Unit 3.1 | Powering the Universe – Understanding Energy in Physics
- 16 minutes
- 4 formulas
- 18 questions
- 2 videos
This lesson covers what energy actually is and the three types you need for AP Physics 1. Master these and every other lesson in this unit gets easier.
Unit 3 Breakdown
In this lesson:
- You will learn what energy really is (and why it makes physics easier)
- The three types of energy in AP Physics 1 and their equations
- How to calculate kinetic, gravitational potential, and spring potential energy
- What mechanical energy is and where “lost” energy actually goes
- The 2 problem types: “what if you double it?” and “same height, different path”
Introduction
This lesson covers kinetic and potential energy: what energy is, the three types in AP Physics 1, and how kinetic and potential energy trade places as things move.
For the last three units you’ve solved problems with forces. Draw an FBD, find the net force, set it equal to [katex] ma [/katex]. That method works, but it has a weakness.
Forces are vectors. Every time a force changes direction (like on a curved ramp or a swinging pendulum) the math gets messy fast.
Energy fixes this. Energy is a scalar, meaning it has no direction. Instead of tracking every push and pull along the way, you only compare where an object starts and where it ends.
By Unit 3.3 you will use one framework, conservation of energy, to solve almost any problem in this unit in three lines. This lesson gives you the pieces that framework is built from.
What Is Energy?
Energy is the ability to cause change. A moving car can dent a wall. A book on a high shelf can fall and break something. A compressed spring can launch a ball. Each of these objects has energy because it can make something happen.
- Energy is measured in joules (J): [katex] 1 \, J = 1 \, N \cdot m [/katex].
- Energy is a scalar. It has a size but no direction, so you never break it into x and y components.
- Energy is never created or destroyed. It only transfers between objects or transforms from one type into another.
AP Physics 1 uses three types. Here they are side by side, then one at a time.
Kinetic Energy
Kinetic energy is the energy an object has because it is moving. If it has speed, it has kinetic energy.
[katex] KE = \frac{1}{2}mv^2 [/katex]
Here [katex] m [/katex] is the mass in kilograms and [katex] v [/katex] is the speed in meters per second. Two things to notice:
- Kinetic energy is never negative. A car moving left at [katex] 20\,\text{m/s} [/katex] has the same KE as one moving right at [katex] 20\,\text{m/s} [/katex].
- Speed is squared. Double the speed and the kinetic energy goes up by a factor of four, not two.
A [katex] 1500\,\text{kg} [/katex] car is driving at [katex] 20\,\text{m/s} [/katex]. How much kinetic energy does it have? What if it speeds up to [katex] 40\,\text{m/s} [/katex]?
Plug in: [katex] KE = \frac{1}{2}(1500)(20)^2 = 300{,}000 \, J [/katex]. At [katex] 40\,\text{m/s} [/katex]: [katex] KE = \frac{1}{2}(1500)(40)^2 = 1{,}200{,}000 \, J [/katex]. Doubling the speed made the kinetic energy four times larger.
Kinetic energy of a 1500 kg car
This is why a crash at highway speed is so much worse than one in a parking lot.
Gravitational Potential Energy
Potential energy is stored energy, waiting to be turned into motion. The most common type is gravitational potential energy: energy an object has because of its height.
[katex] PE_g = mgh [/katex]
Here [katex] g [/katex] is [katex] 9.8 \, m/s^2 [/katex] (the AP exam also accepts [katex] 10 \, m/s^2 [/katex]) and [katex] h [/katex] is the height in meters.
A [katex] 0.5\,\text{kg} [/katex] ball sits on a shelf [katex] 2\,\text{m} [/katex] above the floor. How much gravitational potential energy does it have?
Answer: [katex] PE_g = (0.5)(9.8)(2) = 9.8 \, J [/katex]. If the ball rolls off the shelf, that [katex] 9.8\,\text{J} [/katex] of stored energy turns into kinetic energy as it falls.
