This topic will look at Kinetic Energy, which follows our previous posts on Energy Stores and Work done. You can view those topics here:

You may recall that energy is a fundamental property of the universe. According to the law of energy conservation, energy can never be created or destroyed, only transferred or converted from one form to another. This means energy is never used up or lost; instead, it is transferred between different energy stores and objects.

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For example, consider a light bulb. When you turn on a light bulb, electrical energy is transferred from the power source to the bulb, where it is converted into light and thermal energy. The light energy illuminates the surroundings, while the thermal energy dissipates into the surrounding environment as heat. When you turn off the light bulb, the energy is not destroyed but rather is transferred back to the power source or the environment.
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Another example is a moving object, such as a ball. When you throw a ball, you transfer energy from your muscles to the ball, giving it kinetic energy. As the ball moves through the air, it loses some of its kinetic energy to the air due to friction, causing it to slow down. However, the kinetic energy lost by the ball is not destroyed but instead transferred to the air as thermal energy.

In both examples, energy is not used up or lost but transferred or converted into other forms of energy. This is true for all energy transformations, whether in a chemical reaction, a mechanical system, or an electrical circuit.

Now that you've got your head around energy stores, it's time to see how you can calculate the amount of energy in Kinetic, Gravitational Potential and Elastic Potential energy stores.

## Kinetic energy stores

Kinetic energy is one of the many forms of energy that objects can possess. The other energy stores include potential, thermal, chemical, nuclear, and electromagnetic energy. Each energy store represents a different way in which energy can be stored or transferred.

Kinetic energy is a type of energy an object possesses due to its motion. When an object is in motion, it has the potential to do work or cause change. Kinetic energy is the energy that is associated with this motion and is dependent on the object's mass and velocity (speed).

So, Kinetic Energy is the energy that an object possesses when it is in motion. Any moving object has kinetic energy; the faster it moves, the more kinetic energy it has.

The formula for calculating kinetic energy is:

$$\mathrm{E}_{\mathrm{k}}=\frac{1}{2} \mathrm{mv}^2$$

In plain English, Kinetic Energy (KE) equals = $$\frac{1}{2}$$ (multiplied by) Mass (m) × (multiplied by) Velocity squared (v²)

This means that kinetic energy is directly proportional to an object's mass and the square of its velocity.

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For example, consider a car moving at a speed of 50 miles per hour (mph) and a bicycle moving at a speed of 10 mph. The car has a greater mass than the bicycle, requiring more force to set it in motion. The car, therefore, has a higher kinetic energy than the bicycle.

Now, let's look at the same car moving at different speeds. Suppose the car initially moves at 50 mph and then accelerates to 100 mph. At 100 mph, the car has four times as much kinetic energy as it did at 50 mph, even though its speed has only doubled.

Another example of kinetic energy is a ball being thrown. When you throw a ball, it has kinetic energy because it is in motion. The harder you throw the ball, the more kinetic energy it has. This kinetic energy is transferred to another object when the ball collides with it, such as a wall or a person's hand.

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So, a car of mass 3000 kg is travelling at 30 m/s. What would be in the kinetic energy store?

Calculation

$$E_k=\frac{1}{2} m v^2=\frac{1}{2} \times 3000 \times 30^2=1,350, \mathrm{000} \mathrm{J}$$

In summary, kinetic energy is the energy that an object possesses due to its motion. An object's kinetic energy depends on its mass and velocity. The faster an object moves, the more kinetic energy it has; the heavier the object, the more kinetic energy it requires to set it in motion.

## Gravitational potential energy stores

Gravitational potential energy is a type of potential energy that is stored in an object due to its position in a gravitational field. The concept of gravitational potential energy is based on the gravitational force between objects with mass. The force of gravity is a universal force that exists between all objects with mass, and it acts to pull these objects together.

When an object is lifted above the ground, it gains gravitational potential energy because it can fall back to the ground and, in doing so, release this potential energy. The amount of gravitational potential energy an object has depends on its mass, height above the ground, and the strength of the gravitational field.

The formula for calculating gravitational potential energy is:

Ep = mgh

So, in the equation Ep = mgh, Ep represents potential energy, m represents mass, g represents the acceleration due to gravity, and h represents height.

The equation shows that the gravitational potential energy of an object increases as its mass and height above the ground increase. For example, a heavier object lifted to the same height as a lighter object will have more gravitational potential energy. Similarly, an object lifted to a greater height will have more gravitational potential energy than an object lifted to a lower height, even if they have the same mass.

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An example of gravitational potential energy is a roller coaster at the top of a hill. The roller coaster gains gravitational potential energy as it is lifted to the top of the hill. The higher the roller coaster is lifted, the more gravitational potential energy it has. When the roller coaster is released and rolls down the hill, it converts its potential energy into kinetic energy, which allows it to move.
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Another example of gravitational potential energy is a rock at the top of a cliff. The rock gains gravitational potential energy as it is lifted to the top of the cliff. When the rock falls from the cliff, it converts its potential energy into kinetic energy, which causes it to move and collide with the ground.

In summary, gravitational potential energy is a type of potential energy that is stored in an object due to its position in a gravitational field. It depends on an object's mass and height above the ground and can be converted into other forms of energy, such as kinetic energy, when the object falls or moves.

## Elastic potential energy stores

Elastic potential energy is a type of potential energy stored in an object when it is stretched or compressed. This type of energy is due to the elastic properties of certain materials, which allow them to return to their original shape after being stretched or compressed. Elastic potential energy is an important concept in physics and engineering used in many everyday devices and structures.

The formula for calculating elastic potential energy is:

Ee = $$\frac{1}{2}$$ke2

In the equation Ee = $$\frac{1}{2}$$ke2, Ee represents Elastic Energy (Elastic Potential Energy), k represents the spring constant (a measure of the stiffness of the material), and e (extension) represents the displacement from the equilibrium position.

The equation shows that the amount of elastic potential energy stored in any object depends on the material's stiffness and how much it has been stretched or compressed.

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An example of elastic potential energy is a stretched rubber band. When a rubber band is stretched, it stores elastic potential energy that can be released when the rubber band is released. So, the more the rubber band is stretched, the more elastic potential energy it stores, which means it will snap back with greater force when released.
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Another example of elastic potential energy is a compressed spring. When a spring is compressed, it stores elastic potential energy that can be released when the spring is released. The amount of elastic potential energy stored in the spring depends on how much it has been compressed and the material's stiffness. Stronger springs require more force to compress but store more elastic potential energy.
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A third example of elastic potential energy is a diving board. When someone stands on a diving board, it bends and stores elastic potential energy. When the person jumps off the board, the diving board releases its elastic potential energy, causing the person to jump higher than they would have if they had just stood on a non-flexible surface.

In summary, elastic potential energy is a type of potential energy that is stored in an object when it is stretched or compressed. It is due to the elastic properties of certain materials and can be calculated using the equation Ee = $$\frac{1}{2}$$ke2.

## Revision Quiz

To answer the questions correctly, hover over each option and click to select it. After you finish, click 'Submit' to check your score and see the correct answers and explanations. Most questions will include an explanation with the answer. Please take the time to read the explanations accompanying the answers to your questions. Doing so will give you a better overall understanding of the topic. All the best!