# How Is Potential Energy Converted Into Kinetic?

## Definition of Potential and Kinetic Energy

Potential energy is the stored energy an object has due to its position or state. For example, a book sitting on a shelf has gravitational potential energy that can be converted to kinetic energy if it falls off the shelf. Other examples of potential energy include:

• Gravitational potential energy – energy stored due to an object’s height above the ground
• Elastic potential energy – energy stored in compressed or stretched springs or other elastic objects
• Chemical potential energy – energy stored in the chemical bonds of substances

Kinetic energy is the energy an object has due to its motion. The faster an object moves, the more kinetic energy it has. Some examples of kinetic energy include:

• The energy of a moving bullet being fired from a gun
• The energy of wind as it blows through the trees
• The energy of flowing water in a river

## Law of Conservation of Energy

There is a fundamental law in physics stating that energy cannot be created or destroyed, only converted from one form to another, but all the energy in the universe remains constant. This is known as the law of conservation of energy. Energy exists in various forms, like heat or light, chemical energy, mechanical energy, nuclear energy, etc. When energy is being transformed from one type to another, the total amount of energy remains the same.

For example, when a book is resting on a high shelf, it has gravitational potential energy. When the book falls off the shelf, gravitational potential energy converts into kinetic energy as the book starts accelerating towards the floor. Some kinetic energy is also converted into heat from air resistance and when the book hits the floor, making a sound. But the total amount of energy before and after the fall remains constant, even when it transforms between potential, kinetic, thermal, and sound energy. This law underlies all transformations of energy within mechanical systems and phenomena in the physical world.

## Gravitational Potential Energy

Gravitational potential energy depends on the mass of an object and its height above a reference point, as shown in the equation:

PEgrav = mgh

Where m is mass, g is acceleration due to gravity, and h is height. Gravitational potential energy can be thought of as stored energy that an object has due to its position in a gravitational field. The higher up the object is, the more potential energy it possesses.

As the object falls, this potential energy gets converted to kinetic energy – the energy of motion. Using the previous equation, we know the object had more potential energy at a greater height. As it drops in the gravitational field, the potential energy decreases while the velocity – and hence kinetic energy – increases. This conversion occurs according to the law of conservation of energy, which states that energy cannot be created or destroyed but only transformed from one form to another.

A real-world example is a rock sitting at the edge of a cliff. It has high potential energy due to its position high above the ground. When the rock falls off the cliff, that potential energy gets transformed into kinetic energy, causing the rock to accelerate and smash into the ground below.

## Examples of Gravitational Potential to Kinetic Energy

One simple example of gravitational potential energy being converted into kinetic energy is a dropped ball. When a ball sits at rest on a table, the ball has gravitational potential energy due to earth’s gravitational pull. When that ball is dropped off the table, the ball accelerates towards the ground. As it accelerates downward, the ball gains kinetic energy. Just before impact with the floor, the ball has near maximum kinetic energy and almost no gravitational potential energy left.

A pendulum is another example of gravitational potential to kinetic energy conversion. When a pendulum is pulled back to one side, it gains gravitational potential energy due to the height it sits above the lowest resting point. As the pendulum swings freely to the other side, this potential energy is converted into kinetic energy as the pendulum accelerates downward under gravity. The pendulum continues to swing back and forth, converting between potential and kinetic energy.

## Elastic Potential Energy

Elastic potential energy refers to the energy that is stored in elastic objects such as springs when they are deformed or displaced. The magnitude of the elastic potential energy depends on two main factors:

• Spring constant – This is an inherent property of the spring that measures its stiffness. A spring with a bigger spring constant will store more elastic potential energy when compressed or stretched by the same distance.
• Displacement or compression – This refers to how much the spring is compressed or stretched from its relaxed length. The greater the displacement, the higher the elastic potential energy.

When a spring stretches or compresses, the work done to stretch or compress it gets stored as potential energy. This potential energy is directly proportional to the square of the displacement. When the external force is released, the spring converts the potential energy into kinetic energy, as its length relaxes back to normal. This is why a compressed or stretched spring exerts a restoring force trying to reach its equilibrium length. The kinetic energy allows the spring to do work as it oscillates between its relaxed state and compressed state doing work on anything restricting the motion.