Height is relative
Height from where? You choose. The spot you call [katex] h = 0 [/katex] is the reference point. Usually you pick the lowest point in the problem. Just stay consistent, because only changes in potential energy matter.
Gravitational potential energy depends on height, not path. Lifting a box [katex] 1\,\text{m} [/katex] straight up or rolling it up a long ramp to the same height gives it exactly the same [katex] PE_g [/katex].
Spring Potential Energy
In Unit 2.2 you met the spring force, [katex] F = kx [/katex]. A stretched or compressed spring also stores energy:
[katex] PE_s = \frac{1}{2}kx^2 [/katex]
Here [katex] k [/katex] is the spring constant in N/m (how stiff the spring is) and [katex] x [/katex] is how far the spring is stretched or compressed from its relaxed length. Like speed in KE, [katex] x [/katex] is squared: compress a spring twice as far and it stores four times the energy.
A spring with [katex] k = 200 \, N/m [/katex] is compressed [katex] 0.1\,\text{m} [/katex]. How much energy does it store?
Answer: [katex] PE_s = \frac{1}{2}(200)(0.1)^2 = 1 \, J [/katex].
Mechanical Energy
The mechanical energy of an object is its kinetic plus its potential energy:
[katex] E_{mech} = KE + PE_g + PE_s [/katex]
Picture a roller coaster. Energy shifts back and forth between kinetic and potential, but without friction the total never changes. The bar charts below show it: each bar is one type of energy, and the bars always add up to the same height.
Charts like these are called energy bar charts, and the AP exam asks you to read and draw them. You’ll use them a lot in Unit 3.3.
So where does “lost” energy go?
Real coasters slow down. Real balls stop bouncing. Friction and air resistance turn mechanical energy into thermal energy (heat). Rub your hands together fast and you’ll feel it. The energy is still there, it just no longer moves the object.
Mechanical energy can decrease. Total energy never does.
▶ Watch: how to spot which types of energy a question is really about (starts at 11:44).
Recap
| Type | Equation | Depends on |
| Kinetic energy | [katex] KE = \frac{1}{2}mv^2 [/katex] | Speed (squared) |
| Gravitational potential energy | [katex] PE_g = mgh [/katex] | Height above your reference point |
| Spring potential energy | [katex] PE_s = \frac{1}{2}kx^2 [/katex] | Stretch or compression (squared) |
| Mechanical energy | [katex] E_{mech} = KE + PE [/katex] | The sum of all three |
Note – the AP formula sheet writes kinetic energy as [katex] K [/katex] and potential energy as [katex] U [/katex]. Same equations, different letters.
Problem Type 1: What if you double it?
How to spot it: “Twice the speed”, “compressed twice as far”, “three times the mass”, or answer choices like [katex] 4K_0 [/katex].
Setup: Find what is squared. [katex] KE = \frac{1}{2}mv^2 [/katex] and [katex] PE_s = \frac{1}{2}kx^2 [/katex] grow with the square of [katex] v [/katex] and [katex] x [/katex]; [katex] PE_g = mgh [/katex] grows in step with each factor.
A spring stores [katex] 2\,\text{J} [/katex] when it is compressed 3 cm. How much energy does it store when compressed 6 cm?
Twice the compression, and [katex] x [/katex] is squared: [katex] 2^2 = 4 [/katex] times the energy, so [katex] 8 \, J [/katex].
AP trap: Doubling the answer instead of quadrupling it. Twice the speed is four times the kinetic energy.
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Problem Type 2: Same height, different path
How to spot it: Lifting straight up vs. pushing up a ramp, or a straight slide vs. a curved one, ending at the same height.
Setup: Gravitational potential energy depends only on the change in height: [katex] \Delta PE_g = mg\Delta h [/katex]. The path does not matter.
AP trap: Thinking a longer ramp means more work against gravity. A longer path only matters when there is friction.
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Lesson 3.2 Preview
In the next lesson we will cover work: how forces add energy to an object or take it away, and the work-energy theorem that links Unit 2 forces to this unit.
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This article was written by Jason