# 5 Examples Of Potential Energy In Physics And Chemistry

What is energy? There are many different kinds of energy, kinetic energy, chemical energy, heat energy, and electromagnetic energy, but fundamentally all energy is the same. At its simplest, energy can be defined as the capacity of a system to do work. Energy is not a material substance, but it is a capacity possessed by a system in virtue of its properties. Energy is not created or destroyed but gets converted from one form into another.

For example:

• A bowling ball possesses kinetic energy in virtue of its movement down the alley. This kinetic energy is transferred to the pins when the bowling ball strikes them, causing them to move.
• A substance possesses chemical energy in virtue of the electrostatic attractions of its chemical bonds.
• A hot bowl of soup has thermal energy, which it gained from work done by a microwave, which requires electrical energy.

Mathematically, energy is defined as a force applied over some distance:

E = F × d

The SI unit for energy is called the joule (J). 1 joule is defined as the amount of energy transferred when a force of 1 Newton moves a 1 kg object a distance of 1 meter.

Potential energy is the energy possessed by an object in virtue of its position or height relative to other bodies. Along with kinetic energy, potential energy is one of the main kinds of mechanical energy—the capacity of an object to do work in virtue of its position and motion. Potential energy can be understood as the energy that gets “stored” in an object when it is moved to a certain position. Potential energy is just that; a potential to do work.

For instance, consider a bow and arrow. When not pulling back on the string, the bow exists at rest in an equilibrium position. When the bowstring gets pulled back, there is a certain amount of potential energy stored in the tension of the bow and its string. The magnitude of potential energy is directly proportional to how far back the string is pulled.  When the string is released, the potential energy stored as tension in the bow is converted into to kinetic energy which is what launches the arrow through the air. The bow then returns back to its equilibrium position. The change in potential energy from the string going from being nocked to an equilibrium position is exactly equal to the amount of work done on the arrow.

## 5 Examples Of Potential Energy

### 1.) Gravitational Potential Energy

Gravitational energy is the potential energy stored in a body due to its vertical height from the ground. Gravitational potential energy is a result of the gravitational attraction between the object and the Earth. Say you are working construction and lift a large wrecking ball into the air. When the ball is suspended in the air, gravity is exerting a particular amount of downward force per unit of mass of the ball. The gravitational potential energy stored in the wrecking ball is determined by the mass of the ball, its height from the ground, and the strength of gravitational attraction. Mathematically, this is:

gravitational potential energy = mass × height × acceleration due to gravity

PEGmgh

where m is mass, is the vertical height, and g is the acceleration due to gravity. The exact value of g differs depending on location. On Earth, g has been measured to be approximately 9.8 N/kg, meaning that gravity exerts 9.8 newtons of force per kilogram of mass. Strictly speaking, g is not a constant value because gravitational strength decreases the further you go from the Earth, but it is a close enough approximation for most real-world situations. The gravitational potential energy is proportional to the height. As the ball rises, its gravitational potential energy increases. Credit: M Run via WikiCommons CC BY-SA 4.0

To find the gravitational potential energy, you must first assign a zero-height position. In most cases dealing with gravitational potential energy, the ground is defined as the zero-height position. Because the gravitational potential is directly proportional to the height, the higher up an object is the greater gravitational potential energy it possesses. Doubling the height doubles the potential energy and tripling the height triples it.

Say we lift a 30 kg block to a height of 12 meters above the ground. What is the gravitational potential energy of the box in this position? Since the box has a height of 12 meters and a mass of 30 kg, the potential energy can be determined as such:

PEG = 30kg × 12 meters × 9.8 N/kg

PEG = 3528 J

At a height of 12 meters, a 30 kg box has a gravitational potential of 3,528 joules.

### 2.) Elastic Potential Energy

Elastic potential energy is the energy stored in an elastic material due to its stretching or compressing. The example of the bow and arrow is an example of elastic potential energy at work. A force is exerted on an elastic material that deforms it. This energy gets stored in the elastic material in the form of tension. When the material gets released, the energy stored as tension is released and the material snaps back to its equilibrium position. When you stretch a rubber band potential energy get stored in the stretchy material. When you release, the potential energy is released and the rubber band snaps back to normal. The more stretch, the more stored energy.

