At what position is the kinetic energy equal to the potential energy?

$\begingroup$

Closed. This question is off-topic. It is not currently accepting answers.

Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better

I've been given that there is a spring holding a $.25kg$ mass where $k=10N/m$ and is held at $40cm$ and then let go. I've found that the max velocity is $2.53m/s$ and that when the spring is at $20cm$ the velocity is $2.19m/s$

What I'm having a hard time wrapping my head around is finding the position when the kinetic energy and potential energy are equal.

I keep trying to arrange it like so but end up with two unknowns

$.5(10N/m)(\Delta x)^2 = .5(.25kg)v^2$

Energy is a fascinating concept. It can neither be created nor destroyed, but it can be altered. Whenever you use or store energy, you deal with potential or kinetic energy. Read on as we discuss these two energy forms in greater detail and explore the relationship between them. 

What Is Potential and Kinetic Energy and What Are Their Differences?

You need energy to do any work, which is why the ability to do any work is energy.   

Read that again.  

Potential and kinetic energy are two forms of energy that can be converted into each other. Potential energy can be converted to kinetic energy and vice versa.   

Potential energy is the stored energy in any object or system by virtue of its position or arrangement of parts. However, it isn’t affected by the environment outside of the object or system, such as air or height.   

On the other hand, kinetic energy is the energy of an object or a system’s particles in motion. Contrary to potential energy, the kinetic energy of an object is relative to other stationary and moving objects present in its immediate environment. For instance, the kinetic energy of the object will be higher if the object is placed at a greater height.  

Potential energy isn’t transferrable and it depends on the height or distance and mass of the object. Kinetic energy can be transferred from one moving object to another (vibration and rotation) and is dependent on an object’s speed or velocity and mass.  

Let’s explain P.E and K.E with the help of an example.  

Imagine you have a hammer in your hand. When you raise the hammer higher, it’ll have potential energy. But as you drop the hammer downwards to bang on a table’s surface, it’ll have kinetic energy.  

There are three interesting things you should note here.   

First, the raised hammer has more potential energy since it has the potential to go higher or lower. Second, when you hit the hammer on the table, the stored potential energy is converted to kinetic energy as the hammer is falling. (It’s the falling hammer that has kinetic energy.) Third, as soon as the hammer hits the table, the energy changes. The stationary hammer then has stored energy in the form of potential energy.  

As this example demonstrates, energy is neither destroyed nor lost during the whole process – it’s only altered from one form to another, proving the law of conservation of energy.[1]  

What Is the Relationship Between Potential and Kinetic Energy? 

You now know that potential energy is position relative, and kinetic energy is motion relative.   

The primary relationship between the two is their ability to transform into each other. In other words, potential energy transforms into kinetic energy, and kinetic energy converts into potential energy, and then back again. It’s a never-ending cycle.  

Let’s use another example: Imagine there is a book on a table.   

When the book is at rest, it has potential energy. But when you accidentally knock it off the table, this potential energy will turn into kinetic energy while the book falls since it’s in motion. However, as soon as the book hits the floor, this energy of motion will again convert to potential energy.[2] 

What Are Examples of Potential Energy? 

There are three main types of potential energy: elastic potential energy, gravitational potential energy, and chemical potential energy.[3]  

Elastic potential energy is stored in objects that can either be stretched or compressed. The more the object is stretched or compressed, the more elastic potential energy it’ll have. A classic example is a stretched rubber band. While it already has more potential energy, the further you stretch it, the higher the elastic potential energy will be.[4]  

You should also know that gravitational potential energy and elastic energy potential energy can be differentiated even further based on mechanical energy.   

For instance, a car parked at the top of a hill is an example of mechanical gravitational potential energy since the automobile has the potential to come down the hill. It’s the same with a roller coaster that halts at the highest point of the rails.[5]  

On the other hand, when an archer pulls a bow before taking aim, the pulled string has more mechanical elastic potential energy that is released once the arrow is out of the bow.  

We’ll discuss gravitational potential energy and chemical potential energy in greater detail later.  

Specific Variations:

Now that we’ve reviewed the basics, it’s time to focus on the specifics. Below, we’ll explain some of the most common forms of energy to show why they have potential or kinetic energy. 

What Is the Potential Energy of an Electron? 

Everything in the universe is made up of atoms. These atoms are composed of protons, neutrons, and electrons, which give them the power to transfer kinetic energy.  

Every atom has a nucleus around which the electrons orbit. Since these electrons are always in motion, they have kinetic energy. But things change, albeit temporarily, when you apply pressure or energy to the atom.[6]  

You see, the kinetic energy of the electrons increases when pressure is applied, causing them to move faster, ultimately making them jump into a wider orbit. After this, every electron will have stored energy that will become its potential energy.   

As this whole arrangement is temporary, the electron will release this potential energy, converting it into kinetic energy while returning to its previously smaller orbit. This is also why the total energy of an electron is the sum of its potential energy and kinetic energy.[7] 

Is a Battery Kinetic or Potential Energy? 

A battery is a form of potential energy. To explain this, we’ll have to get a little technical.  

The battery stores electrical potential energy when the electrons move from the cathode to the anode. It’s how the battery is charged.   

When the electrons move in another direction, they convert this chemical potential energy to electricity in the circuit, thus discharging the battery.[8] So, the battery is all potential energy. 

Is Electrical Energy Potential or Kinetic? 

Electrical energy can be either potential or kinetic energy since it’s created from an electric charge flow.   

Continuing with the example of a battery, we know it has electrical potential energy while charging. But once you apply force to the battery, the charged particles start to do some work, converting the potential energy into kinetic energy.   

