Welcome to Lesson 2!

In our last lesson, we explored the forms and sources of energy—from the chemical energy in your breakfast to the radiant energy streaming from the Sun. We learned that energy is the capacity to do work or produce heat, and that it can change forms but is never created or destroyed.

Now, we're adding a crucial piece to that foundation. Have you ever noticed that your phone battery drains faster when you're streaming video versus just texting? Or that a 13-watt LED light bulb uses electricity differently than a 100-watt bulb?

These everyday observations point to a key distinction that scientists, engineers, and even your utility company rely on:

Energy and Power are related, but they are not the same thing.

Think of it this way:

• Energy is the total amount of "fuel" you use—like the total gallons of gas put in your car this month.
• Power is the rate at which you use it—like how fast you burn that gas while accelerating onto the highway.

In physics terms:

Energy (measured in joules or kilowatt-hours) = how much work gets done

Power (measured in watts) = how fast that work happens

In this unit, we will be looking at how to convert energy and power units as well as reading electric bills. We will also learn how to calculate how much energy our household devices use and how much that costs us.

Lesson 2: Learning Objectives

By the end of this lesson, you'll see physics in action every time you flip a switch—and understand exactly what you're paying for when that bill arrives.

• Distinguish work, energy, and power using everyday examples
• Convert between units (joules ↔ kilowatt-hours) to connect physics class to your utility bill
• Calculate energy use: Energy = Power × Time (e.g., a 100 W bulb running 10 hours = 1 kWh)
• Interpret appliance labels to estimate real-world costs
• Decode an actual electricity bill—spotting how many kWh you used and why your cost per kWh isn't just the "supply rate"

In everyday life, we say we’re “working” when we study, carry groceries, or hold a heavy box. But in physics, the word work has a very specific meaning:

Work is done only when a force causes an object to move in the direction of the force.

That means three things must happen for work to occur:

1. A force must be applied.
2. The object must move (undergo displacement).
3. The motion must have a component in the direction of the force.

The Formula for Work

Where:

• Force is measured in newtons (N)
• Distance is measured in meters (m)
• θ (theta) is the angle between the force and the direction of motion
• Work is measured in joules (J) → 1 J = 1 N·m

But don’t worry—you don’t need trigonometry here. You may get in much more detail in a physics class, but not here. When force and motion are in the same direction (like pushing a shopping cart forward), cos(0°) = 1, so:

$\text{Work = Force × Distance}$

Real Examples of Work Being Done

• Pushing a stalled car 5 meters down the road → you apply force, and it moves → work is done.
• Lifting a backpack from the floor to your desk → you apply upward force against gravity, and it moves up → work is done.
• Pedaling a bike uphill → you push on the pedals, and the bike moves upward against gravity → work is done.

Common Situations Where NO Work Is Done (in physics terms!)

• Holding a heavy suitcase while standing still: You’re applying force (to counteract gravity), but there’s no displacement → zero work.
• Pushing hard against a wall that doesn’t move: Force? Yes. Motion? No → zero work.
• Carrying a box horizontally across a room: You apply upward force to hold it, but motion is horizontal. Since force (up) and motion (sideways) are perpendicular, no work is done against gravity. (You might get tired—but that’s biology, not physics!)

Units for Work: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

Energy – The “Ability” to Do Work

If work is the act of moving something with force, then energy is what enables you to do that work. As we learned in the last lesson,

Energy is the capacity to do work.

Think of energy as your “work potential.” You can store it, transfer it, or convert it—but you can’t create or destroy it (thanks to the Law of Conservation of Energy).

For example:

• A raised hammer has gravitational potential energy → when dropped, it does work on a nail.
• A charged battery has chemical energy → it can do work to light a bulb or spin a motor.
• A moving soccer ball has kinetic energy → it can do work by knocking over a cup.

Energy Units: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

**Note: Energy and Work have the same units!

Power: The rate at which we work (or energy) is done.

