Energy, Work, and Power Speed Review
- 12 minutes
- 5 formulas
- 30 questions
- 1 videos
Energy is a fundamental concept in physics that is involved in a wide range of phenomena. It is the ability to do work or produce change, and exists in various forms such as kinetic energy, potential energy, thermal energy, and electrical energy. In this article, we will explore these different forms of energy and how to solve energy problems.
Forms of Energy
There are 2 main types of energy, plus work, which transfers energy.
- Kinetic (any mass that has velocity)
- Potential (any mass has stored energy)
- Work (not a form of energy: it is energy transferred into or out of a system by a force).
Note that Elastic Energy also called spring potential energy is a type of potential energy.
Note that Mechanical Energy is only the sum of Kinetic and Potential energy.
Now let’s dive into each type of energy and cover some misconceptions.
Kinetic Energy
Kinetic energy (KE) is the energy of motion, and is given by the formula:
[katex] KE = \frac{1}{2}mv^2 [/katex]
For example, a car moving at a high speed has more kinetic energy than a car moving at a slow speed.
Now to speed something up would mean to increase kinetic energy, which would come from an external source (work done on it). This is why [katex] \Delta KE = W_{\text{net}} [/katex] (the net work)
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Potential Energy
Potential energy is the energy of position or configuration. It is stored energy that an object possesses due to its position or arrangement. There are several types of potential energy, such as gravitational potential energy, elastic potential energy, and chemical potential energy.
Gravitational potential energy \(PE_g\) is the energy of an object due to its height. It is given by the formula
[katex] PE_g = mgh [/katex]
Where “\(m\)” is mass, “\(g\)” is the value of gravity, and “\(h\)” is the height of the object.
For example, a rock at the top of a hill has more gravitational potential energy than a rock at the bottom of the hill.
Elastic (or Spring) potential energy is the energy stored in a stretched or compressed spring. It is given by the formula
[katex] U_s = \frac{1}{2}k\Delta x^2 [/katex]
Where “\(k\)” is the spring constant (how stiff the spring is), and “\(\Delta x\)” is the amount of stretch/compression in meters.
For example, a spring that is stretched more has more elastic potential energy than a spring that is stretched less.
Chemical potential energy is the energy stored in the chemical bonds of a substance. It is the energy that is released or absorbed during a chemical reaction. For example, gasoline has a high chemical potential energy, which is released when it is burned to produce energy.
Work Energy
[katex] \text{Work} = Fd\cos\theta [/katex]
In simple terms work is the force applied over a certain distance. Pushing a box is a simple example of positive work being done. The force of friction is an example of negative work being done.
Keep in mind the other definition of work:
[katex] \text{Net Work} = \Delta KE [/katex]
There are two important things to note. (1) Energy is a scalar. Positive and negative simply mean that the object is either gaining \(+\) or losing \(-\) energy. (2) Only the part of the force parallel to the displacement does work: \(\theta\) is the angle between the force and the displacement, so a force perpendicular to the motion does no work.
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Other Types of Energy
Here are a few more types of energy. You won’t calculate these on the AP Physics 1 exam, but you should know that friction turns mechanical energy into thermal (internal) energy.
Thermal energy is the energy of heat. A common example is friction. It is the energy that is transferred from one body to another as a result of a temperature difference. Thermal energy is related to the temperature of an object, with hotter objects having more thermal energy than cooler objects.
Electrical energy is the energy of electric charge. Energy is transferred through an electric circuit due to the force applied over a distance (Work done) on charged particles.
Energy Conservation
The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant, even if the energy changes form.
No change in energy → [katex] \Delta E = 0 \rightarrow E_f – E_i = 0 \rightarrow E_f = E_i [/katex]. In simple terms, this means the amount of energy a system starts with should be the exact same amount it ends with.
For example, consider a ball being thrown into the air. The ball has kinetic energy due to its motion, and it also has gravitational potential energy due to its height. As the ball rises, its kinetic energy decreases and its gravitational potential energy increases, but the total amount of energy remains constant.
Energy of a ball on the way up
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Framework for Solving Energy Problems
When solving energy problems, it is important to identify the forms of energy involved and use the appropriate formulas to calculate the energy.
- Start with the Law of Conservation of Energy which states → [katex] E_i = E_f [/katex]
- Read the scenario and identify the initial forms of energy. Write it down under [katex] E_i [/katex]
- Identify the final forms of energy. Write it down under [katex] E_f [/katex]
- Substitute the equations for each form of energy. Rearrange your equation and solve for asked variable.
