# Calculating Changes in Kinetic & Potential Energy of a System

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

A system of interacting objects can have both kinetic and potential energy. As potential energy changes, this can change the kinetic energy of the system, too. In this lesson, learn about these important types of energy and how they can change.

## Kinetic Energy

In an important game, Sarah throws a basketball into the air and watches as it goes up and then comes back down to the hands of her teammate. While it's in the air, does the ball have energy? Yes, of course it does! When an object, like the basketball, is moving, then it has a type of energy called kinetic energy.

Kinetic energy is the energy of motion, and the amount of kinetic energy that an object possesses depends on two things: the mass of the object and how fast it is moving. This means that a really heavy object, like a car, could have the same kinetic energy as a fast moving light object, like the basketball, even if the car was moving very, very slowly.

## Work and Kinetic Energy

How do you change the kinetic energy of an object like the basketball? You probably could guess that you need to push on it, right? When Sarah wanted to throw the ball, she pushed on it with her hands, transferring energy from her body to the ball. When a force is exerted on an object over a certain distance, we say that work is being done on the ball. The amount of work done is always equal to the change in the object's kinetic energy.

## Choosing a System

In physics, a system includes just the object or objects whose motion you want to consider. In any situation, you get to choose what you want to include in the system, and what you choose to include will have a big impact on how you solve the problem! Everything that is not part of the system is considered to be part of its surroundings.

Even though we did not explicitly define it in the previous example, it is pretty obvious that the system was just the basketball because that was the object whose motion we were looking at. As we already saw, when work was done by the surroundings (the basketball player's hands) on the system (the ball), it changed the kinetic energy of the ball.

What would happen if we chose a different system, though? What if we included both the player and the basketball in the system? Then, the force exerted between the player's hands and the ball is inside the system and there are no forces from the surroundings that act on the ball. So, how does the system's kinetic energy change then?

When you have a system containing multiple objects, the total energy inside the system, known as internal energy, will remain unchanged if no objects in the surroundings do any work on the system. However, kinetic energy is not the only kind of energy that a system can have. The system can also have potential energy due to the configuration of the objects in the system.

## Potential Energy

Although there are several types of potential energy, one of the most commonly encountered is gravitational potential energy. In many situations, it makes sense to include the Earth in the system along with the object whose motion you want to understand. This is because the Earth always exerts a gravitational force on any object that is near its surface. By including this force inside the system, you don't have to worry about calculating how much work is being done by the Earth on the object. Instead, you can calculate how much gravitational potential energy is contained in the system and then add this to the kinetic energy of the object to determine the total internal energy of the whole system.

The gravitational potential energy of an object depends on its weight and its current height.

## Energy Transformations within a System

Remember that even if no forces from the surroundings are doing work on the system, energy within the system can still change forms. To see this in action, hold up a ball and then let go of it. What happened?

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