetic, kinetic might change into thermal energy and so on. But the total amount always remains the same.

It’s important to note that this law specifies an isolated system. An isolated system is one in which can in no way interact with its surroundings. The only possibly perfectly isolated system in the universe is, well, the universe itself. However, it’s possible to make many systems on Earth that are close to being isolated (just as it’s possible to make friction negligible, even if it is never 0.)

Energy conversion can happen in many ways, usually from stored energy being released as kinetic energy of some sort or as radiant energy.

Chemical energy, for example, can be released during chemical reactions. During such a reaction it changes from chemical potential energy into some other form, which might include radiant energy or heat energy.

Nuclear energy is released during a nuclear reaction. This is where Einstein's famous ​E = mc2​ equation comes into play (energy equals mass times the speed of light squared). The mass of a nucleus that splits apart to release energy will be slightly lighter in the end by an amount determined by Einstein’s formula. As crazy as it sounds, mass itself can be considered a form of potential energy.

Sources of Usable Electrical Energy on Earth

Here on Earth, you likely use electrical energy often. Every time you turn on a light in your house or read something off of an electronic screen like you are right now, you are using electrical energy. But where does this energy come from?

The obvious answer is batteries or the wall outlet, but what is the actual primary source?

When it comes to batteries, energy is often stored chemically in a battery cell, but many electronic devices require that their batteries be recharged by connecting them to a wall outlet.

The energy that comes to your house through power lines originates at a power plant somewhere. Power plants have many different ways of harvesting energy and turning it into electrical energy.

Some common sources of energy harvested by power plants and converted into electricity include:

  • Solar energy:​ This is radiant energy that comes from the sun and can be captured by solar cells.
  • Geothermal energy:​ This is thermal energy found deep in the ground that can then be transferred to the surface of the Earth for use.
  • Fossil fuels:​ These include coal and oil, which are often burned to release energy stored in chemical bonds.
  • Nuclear energy:​ Nuclear power plants generate energy by breaking apart atomic nuclei and harnessing the energy that was stored in the nuclear bonds.
  • Hydroelectic energy:​ This is energy that comes from gravitational potential energy as well as kinetic energy in flowing water. 
  • Wind energy:​ To harvest wind energy, giant turbines are used. The wind turns the turbines, transferring its energy to them.

Energy in the Human Body

Remember back at the beginning of this article where the phrases, “I just don’t have the energy today,” and, “Those kids need to burn off some energy” were mentioned? Humans make use of energy all the time, and not just from their electronic devices. Both the large motions of your body and small processes within your body require energy.

It takes energy to run, hike, swim or even just brush your teeth. Remember kinetic energy? When you move, you are doing so via kinetic energy. That energy has to come from somewhere.

Many invisible processes that go on in your body also require energy, such as breathing, circulating your blood, digesting and so on.

Where do humans get their energy from? Food, of course! The food you eat has stored chemical energy within it. When that food makes its way into your stomach, your stomach acid breaks down the food, and certain molecules from the food make their way to all of the different places in your body that might need energy. Then, when the need arises, energy is obtained via a small chemical reaction.

Now, if you don’t eat all day and do a lot of running around, you expend a lot of energy and will feel “drained” until you eat and provide your body with more of what it needs.

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