Kinetic & Potential Energy - Online Tutor, Practice Problems & Exam Prep

Mechanical energy encompasses both kinetic energy and potential energy, which are interconvertible forms of energy related to an object's motion and position, respectively. Kinetic energy (KE), measured in joules (J), is calculated using the formula:

$\mathrm{KE}=\frac{1}{2}m{v}^2$

where 'm' represents mass in kilograms and 'v' is velocity in meters per second. Potential energy (PE), also measured in joules, is determined by the formula:

$\mathrm{PE}=mgh$

with 'm' being the mass, 'g' the acceleration due to gravity (9.8 m/s² on Earth), and 'h' the height in meters. Understanding these concepts and their formulas is crucial for converting between kinetic and potential energy, providing a foundational knowledge for physics and other sciences.

Kinetic & Potential Energy

Kinetic energy and potential energy are connected to one another because they form part of mechanical energy. Now mechanical energy is energy an object possesses due to its motion as kinetic energy or its position as potential energy. Now with kinetic energy and potential energy we have formulas that are important to remember.

So the kinetic energy formula is used for an object in motion that has a mass and velocity which is connected to its speed. Here we say kinetic energy, which is abbreviated as KE, equals half times m * v². Here M equals the mass of the of the gas in kilograms and V equals velocity of the gas in meters per second. Kinetic energy KE is in Joules, which is capital J. Or just think about it. If this is in kilograms and we're squaring meters per second, that would mean that joules are equivalent to kilograms times meter squared over second squared.

KE = 1 2 m v 2

Potential energy formula is used for a stationary object that has a mass and a height. Now here we say potential energy, which is abbreviated as PE equals m * g * H. Here M equals the mass of the object, again in kilograms. And here we're going to say G is acceleration due to gravity, and here on Earth that is 9.8 meters over seconds squared. So that's going to be as close as we get to physics this semester. So just keep that in mind in terms of acceleration due to gravity.

PE = m ⁢ g ⁢ H

For those of you who are going to take physics or have taken physics, you should know this, umm type of idea. And then H equals the height of the object in meters. So just remember kinetic energy and potential energy are different, but they form the sum of mechanical energy.

Kinetic & Potential Energy Example 1

Calculate the kinetic energy in kilojoules of an electron which has a mass of 9.11 * 10 to the -31 kilograms moving at 1.59 * 10 to the 20 meters per second. All right, so we need to find the kinetic energy. Remember, kinetic energy, which is KE, equals half times your mass in kilograms times your velocity squared. Your velocity here would be in meters per second.

So all we got to do here is plug in the values that are given to us. They're already in the right units. So we have half the mass of our electron is 9.11 * 10 to the -31 kilogram. Our velocity here is 1.59 * 10 to the 20 meters per second. Remember this is going to be squared. We're going to have half times again R mass of our electron.

When I square the velocity, what I'm going to get initially is

2.582 5 / 2 8 1 * 10 40 meters per second over seconds meters squared over second squared

O. Now we have that. Now I'm going to multiply everything together so half times the mass times the velocity that I just squared here. When I plug all those in to get together into my calculator, I'm going to get

1.15 * 10 10

Now what units will we have here? Well, I have kilograms here, and it's multiplying meters squared over seconds squared. When I do that, I'm going to get kilograms times meters squared over second squared. Remember, this is the same thing as saying joules, So my units here will be in joules. If we look at the question, it doesn't want the answer in joules. Who wants it in kilojoules?

So there's one step left to do. We want to get rid of Joules, so Joules go on the bottom. We want kilojoules, so kilojoules goes on top. 1K is 10 to the three, so this comes out to be

1.15 * 10 7 kilojoules

So this would be the kinetic energy of our electron when it's traveling in this particular velocity.

A radioactive particle weighing 7.20 x 10³ ng is found 110 m above the earth's surface. What is its potential energy?

• A. 7.8 x 10^-6 J
• B. 7.2 x 10^-9 J
• C. 7.9 x 10^-9 J
• D. 7.2 x 10^-6 J

Kinetic & Potential Energy

Now remember, since kinetic energy and potential energy are forms of mechanical energy, you can convert between them. So that would mean that kinetic energy equals potential energy.

Which would mean that 12mv2 equals mgh. So just remember, if you're given kinetic energy, there are ways to convert it into potential energy, and if you're given potential energy, you can convert it to kinetic energy.

Kinetic & Potential Energy Example 2

Here we're told that a neutron weighing 1.67 * 10 to the -27 kilograms is shot from a laser projector that is mounted 120 meters above the ground. Was its speed when it hits the ground. All right, so they're talking about the neutrons position initially, and then they're talking about shooting it towards the ground. Therefore it's converting into kinetic energy. From that information we should be able to calculate its speed or velocity.