Let’s practice this framework with 3 commonly asked AP Physics 1 questions on Energy
Example Problem #1
A ball is thrown straight up into the air with an initial velocity of 10 m/s. What is the maximum height reached by the ball?
| FRAMEWORK | Solving the Problem |
| Step #1. Law of Conservation of energy | [katex] E_i = E_f [/katex] |
| Step #2. Identification of initial form of energy | [katex] E_i = KE [/katex] (since the ball is moving as it’s initially thrown up) |
| Step #3. identification of final form of energy | [katex] E_f = PE [/katex] (at the maximum height all the kinetic energy transforms into gravitational potential energy |
| Step #4. Substitute KE and PE into [katex] E_i = E_f [/katex] | [katex] E_f = E_i \rightarrow KE = PE \rightarrow \frac{1}{2}mv^2 = mgh [/katex] |
| Step #5. Rearrange and solve for unknown | Solve for height → [katex] h = \frac{v^2}{2g} [/katex] |
Show Further Explanation
The maximum height of the ball is determined by the balance between its initial kinetic energy and the gravitational potential energy it gains as it rises. As the ball rises, its kinetic energy decreases and its gravitational potential energy increases, until all of the kinetic energy has become potential energy at the maximum height (\(KE = 0\)). At this point, the ball stops rising and begins to fall back down.
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Example Problem #2
A \(0.5 \, \text{kg}\) block is pushed up a frictionless ramp. The block starts at rest at the bottom of the ramp and reaches a height of \(2 \, \text{m}\) at the top, where it is at rest again. How much work is done on the block by the applied force?
| Framework Step | Solving the Problem |
| Step #1. Law of Conservation of energy | [katex] E_i = E_f [/katex] |
| Step #2. Identification of initial form of energy | [katex] E_i = \text{Work} [/katex](since the box is being pushed up) |
| Step #3. identification of final form of energy | [katex] E_f = PE [/katex] (since the work energy being applied is causing the block to gain height, thus potential energy) |
| Step #4. Substitute KE and PE into [katex] E_i = E_f [/katex] | [katex] E_f = E_i \rightarrow W = PE \rightarrow W = mgh [/katex] |
| Step #5. Rearrange and solve for unknown | Solve for Work → [katex] W = mgh [/katex] = (.5)(9.8)(2) = 9.8 J |
Show Further Explanation
As the block is pushed up the ramp, it gains gravitational potential energy due to its increasing height. The work done on the block by the applied force is equal to the change in the block’s gravitational potential energy, which is equal to the applied force times the distance the block moves.
*You might wonder why we couldn’t simply use W = Fd. It’s because we are given the height NOT the length (d) of the ramp. Remember that only the part of the force parallel to the displacement does work.
Conservative vs Non-Conservative Systems
Let’s clear up a misconception: “Non-conservative” does NOT mean energy is not conserved in the system. [katex] E_i = E_f [/katex] (Energy is conserved) as long as no net external work is done on the system.
A conservative force does not depend on the path an object takes. Think about gravity acting on a block. Whether it’s sliding down a ramp, or being dropped straight down from the height of the ramp, it will still have the same energy.
A non-conservative force does depend on the path taken. Think about friction. If you push a block up or down a ramp, there will be energy “dissipated” that can’t be transformed back into potential or kinetic energy.
| Non-Conservative Forces | Conservative Forces |
| Friction and air resistance | Gravitational |
| Tension | Elastic (springs) |
| Motors, engines, or rockets | Electric |
| A person pushing/pulling |
Important things to remember:
- Work done by ALL non-conservative forces, is just [katex] \text{Work} = Fd\cos\theta [/katex]
- Another way to find the work done by a non-conservative force → [katex] W_{NC} = \Delta KE + \Delta PE [/katex]. This simply tells us that the amount of energy lost or gained from both potential and kinetic energies is the total amount of work done by a non-conservative force.
- If there is NO work done by non-conservative forces in a system, then the system has purely mechanical energy.
- HINT: use the problem solving framework above to solve any energy question, regardless of the types of forces in the system.
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Power
Power is the rate at which energy is transferred: the work done per unit of time.
[katex] P = \frac{W}{t} [/katex]
Where “\(W\)” is the work done and “\(t\)” is the time taken.
The units are Joules/second. We commonly call this Watts (common in light bulbs) or Horsepower (common in cars).
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This article was written by Jason