We’ve learned a lot so far about how and why things move. What we haven’t learned is what allows one object to exert a force on another. Energy is an important concept in physics that is used to understand large and small processes. Here, we’ll begin with the energy of a moving object by exploring examples of kinetic energy and how to calculate it. We’ll also dive into the differences between kinetic and potential energy.

What is Kinetic Energy?

“Kinetic” and “energy” are both words we should be familiar with at this point. “Kinetic” comes up when discussing the friction of a moving object. “Energy” is one you’ve probably heard a lot in your life. It probably has a meaning similar to “the ability to do something” and that’s what it means in physics, too. We refine it a bit to mean the ability to do work or exert a force on an object over a displacement. From this, we can guess that kinetic energy should have something to do with things moving and their ability to exert a force. While that isn’t a perfect definition, it is fairly close.

Definition

Kinetic energy does, indeed, have to do with an object in motion. It is the energy an object has because of its motion and we can think of it in terms of the force that can be exerted on an object or the force it would take to stop the object. The way we want to think about this force will change in different situations. In general, though, the kinetic energy of a moving object can be thought of as a measure of how far the object’s velocity is from zero. The greater the velocity, the greater the energy.

Examples of Kinetic Energy

One familiar example of kinetic energy and how it changes depending on velocity could be walking versus running. It’s much harder to stop quickly when running at full speed than it is when walking slowly. The same applies to driving a car – the faster it’s going, the sooner the brakes need to be hit. This applies to our everyday lives but is also often built into video games. Have you noticed how much harder it can be to take a sharp turn in a racing game when driving at full speed than it is when slowing down? You have kinetic energy to thank for that.

How to Calculate Kinetic Energy

So far, we’ve been talking a lot about the velocity of a moving object relative to kinetic energy. While that is an important factor, there is another factor – mass. The mass of an object is a measure of its inertia, of how hard it is to change its motion. To find the kinetic energy of an object, then, we must account for both its velocity and its mass. These two values don’t have the same impact on the kinetic energy of a moving object, though.

Kinetic Energy Formula

The formula for kinetic energy is written as:

Here, the E_{K} symbol is used to represent kinetic energy, m represents the mass, and lastly v represents the velocity. We’ll work with this equation in just a moment, but first, there are two very important conceptual points to be made here. First, is that we haven’t seen this combination of values before, which means we have a new unit to work with. Energy is measured in Joules, which is denoted J. Second, the velocity is squared while the mass is not.

How Mass and Velocity Affect Kinetic Energy

Because the velocity has a higher exponent than the mass does, the velocity will have a larger impact on the kinetic energy of a moving object. For example, if the mass were to double the kinetic energy would also double, but if the velocity doubled the kinetic energy would be quadrupled. Similarly, if the mass were halved then the kinetic energy would be halved, but if the velocity were halved the kinetic energy would be quartered.

Examples of Calculating Kinetic Energy

Now that we know the equation, we can start using it to calculate kinetic energy. We’ll follow our normal problem-solving method to first find kinetic energy and then to find mass from kinetic energy and velocity.

Example 1: Finding Kinetic Energy from Mass and Velocity

A 6\text{ kg} bowling ball is rolling toward the pins at 7\text{ m/s}. What is the kinetic energy of the bowling ball?

Solution:

• m=6\text{ kg}
• v=7\text{ m/s}
• E_{K}=\text{?}
• E_{K}=\frac{1}{2}mv^{2}

E_{K}=\frac{1}{2}mv^{2}

E_{K}=\frac{1}{2}(6\text{ kg})(7\text{ m/s})^{2}

E_{K}=147\text{ J}

Example 2: Finding Mass From Kinetic Energy and Velocity

A flamboyance of flamingo flies at an average speed of about 17\text{ m/s}. If one of the flamingos has a kinetic energy of 430\text{ J}, what is its mass?

Solution:

• v=17\text{ m/s}
• E_{K}=430\text{ J}
• m=\text{?}
• E_{K}=\frac{1}{2}mv^{2}

E_{K}=\frac{1}{2}mv^{2}

m=\dfrac{2\cdot E_{K}}{v^{2}}

m=\dfrac{2\cdot 430\text{ J}}{(17\text{ m/s})^{2}}

m=3\text{ kg}

Differences Between Kinetic and Potential Energy

Kinetic energy is not the only important energy type in mechanical physics. The other energy you’re likely to encounter is potential energy. Both kinetic energy and potential energy are important to how we view and understand the world and there is one key difference between them.

What is Potential Energy?

Potential energy is the energy stored in an object that gives it the potential to do something. This is the energy in an object that is not moving or exerting a force, but it could. We often see this as gravitational potential energy – the potential to fall – or as spring potential energy – the potential to launch something with a spring. A more in-depth explanation of potential energy can be found in a separate post, but the important thing to remember is that potential energy is the potential to complete an action.

How Kinetic and Potential Energy Relate to Each Other

Kinetic energy is energy that comes from motion. Potential energy, on the other hand, is the energy an object has the potential to use for motion. These energies can be transformed into one another. Let’s consider an example of potential energy transforming into kinetic energy. Before jumping out of a plane, a skydiver has no kinetic energy but does have a lot of potential energy. Once they jump out of the plane, their potential energy will decrease as they get closer to the ground and that energy will be shifting into kinetic energy as the skydiver’s velocity increases. The skydiver’s kinetic energy will increase at the exact same rate that its potential energy decreases. The same would be true for any object whose potential energy is transforming into kinetic energy or for one whose kinetic energy is transforming into potential energy.

Conclusion

Mechanical energy is constantly present in our lives and it’s an important part of how we understand the universe. Kinetic energy can be found in any moving object and there are examples of kinetic energy in many aspects of daily life. It is far from the only type of mechanical energy you’ll learn about on your physics journey, but knowing how to identify and calculate kinetic energy will help as you continue to expand your knowledge of how and why objects behave as they do.