Remember, kinetic energy can equal potential energy. Since they're both part of mechanical energy. That mean half times m * V² = m * g * H Here the mask for both would be the same, since it's a neutron that's stationary first and then it's moving. We're looking for velocity or speed so that v² is what we're solving for. Mass again is the same. Then we're going to say gravity duo. Acceleration here on Earth is 9.8 meters over second squared, and it's mounted 120 meters above the ground.

We're going to multiply these together and multiply everything here together. When we do that, we get 835 * 10 to the -28, and that's v² = 1.96392 times 10 to the -24. Then we're going to divide both sides by 8.35 * 10 to the -28. So when we do that, that's going to isolate our v² here. So when we do that, we're going to get v² = 2 three 5-2, and that's going to be meters squared over, seconds squared.

Taking the square root of both of those sides will isolate our velocity or speed. So here when we do that, we get our velocity equal to four 8.4974 meters over seconds. Here, this has three sig figs. This has four sig figs. So let's just go with lease number sig figs. So that's going to be 48.5 meters per second. So that would be the speed or velocity of the neutron as it strikes the ground.

Here’s what students ask on this topic:

What is the difference between kinetic and potential energy?

Kinetic energy and potential energy are two fundamental forms of energy that describe different states of objects. Kinetic energy is the energy that an object possesses due to its motion. It is dependent on the mass of the object and the square of its velocity. The faster an object moves, or the more massive it is, the more kinetic energy it has. The formula for kinetic energy (KE) is:

$\mathrm{KE}=\frac{1}{2}m{v}^2$

where m is mass and v is velocity.

Potential energy, on the other hand, is the stored energy in an object due to its position or configuration. It is the energy that an object has the potential to release as another form of energy, such as kinetic energy. Gravitational potential energy, for example, depends on an object's mass, the height above the ground, and the acceleration due to gravity. The formula for gravitational potential energy (PE) is:

$\mathrm{PE}=mgh$

where m is mass, g is the acceleration due to gravity, and h is height. Potential energy can also be elastic, such as the energy stored in a stretched or compressed spring.

What is the relationship between potential and kinetic energy?

The relationship between potential and kinetic energy is fundamentally intertwined through the principle of energy conservation. Potential energy is stored energy based on an object's position or configuration, while kinetic energy is the energy of motion. When an object with potential energy begins to move, its potential energy is converted into kinetic energy.

For example, if you lift a ball to a certain height, it gains gravitational potential energy. When you let it go, this potential energy is transformed into kinetic energy as the ball falls, increasing its speed until it hits the ground or reaches its maximum speed. The total amount of energy remains constant if we ignore air resistance and other losses - this is the law of conservation of energy.

In essence, potential energy can be seen as the energy ready to be transformed into kinetic energy, which is the energy an object exhibits while in motion. The two forms of energy are directly related; as one increases, the other decreases proportionally, assuming no energy is lost from the system.

What are potential and kinetic energy?

Potential energy is the energy that an object possesses due to its position or condition. For example, when you lift a ball off the ground, it has gravitational potential energy because of its elevated position relative to the Earth. There are other forms of potential energy as well, such as elastic potential energy found in stretched or compressed springs, and chemical potential energy stored in the bonds of molecules.

Kinetic energy, on the other hand, is the energy of motion. Any moving object has kinetic energy, which depends on its mass and velocity. The faster an object moves, or the more massive it is, the more kinetic energy it has. When you let go of the ball that you lifted, its potential energy converts into kinetic energy as it falls.

Both potential and kinetic energy are fundamental concepts in physics, and they play a key role in the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

How are potential energy, kinetic energy, and total energy related?

Potential energy and kinetic energy are two primary forms of mechanical energy. Potential energy is the energy stored in an object due to its position or configuration, while kinetic energy is the energy of motion, depending on the object's mass and velocity.

The relationship between potential energy (PE), kinetic energy (KE), and total energy (TE) of a system is described by the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In an isolated system with no external forces, the total energy remains constant. This means that as potential energy increases, kinetic energy decreases by the same amount, and vice versa.

Mathematically, this relationship can be expressed as:

$\mathrm{TE}=\mathrm{PE}+\mathrm{KE}$

As an object moves and changes position in a system, such as a roller coaster reaching the top of a hill (maximum PE and minimum KE) and then descending (decreasing PE and increasing KE), the total energy remains the same if we ignore friction and air resistance.

How does energy change from potential to kinetic?

Energy can change from potential to kinetic through various processes where a system's state alters in such a way that the stored energy (potential energy) is converted into energy of motion (kinetic energy).

For example, consider a ball held at a certain height above the ground. It has gravitational potential energy due to its position in the Earth's gravitational field. When the ball is released, the force of gravity acts upon it, causing it to accelerate towards the ground. As the ball falls, its potential energy decreases while its kinetic energy increases proportionally, because the energy is being transformed from being stored (due to its height) into motion (as it speeds up).

This conversion also applies to other forms of potential energy, such as elastic potential energy in a stretched or compressed spring, or chemical potential energy stored in fuel. When the spring is released or the fuel is burned, the potential energy is converted into kinetic energy, causing movement or work to be done.