Now, imagine two people lift identical boxes to the same shelf:

• Person A does it in 2 seconds.
• Person B takes 10 seconds.

Both did the same amount of work (same force, same distance).
Both used the same amount of energy.
But Person A delivered more power.

Power is the rate at which work is done or energy is transferred.

 The Formula for Power

$\text{Power = }\frac{Work}{Time}\text{ = }\frac{Energy}{Time}$

• Measured in watts (W) → 1 W = 1 joule per second (J/s) 

  Bicycling Example

• Imagine two bicyclists pedal 10 miles uphill → same work, same energy (218 calories) **assuming the cyclists are approximately the same weight
• If Cyclist Y finishes in 30 minutes; while Cyclist Z the other finishes in 60 minutes
• The amount of energy used in both situation is the same, Cyclist’s Y power output is twice as high—not because he did more, but because he did it faster.
• Cyclist Y completed 10 miles in 30 minutes versus Cyclist Z 10 miles in 60 minutes

Common Units of Power: Watt (W), kilowatt (kW), horsepower (hp), British Thermal unit per hour (BTU/hr), Joule/sec (same as a Watt).

Energy, Work, and Power (3:33)

Why Unit Conversion Matters

You convert units all the time—often without even thinking about it!

• You know that 1 foot = 12 inches, so you can quickly figure out that 4 feet = 48 inches.
• You might also know that 1 yard = 3 feet, or that 1 mile = 5,280 feet.
• Maybe you’ve even heard that 1 mile ≈ 1.609 kilometers—useful when traveling or watching international sports!

When you’re familiar with the units, conversions feel easy. But what if you need to convert something less familiar—like miles to meters, gallons to liters, or joules to calories? That’s where a powerful tool comes in: the factor-label method.

What Is the Factor-Label Method?

The factor-label method (also called dimensional analysis) is a step-by-step strategy that lets you convert any unit to any other unit—as long as you know the right conversion factor.

The best part?
You never have to guess whether to multiply or divide!
The units themselves guide you.

How It Works: A Simple Example

Let’s convert 7.5 miles to feet.
We know: 1 mile = 5,280 feet

Step 1: Write down what you’re starting with

$\text{7.5 miles}$

Step 2: Multiply by a conversion factor written as a fraction

Choose the form that cancels the original unit (miles) and leaves the desired unit (feet):

$\text{7.5 miles × }\frac{\text{5,280 feet}}{\text{1 mile}}$

Notice how “miles” cancels out (one in the numerator, one in the denominator), leaving only feet.

$\text{7.5 }\cancel{\text{miles}}\text{ × }\frac{\text{5,280 feet}}{\text{1 }\cancel{\text{mile}}}$

Step 3: Do the math

$\text{75. × 5,280 = 39,600 feet}$

Why This Method Always Works

The key idea is this:

Any conversion factor is equal to 1—so multiplying by it doesn’t change the actual amount, just the units.

Since $\frac{5,280 \mathrm{ft}}{1 \mathrm{mi}}=1$, multiplying by it is like multiplying by 1—you’re just changing how you express the quantity.

This works for any unit:

• Time: seconds ↔ minutes ↔ hours
• Distance: inches ↔ cm ↔ meters ↔ km
• Energy: joules ↔ calories ↔ kilowatt-hours
• Mass: grams ↔ kilograms ↔ pounds

Pro Tips for Success

• Always write units—even in calculations. They’re your roadmap!
• Set up the fraction so the old unit cancels.
• Chain multiple steps if needed (like hours → minutes → seconds).
• Double-check: Does your answer make sense? (e.g., 7.5 miles should be many feet—not just 7!)

Final Thought

Once you master the factor-label method, no unit conversion will ever stump you again. Whether you’re solving physics problems, following a recipe, or planning a road trip abroad, this skill will serve you for life.

 Remember: Units are your friends. Let them guide you!

Want to see it in action?

