The following formula is used to describe the conservation of energy within a system that contains both kinetic and potential energy.

## What is conservation of energy?

Conservation of energy is a fundamental law of physics. The law states that energy within a system cannot be created or destroyed. That means that in order for the overall energy of a system to change, it must either act as a force on an outside object or be acted on.

You might be thinking, well yes, but then what about a system of a car? It clearly can gain and lose kinetic energy. Yes, cars obviously move, but, they gain kinetic energy through the loss of potential energy. This potential energy is contained within the fuel of the car. Combustion changes the composition of the fuel, which changes potential energy to kinetic heat/pressure which in turn move the car.

## Example Problem

Let’s take the example of the car above an analyze this problem with numbers.

First, we need to find the kinetic energy of the car initially. We will assume it’s at rest, which means it has 0 kinetic energy to start.

Next, we need to find the potential energy of the car. We will say that the car is on a flat road, so the only potential energy is that contained within the fuel. We determine this to be 1,000 Joules. (Not realistic numbers)

Next, we need to determine the final kinetic energy. It’s found that the car contains 500 Joules of kinetic energy after some time of acceleration.

Finally, we can calculate the final potential energy using the formula above, so, 1,000 – 500 – 0 = 500 Joules of potential energy.

## Related Calculators

- Kinetic Energy Calculator
- Rotational Kinetic Energy Calculator
- Gravitational Potential Energy Calculator

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