## Examples of Elastic Potential to Kinetic

A common example of elastic potential energy being converted into kinetic energy is a slingshot. When you pull back the rubber band on a slingshot, you are storing elastic potential energy. When you let go, the stored elastic potential energy is converted into kinetic energy as the projectile shoots forward.

Another everyday example is a bouncing ball. When a ball bounces, it is temporarily deformed on impact and elastic potential energy is stored. As the ball rebounds, this elastic potential energy is converted into kinetic energy.

In both cases, the elastic material (rubber band or bouncy ball) is stretched or compressed. When released, the elastic forces restore it to its original shape – the potential energy that was stored gets released as kinetic energy.

## Chemical Potential Energy

Chemical potential energy is the energy stored in chemical bonds in molecules, or in the electron arrangements of atoms/molecules. Common examples are molecules like glucose used as an energy source by the human body, gasoline in a car, and lithium ion batteries used in portable devices and electric vehicles. In all of these cases, potential energy is locked into the atomic/molecular structure and can be released as kinetic energy to do work.

Specifically, when chemical reactions break existing bonds and/or form new bonds, electrons are transferred between atoms and molecules. This electron flow is harnessed as an electric current which can then be used to power electric motors or other work. In the human body, enzymes and cellular respiration are used to release the chemical energy from glucose and create ATP molecules which drive various mechanical and electrical processes inside cells. Lithium ion batteries rely on the movement of lithium ions and electrons between the anode and cathode electrodes – this electron flow provides an electrical current that can drive an electric motor to propel an electric car. Thus in various ways, the potential energy stored in chemical bonds and structures gets converted into kinetic energy to perform useful work.

## Equations for Potential and Kinetic Energy

The following key equations demonstrate how potential energy can be converted into kinetic energy:

Gravitational Potential Energy Equation:

GPE = mgh

Where m is mass, g is the gravitational acceleration constant, and h is vertical height above a reference point. This gravitational potential energy can be converted into kinetic energy according to the following equation:

Kinetic Energy = 1⁄2mv2

Where m is mass and v is velocity.

As the height (h) increases in the gravitational potential energy equation, that potential energy increases. When an object falls, that potential energy is converted into kinetic energy, resulting in higher velocity squared (v2) in the kinetic energy equation.

Elastic Potential Energy Equation:

EPE = 1⁄2kx2

Where k is the spring constant and x is the compression or elongation distance. The elastic potential energy can convert into kinetic energy with the same kinetic energy equation above.

## Real World Examples

We see many examples of potential to kinetic energy conversions in our everyday lives:

• Rollercoasters are a great example. At the beginning of a drop on a rollercoaster, the riders have gravitational potential energy due to their height. As gravity accelerates the riders downward toward earth, this potential energy is converted into kinetic energy, the energy of motion. This is responsible for the “whooshing” feeling many riders feel in the pit of their stomach on drops.

• Throwing a ball involves elastic potential energy stored in the muscles and tendons. As you release the ball, this potential energy becomes kinetic energy as the ball flies through the air at speed.

• Burning fuel in a car engine involves converting chemical potential energy stored in gasoline into kinetic energy that powers the wheels and moves the car.

There are many more examples we could give, but this illustrates how potential energy transfers and conversions occur around us every day!

## Summary

In summary, we have covered the key concepts around potential and kinetic energy conversion:

• Potential energy is stored energy due to an object’s position or arrangement, while kinetic energy is the energy of motion.
• The law of conservation of energy states that energy can neither be created nor destroyed, only converted between different forms.
• Three main types of potential energy exist: gravitational (objects at height), elastic (springs, etc.), and chemical (e.g. food).
• When objects gain height or stretch elastic materials, they gain potential energy. This can be converted into kinetic energy of motion when released.
• Combustion and metabolism of food converts chemical potential energy into heat and motion.
• Equations allow potential energy to be quantitatively related to kinetic energy for a system.
• Many examples exist in everyday life of potential to kinetic conversion: falling objects, slingshots, windup toys, combustion engines, etc.

The key takeaway is that energy is always conserved – it only transforms between potential and kinetic states. This understanding allows us to solve problems and build machines by leveraging energy conversions.