Similarly, when you switch on a light, the potential energy travels down your wiring and is converted into light and heat that are both forms of kinetic energy.[9] 

Is Sound Energy Potential or Kinetic? 

Just like electrical energy, sound energy can be a type of potential energy as well as kinetic energy. But before getting into specifics, let’s understand what sound energy is. 

 Sound energy refers to the energy released by vibrating objects. Sound, though, is a wave that travels through a medium, such as air, which allows it to store kinetic energy and potential energy.[10, 11]  

For instance, when you play the drums, they vibrate as a result of sound waves being emitted. These waves oscillate and travel, creating kinetic energy. But when the drums are left untouched, they have more potential energy since the equipment is not in motion and has the potential to make a sound. 

Is Thermal Energy Potential or Kinetic? 

Thermal energy is just a fancy word for heat energy. It’s a form of both potential and kinetic energy.   

If you remember, the electrons of an atom have potential energy. Once you apply pressure to the electrons, they start to move rapidly, banging into each other, and releasing thermal energy as heat.   

Think of boiling water for a bit. Water, when placed on the stove, has potential energy. But once it starts to heat, the water molecules begin to move faster, creating kinetic energy.  

Thermal potential energy is potential energy at the atomic and molecular levels when the particles show the potential of converting into kinetic energy. On the other hand, thermal kinetic energy is when the atoms and molecules start moving due to heat and temperature.[12] 

Is Radiant Energy Potential or Kinetic? 

Radiant energy is a form of kinetic energy that’s created when electromagnetic waves travel through space. It might surprise you to learn that the sun is one of the biggest sources of radiant energy on our planet.[13]  

Remember that warm feeling you get once you step out of the sun? It’s the sun’s radiant energy that touches our skin. More precisely, the electromagnetic waves make our skin’s molecules move faster, which, in turn, creates kinetic energy.[14] 

Variations of Potential Energy 

There are six types of potential energy: mechanical energy, electrical energy, chemical energy, radiant energy, nuclear energy, and thermal energy.[15]   

However, our primary focus here is potential chemical potential energy and gravitational potential energy. 

What Is Chemical Potential Energy? 

Chemical potential energy is the stored chemical bonds of a substance. When you charge a battery, the battery ends up storing the chemical potential energy, which is later converted to electrical energy.[16] 

Define Gravitational Potential Energy 

The earth’s gravitational field is responsible for gravitational potential energy. The British Broadcasting Corporation describes this form of potential energy as the energy an object has by virtue of its position above the surface of the Earth.[17]  

You may have noticed that when a person dives, they always land with more force when making a splash into the swimming pool.   

*Enter earth’s gravity*  

The force of gravity uses the diver’s weight to produce kinetic energy (the diving motion) that causes the diver to splash into the pool. So, when the diver stands at the top of the diving board, it’s their gravitational potential energy, which is then converted into kinetic energy when they jump off the board. 

The Science 

With the specifics and variations out of the way, let’s examine energy further by considering how potential energy is described in other forms of studies. 

What Is Potential Energy in Physics? 

In physics, potential energy is the stored energy in an object due to its position relative to some zero position, which is an arbitrarily assigned position like the ground.[18] It adheres to several physics-related laws, such as the law of conservation of energy and the first law of thermodynamics, which state that energy is always conserved and cannot be created or destroyed.[19] 

What Is Potential Energy in Chemistry? 

Chemical potential energy is the stored energy in the chemical bonds of a substance and is broken down through different chemical reactions. The newly generated chemical energy is used in different ways, also known as work.[20]  

Work is energy in motion. Hence, chemical potential energy remains true to the basic law: potential energy is converted to kinetic energy and never created or destroyed. 

What Is Kinetic Energy and Potential Energy Formula? 

Potential energy and kinetic energy are both measured in joules (J), named after the English mathematician, James Prescott Joule. But they have different formulas with respect to their different attributes.  

Potential energy depends on the force acting on the two objects, so its formula is:[21]  

Potential Energy = mgh  

• m is the mass measured in kilograms 
• g is the acceleration due to gravity 
• h is the height in meters 
  

Kinetic energy is directly proportional to an object’s mass and the square of its velocity. Putting it in a formula[22] we get:  

Kinetic Energy = 1/2 m v²  

• m is the mass measured in kilograms 
• v is the velocity of meters per second 

Potential and Kinetic Energy Are Indispensable 

Potential energy and kinetic energy are an indispensable part of our daily lives. From simple things like brushing your teeth to just standing – everything we do involves both forms of energy.   

You’ll find various forms of energy, ranging from thermal energy to sound energy to electrical energy. But if there is one thing that they all have in common: you can categorize all of these under potential energy or kinetic energy – and sometimes both.  

Kinetic energy and potential energy play a crucial role in making our earth greener too as they help create renewable sources of energy like wind energy. In short, we’re never not going to deal with these energy forms, especially since energy isn’t ever lost – it only changes form. 

Brought to you by justenergy.com

Sources:

1. Electric Current. Lumen. . Accessed November 10, 2020.
   

1. Sound Energy. Solar Schools. https://www.solarschools.net/knowledge-bank/energy/types/thermal. Accessed November 10, 2020.
   

1. Examples of Potential Energy. Your Dictionary. https://examples.yourdictionary.com/examples-of-potential-energy.html. Accessed November 10, 2020.
   

1. Law of Thermodynamics. Estrella Mountain Community College. . Accessed November 10, 2020.
   

All images licensed from Adobe Stock.
Featured image: