5.1 Work, Kinetic, and Potential Energy
Joey Wu and Adam Maltese
5.1 Work and energy
Learning Objectives
- Describe work, energy, kinetic energy, and potential energy.
- Describe how potential and kinetic energy can be transferred from one form to another (6.PS.3).
- Calculate work, kinetic energy, and potential energy.
Work
Have you ever tried pushing a heavy couch across the room or lifting a heavy backpack onto your shoulders? Those tasks require effort and force, right? That’s what we call “work” in science. Work happens when you apply force to move or change the position of an object. For example, when you push a shopping cart at the grocery store, you’re doing work by using force to move the cart. Or when you pull a wagon filled with toys, the force you use to pull the wagon is considered work.
Work is closely related to energy. Whenever you do work, you’re transferring energy from your body to the object you’re moving or changing. Think about pedaling a bicycle – you use energy from your legs to pedal, and that energy gets transferred to the wheels, making them spin and moving the bike forward. The more force you apply and the farther you move an object, the more work you’ve done and the more energy you’ve transferred. Work helps us understand how energy gets transferred from one place to another through the application of force.
Energy
Work and energy are closely related. When you do work to move an object, you make a change to the object’s energy. You (or an object) also expend energy to do work. In fact, energy can be defined as the ability to do work or cause changes.
There are many types of energy in our life. Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy.
| Type of energy | Description |
| Mechanical | the sum of kinetic and potential energies |
| Kinetic | Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together |
| Electric | potential energy due to or stored in electric fields |
| Magnetic | potential energy due to or stored in magnetic fields |
| Gravitational | potential energy due to or stored in gravitational fields |
| Chemical | potential energy due to chemical bonds |
| Ionization | potential energy that binds an electron to its atom or molecule |
| Nuclear | potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions) |
| Chromodynamic | potential energy that binds quarks to form hadrons |
| Elastic | potential energy due to the deformation of a material (or its container) exhibiting a restorative force as it returns to its original shape |
| Sound wave | kinetic and potential energy in a material due to a sound propagated wave (a particular type of mechanical wave) |
| Radiant | potential energy stored in the fields of waves propagated by electromagnetic radiation, including light |
| Thermal | kinetic energy of the microscopic motion of particles, a kind of disordered equivalent of mechanical energy |
Figure 4.1.1 Types of Energy
Extension: Power (This content is good to know, but is not among the core concepts of this chapter)
In applications that involve work, we are often interested in how fast the work is done. For example, in roller coaster design, the amount of time it takes to lift a roller coaster car to the top of the first hill is an important consideration. Taking a half hour on the ascent will surely irritate riders and decrease ticket sales. Let’s take a look at how to calculate the time it takes to do work.
Recall that a rate can be used to describe a quantity, such as work, over a period of time. Power is the rate at which work is done. In this case, rate means per unit of time. Power is calculated by dividing the work done by the time it took to do the work.
𝑃=𝑊/𝑡
Power can be expressed in units of watts (W). This unit can be used to measure power related to any form of energy or work. You have most likely heard the term used in relation to electrical devices, especially light bulbs. Multiplying power by time gives the amount of energy. Electricity is sold in kilowatt-hours because that equals the amount of electrical energy consumed.
Let’s consider an example of rock climbing. If a rock climber did 200J to himself (by lifting his body up for a distance) in 20 seconds, the power of his work would be equal to:
P=W/t=200J/20s=10w
Kinetic energy and Potential energy
Kinetic energy is also called energy of motion. Kinetic energy is the energy of moving matter. Anything that is moving has kinetic energy—from atoms in matter to stars in outer space. Things with kinetic energy can do work.
The amount of kinetic energy in a moving object depends directly on its mass and velocity. An object with greater mass or greater velocity has more kinetic energy. You can calculate the kinetic energy of a moving object with this equation:
𝐾𝐸=1/2𝑚𝐯2
Potential energy, sometimes called stored energy, comes in several forms. Often, the person or object has potential energy because of its position or shape.
Gravitational potential energy is the stored energy an object has as a result of its position above Earth’s surface (or another object in space). Like the diver on the diving board in the picture above, anything that is raised up above Earth’s surface has the potential to fall because of gravity. A roller coaster car at the top of a hill has gravitational potential energy.
Gravitational potential energy depends on the mass of an object and its position relative to the Earth’s Surface.
P𝐸=𝑚gh
If you remember the formula of weight from previous chapters, you will find the “mg” in Potential Energy is equal to the Weight of the object. Thus, we can rewrite the formula of PE as
PE = Weight * Height
CALCULATING THE KINETIC ENERGY OF A PACKAGE
Suppose a 20.0-kg package on a roller belt conveyor system is moving at 0.50 m/s. What is its kinetic energy?
Strategy
Because the mass (m) and speed or velocity (v) are given, the kinetic energy can be calculated from its definition as given in the equation KE = (1/2) mv2.
Solution
The kinetic energy is given by KE = (1/2) mv2. Entering known values gives
KE = 0.5 * (20.0kg)*(0.50m/s)2
which yields
KE=2.5kg⋅m2/s2=2.5 J.
Exercises
Q: In the picture below, Simone Biles took part in the Balance Beam Final at Tokyo 2020. Biles on the balance beam pictured in the Figure below weighs 463 Newtons. If the balance beam is 1.2 meters above the ground, what is her gravitational potential energy?
Solution
The potential energy is given by PE = weight * height. Entering known values, we have
PE = 463N * 1.2m = 555.6J
Elastic Potential Energy
Although gravitational energy is the most common potential energy, there are other types of potential energy. Potential energy due to an object’s shape is called elastic potential energy. This energy results when an elastic object is stretched or compressed. The farther the object is stretched or compressed, the greater its potential energy is. A point will be reached when the object can’t be stretched or compressed any more. Then it will forcefully return to its original shape.
Look at the pogo stick in the Figure below. Its spring has elastic potential energy when it is pressed down by the boy’s weight. When it can’t be compressed any more, it will spring back to its original shape. The energy it releases will push the pogo stick—and the boy—off the ground.
Discussion
Kinetic energy is the energy an object has due to its motion. The faster something moves, the more kinetic energy it has. However, even a heavy package moving slowly doesn’t have a lot of kinetic energy. That’s why people can move heavy things without getting too tired – the kinetic energy isn’t that high at low speeds.
Potential energy is energy that’s stored based on an object’s position or situation. One type is gravitational potential energy, which depends on how high up an object is. The higher you lift something, the more gravitational potential energy it gains. It’s kind of like winding up a toy car – you’re storing energy that can be released later when you let it go.
When you lift a backpack onto a high shelf, you’re increasing its gravitational potential energy by moving it higher off the ground. If it falls, that stored potential energy gets transferred into kinetic energy of motion as it drops.
An important idea is that the total energy in the universe always stays constant. Energy can change forms, like from potential to kinetic, but it can’t just appear from nowhere or disappear completely. The amount stays the same, it just gets shifted around and transformed.
Key Takeaways
The key takeaways from this chapter include:
- Energy can be defined as the ability to do work or cause changes.
- Kinetic energy (KE) is the energy of moving matter. Anything that is moving has kinetic energy.
- The amount of kinetic energy in a moving object depends directly on its mass and velocity. It can be calculated with the equation
- KE = 1/2 * mass * velocity2
- Potential energy is energy that is stored in a person or object.
- Gravitational potential energy is due to the position of an object above Earth’s surface. The object has the potential to fall due to gravity. Gravitational potential energy depends on an object’s weight and its height above the ground (GPE = weight x height).
- Elastic potential energy is due to an object’s shape. It results when an elastic object is stretched or compressed. The more it is stretched or compressed, the greater its elastic potential energy is.
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Information gathered and edited from:
https://openstax.org/books/physics/pages/9-introduction
https://openstax.org/books/physics/pages/9-1-work-power-and-the-work-energy-theorem
https://en.wikipedia.org/wiki/Energy
https://flexbooks.ck12.org/user:c1a5964ef3e3/cbook/q205-stem-for-educators/section/8.3/primary/lesson/potential-energy-ms-ps/
Media Attributions
- Shopping cart
- pedaling-cadence
- Diver
- Simone Biles
- pogo stick
The rate at which work is done. Here, rate means per unit of time. Power is calculated by dividing the work done by the time it took to do the work.
energy of motion
stored energy