The force required to compress or stretch a spring is given by Hooke’s law. Hooke’s law states that the force required to stretch or compress a spring is directly proportional to the distance the spring is moved from its equilibrium position. Mathematically:

Fspring× d

where d is distance and k is the spring constant. The spring constant is a constant of proportionality that describes the amount of force exerted on a spring per unit of distance. The thicker the spring, the harder it is to compress or stretch and the larger the spring constant. The potential energy stored in such a spring is given by:

PEspring = ½ × k × x

So, how much potential energy is stored in a given spring when it is stretched 4 meters and k = 1.67?:

PEspring = 0.5 (1.67) (4)

PEspring = 3.34 J

The spring has an elastic potential energy of 3,34 J.

### 3.) Electrostatic Potential Energy

Electrical potential energy is the potential energy that exists between two electrical charges. Charged particles have potential energy due to electrostatic forces acting on them. If you take two objects with electric charges and place them a certain distance apart, an electrical potential will form due to the interaction of their electromagnetic fields. For example, if you bring two positive charges close together, they will repel each other and so have potential energy. Unlike gravitational potential energy, electrical potential energy can be positive or negative because electric forces can be attractive or repulsive. Electrical potential energy can be negative (attractive) or positive (repulsive). Credit: RJB1 via WikiCommons CC-BY 3.0

The potential energy between two charged points in space depends on their respective electric charges and the distance between the two. Mathematically, this is:

PEelectric = (k × q1 × q2)/r

Where q1 and q2 are the electric charges measured in coulombs, r is the distance between the charges, and k is the Coulomb constant. The Coulomb constant has a numerical value of 8.99×109 N·m2/C2. Since q1 and qcan be either positive or negative, electrical potential energy can be positive or negative. A negative electrical potential signifies that the two charges will attract each other and a positive electrical potential means the two charges will repel each other.

### 4.) Chemical Potential Energy

Chemical reactions involve energy. Chemical reactions can release energy in the case of exothermic reactions or absorb energy in the case of endothermic reactions. Chemical potential energy is the energy stored in the chemical bonds of substances. Gasoline is a substance with a lot of chemical potential energy. When gasoline is put into a car, it undergoes combustion. This combustion produces heat energy, which gets converted into mechanical energy that makes the car wheels turn. That heat energy released during combustion is derived from the chemical energy stored in the chemical bonds of gasoline.

Think of chemical potential energy this way: Imagine a molecule of gasoline as a system of springs and balls connected to each other. In its equilibrium position, the balls and springs are all exerting a force on each other so there is a certain amount of potential energy stored in the tension of the springs  If we cut the springs, the stored energy would be released and the molecule would break apart. Something similar is going on with chemical potential energy. A compound has a certain amount of energy stored in its chemical bonds (like the tension in springs) Breaking these bonds releases that potential energy in the form of heat which can be used to do work. The human body uses the potential energy stored in chemical substances to run their biological processes.

### 5.) Magnetic Potential Energy

It is a fundamental rule of physics that charged particles produce a magnetic dipole. The movement of charged particles creates a magnetic field. Magnetic fields exert a force on the magnetic dipoles of charged particles. The magnetic potential energy of an object is related to the strength of the magnetic field, the distance between the points, and the orientation of the fields with respect to each other. Magnetic potential energy is minimized when the magnetic fields all point in the same direction.

This is why two magnets attract each other’s opposite poles. If you place a strong magnet next to a weaker magnet with like poles facing each other, the weaker magnet will flip around and come close to the larger magnet to minimize the magnetic potential energy between the two. Similarly, the magnetic potential of a compass needle is minimized when it is facing north. Nudging a compass needle to the side increases the magnetic potential energy, which is why it returns to facing north when you let go.

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