Check out this helpful video tutorial:

Unit Conversion the Easy Way (6:14)

Now that we learned the factor label method for conversions, we can now try more complex conversions. Sometimes we need to convert several items in one problem.  We can do it the same, just follow the units.  

Example: Convert 55 mph to m/s

We want to change miles → meters and hours → seconds.

That means we need two conversion factors:

• 1 mile = 1,609 meters
• 1 hour = 3,600 seconds

Though it’s two changes, we use the same factor-label method—just with two fractions!

 Step-by-Step Using Factor-Label

Start with what you know:

$\text{55}\frac{\mathrm{miles}}{\mathrm{hour}}$

Step 1: Convert miles → meters

Use the fraction that cancels "miles":

$\text{55}\frac{\cancel{\mathrm{miles}}}{\mathrm{hour}}\text{×}\frac{1,609\mathrm{meters}}{1 \cancel{\mathrm{mile}}}$

→ "Miles" cancels out. Now we have meters/hour.

Step 2: Convert hours → seconds

We have “hours” in the denominator, so we need a fraction with “hours” on top to cancel it:

$\text{×}\frac{1 \mathrm{hour}}{3,600 \mathrm{seconds}}$

→ Now “hours” cancels too!

Put it all together:

$\text{55}\frac{\cancel{\mathrm{miles}}}{\cancel{\mathrm{hour}}}\text{×}\frac{1,609 \mathrm{meters}}{1 \cancel{\mathrm{mile}}}\text{×}\frac{1 \cancel{\mathrm{hour}}}{3,600 \mathrm{seconds}}$

Here's another way to look at it:

Now multiply the numbers:

$\frac{55\times 1,609}{3,600}=\frac{88,495}{3,600}\approx 2.46$

 Final answer: 55 mph ≈ 24.6 meters/second

 Key Tips for Multi-Step Conversions

1. Treat compound units (like mph) as two separate units:
   → “miles per hour” = miles ÷ hours, so convert numerator and denominator separately.
2. Always arrange conversion fractions so unwanted units cancel:
   • Want to cancel miles? Put miles in the denominator of your conversion factor.
   • Want to cancel hours? Put hours in the numerator.
3. You can chain as many steps as needed:
   Example: gallons → liters → milliliters → cm³ → m³… just keep adding fractions!

 Real-World Why It Matters

• Scientists and engineers always use metric units (like m/s), but speed limits are in mph in the U.S.
• Knowing how to convert helps you understand car safety data, physics problems, or even video game physics!
• 24.6 m/s is about how fast a major league fastball travels—so 55 mph is roughly fast-pitch softball speed!

 Quick Check: Does the answer make sense?

• 1 m/s ≈ 2.24 mph
• So 55 mph ÷ 2.24 ≈ 24.5 m/s → matches our result! 

When your estimate lines up, you know you’re on the right track.

Final Thought

Multi-step conversions might look intimidating at first—but with the factor-label method, you just add one fraction at a time, let the units cancel, and follow the math.

No memorizing “multiply or divide”—just let the units guide you!

Spot the Power Label!

Take a look around you right now. Chances are, you’re using a laptop, phone, or tablet—and it’s plugged into a charger. Flip that charger over (or look at the label), and you’ll likely see something like this:

Credit: Jennifer Clemons

Quick Check: Is Watt a unit of energy or power?

Remember from our earlier lesson:

• Power = how fast energy is used → measured in Watts (W)
• Energy = total amount used → measured in Watt-hours (Wh) or kilowatt-hours (kWh)

So Watt (W) is a unit of power—not energy!

Let’s Calculate: How Much Energy Does Your Laptop Use?

Suppose your laptop charger is rated at 65.0 W, and you use it for 10 hours each day.

$\text{Energy = Power × Time = 65.0 W × 10 hours = 650 Watt-hours }\left(\mathrm{Wh}\right)$

But utility bills don’t use Watt-hours—they use kilowatt-hours (kWh).

Since kilo = 1,000, we convert:

$\text{650 Wh × }\left(\frac{1 \mathrm{kWh}}{1,000 \mathrm{Wh}}\right)\text{ = 0.650 kWh}$

So your laptop uses 0.65 kWh per day.

What Does That Cost?

If we estimate electricity to cost about $0.15 per kWh (check your bill for your exact rate!).

$\text{0.65 kWh × \$0.15}/\text{kWh = \$0.0975 }\approx \text{ \$0.10 per day}$

That’s just 10 cents a day—or about $3 per month to run your laptop!

Depending on how much your electricity costs, you can now determine how much that one day of laptop use costs you each day (or month or year).

We will discuss appliances in more depth in a later lesson, but here is a list of common household appliances and their power ratings.  Again, they can vary greatly depending on the manufacturer and age.  Some appliances are getting significantly more efficient over time.   For the most up to date information, please check the manufacturers rating on the device you are interested in.  The table below is just an estimate. 
 

How electricity companies charge you

Have you ever looked at a utility bill? Really looked at the bill? More than just looking at the amount due. If you can, I would encourage you all to look at the bill to see some of the numbers on there. For this lesson, we are going to look at this utility bill. This is from PPL for June 2024.

At the top of the bill, you will see basic information, including:

• Account Number
• Due Date
• Amount Due
• Service Address
• Billing Period

In terms of this class, we really want to understand the usage. As we have already discussed, kWh (kilowatt-hour) is the basic unit of electricity and a unit of energy. This should be the unit on any electric bill might read. (You might see some additional units on there, including kW or BTUs, especially if your utility provides both electricity and natural gas service to your home.)

Total Usage: The amount of electricity (energy) used in the billing period. For the example bill it is 1,,434 kWh

Supply Charge versus Delivery Charge

This may be the most confusing part. This bill contains different charges for both Supply and Delivery. So what's the difference?

Supply Charge is for generating the electricity, typically from a power plant. In this example, the supply charge is $141.82 (which is the electricity usage 1,434kWh × $0.09890/kWh).

Unfortunately, that is not the only charge in this bill. Here we see a Delivery Charge. The Delivery charge is to maintain the poles and wires to deliver the electricity to your home. In this case, the Delivery Charge is $82.31, which includes all customer charges and distribution fees. You might be surprised to see the delivery charge is nearly 1/3 of the total bill. 

Depending on the provider, your bill may be more complicated or simpler than this bill. Not every utility separates out delivery and supply charges, however some companies may include additional charges like a demand charge.

So, looking at this example bill, what is the actual cost per kWh of usage?

$\text{\$224.14 total bill / 1,434 kWh = \$0.1563/kWh}$

This is much higher than the electric charge shown, because we included all the charges, taxes, and fees.

This bill also shows your usage over time. The chart on the first page of the bill shows the total electricity used between July 2023 and June 2024.   

Take a look at this bill and try and answer the following questions.  

• How much electricity was used in this time frame? (Answer: 12412 kWh)
• What is the average usage? (Answer: 1034 kWh)
• What month used the most electricity? (Answer: August)

Real-World Application

Your Turn: Grab your own (or a family member's) electricity bill and:

1. Circle the account number and due date
2. Calculate kWh used: (Current reading – Previous reading)
3. Find the split between supply vs. delivery charges
4. Note one thing that surprised you

Understanding your bill is the first step to managing energy costs wisely!

If you do not have access to an electric bill of your own, use this example electric bill from PPL Electric Utilities.

Basic Calculation

Your June bill shows:

• Supply charge: $90.00
• Delivery charge: $40.00
• Total kWh used: 875 kWh

Calculate:

Total bill = $90 + $40 = $130.00

Effective cost/kWh = $130 ÷ 875 = $0.1486/kWh

Compare Two Months

August (high usage): 1,500 kWh → $150 supply + $65 delivery = $215 total

September (low usage): 600 kWh → $75 supply + $30 delivery = $105 total

Calculate effective rates:

• August: $195 ÷ 1,500 = $0.130 /kWh
• September: $90 ÷ 600 = $0.150/kWh

Even with the same rates, September costs more per kWh because fixed delivery fees ($15–$20) get spread over fewer kWh.

Demand Charges Versus Energy Charges

We saw in an earlier part of this lesson the difference between energy and power.   For our electricity provider, our Energy use is how much kWh we use.   But we can also talk about the rate at which we use electricity, which is Power. 

For most homes, you only pay for energy (kWh). But businesses and some large facilities also pay a demand charge based on their highest power draw during the billing period. Why? Because the utility must build infrastructure (transformers, wires) sized for your peak demand not your average use.

Take for instance this example commercial bill.  It is also from PPL in June 2024, however it is much bigger than what most homeowners would pay for one month.   
PPL bill with demand charge: Commercial Bill 

On the Bill we can see the following: 

• Total Energy Used - 598,000 kWh
• Peak Demand - 1,095 kW
• Energy Charge         
• Demand Charge - $2.54701/ kW
• Days in Billing Cycle - 2
• Supply Charge $ - $0.00
• Delivery Charge - $3,133.19

In this case, the energy charge is negligible, but the customer paid a lot in their demand charge.   This customer could reduce their bill by reducing their electricity use when their draw is the highest.  Why?  Because the utility must build the infrastructure (wires and transformers) to account for your peak demand, not the average usage.

Time-of-Use Billing: 

Some utility bills use time-of-use (TOU) pricing, which charges different rates depending on the time of day you consume electricity—similar to "surge pricing" for rideshares or toll roads. During peak periods (typically 4 PM–9 PM on weekdays), rates are highest because demand on the grid spikes as people return home, cook dinner, and turn on appliances. During off-peak hours (usually 10 PM–6 AM), rates drop significantly due to much lower overall demand.

Why Peak Times Cost More

Electricity must be generated the instant it's used. When millions of households draw power simultaneously during evening hours, utilities must activate expensive "peaker" power plants to meet demand. TOU pricing reflects this real cost—and incentivizes customers to shift flexible loads to times when the grid has excess capacity.

Sample TOU Rate Structure

Hypothetical residential plan (rates vary by utility)

Smart Shifts That Save Money

Because peak rates can be 2 to 3 times higher than off-peak rates, small timing changes yield real savings:

Where TOU Is Common

TOU billing is increasingly standard in high-demand regions like California, Arizona, and parts of the Northeast—especially for customers with solar panels or electric vehicles. Always check your utility's specific peak windows, as they can shift seasonally (e.g., summer afternoons may become peak due to air conditioning demand).
 

You started this lesson distinguishing energy (the total "fuel" used) from power (how fast it's used). Now you can apply that knowledge to something you'll encounter for the rest of your life: your electricity bill.

In this lesson you learned to:

• Convert between physics units (joules) and billing units (kWh)
• Calculate appliance costs using Energy = Power × Time
• Decode a real bill—like identifying that 1,434 kWh used over 32 days equals a 45 kWh/day average
• Separate supply charges (the electricity itself, often shoppable) from delivery charges (grid maintenance, fixed by regulators)
• Recognize why your effective cost per kWh ($0.157 in our example) is higher than the supply rate alone ($0.099/kWh)—because delivery fees and fixed charges get added in

Most importantly, you now see physics not as abstract formulas, but as a lens for financial literacy. When you understand that a 1,500 W space heater running 4 hours costs about 6 kWh—and roughly 95¢ on a typical bill—you make smarter choices about energy use and costs.

This is energy literacy: the ability to translate classroom concepts into real-world decisions. Whether you're comparing electricity suppliers, sizing a solar panel system, or simply deciding whether to unplug that idle charger, the physics of energy and power puts you in control.