【Basic Physics】Energy and Its Uses: A Strategy Guide

Hello! How is your physics study going? You hear the word "energy" all the time in everyday life—in your smartphone battery, the calories in your food, or your electricity bill. In fact, our lives simply couldn't function without it.
In this chapter, we’ll take the abstract concept of "energy" and break it down clearly using formulas and laws. It might feel a bit tricky at first, but if you focus on the key points, you’ll definitely be able to master it. Let’s do this together!

1. What is "Work"?

In physics, the term "work" has a slightly different meaning than it does in everyday conversation. In physics, we say work is done "when you apply a force to an object and move it in the direction of that force."

■ The Formula for Work

When you apply a force \( F \)[N] to an object and move it a distance \( s \)[m] in the direction of the force, the work \( W \)[J] (Joules) done is given by the following formula:
\( W = Fs \)

If there is an angle θ (theta) between the direction of the force and the direction of movement, the formula becomes:
\( W = Fs \cos \theta \)

■ Key Takeaways!

  • Cases where Work = 0: If you push against a wall with all your might but the wall doesn't move, the work done is zero! Also, if you carry a bag while walking horizontally, the lifting force (upward) and the direction of motion (horizontal) are perpendicular (90 degrees); therefore, that force is doing no work.
  • Negative Work: If you apply force in the opposite direction of motion (like using brakes), the work done is negative.

【Common Mistake】
"I've been holding this heavy object for so long, I'm exhausted! I must have done a lot of work!" This makes sense in everyday conversation, but in physics, "if the distance moved is 0, the work is 0." Make sure to keep that distinction in mind!

2. Kinetic and Potential Energy

Simply put, energy is the "ability to do work." There are two main types you should remember.

① Kinetic Energy

The energy an object has because it is moving.
\( K = \frac{1}{2}mv^2 \)
(\( m \): mass [kg], \( v \): speed [m/s])

Example: The faster a car is moving, the greater the impact (work) when it hits something.

② Gravitational Potential Energy

The energy an object has due to its height.
\( U = mgh \)
(\( g \): gravitational acceleration \( 9.8 \text{m/s}^2 \), \( h \): height [m])

Example: A ball dropped from a greater height hits the ground harder.

③ Elastic Potential Energy (Springs)

The energy stored in a spring that has been stretched or compressed.
\( U = \frac{1}{2}kx^2 \)
(\( k \): spring constant [N/m], \( x \): displacement from natural length [m])

【Pro Tip】
The unit for energy is also [J] (Joules), just like work. This is because energy increases or decreases exactly by the amount of work done.

3. The Law of Conservation of Mechanical Energy

This is the highlight of this chapter!
When we ignore friction and air resistance, the total of "kinetic energy" and "potential energy (gravitational/spring)" always remains constant.

\( K + U = \text{constant} \)

【An Analogy to Help You Understand!】
Think of energy like "money in your wallet."
Suppose you have a $10 bill (kinetic energy) and some coins (potential energy). If you exchange your bill for coins halfway through, the total amount of money in your wallet doesn't change, right? When a roller coaster dives from a high point, potential energy (coins) is simply being converted into kinetic energy (the bill), but the total amount of energy remains the same.

【Step-by-Step!】 How to use the Law of Conservation of Mechanical Energy:
1. Choose two moments in time: "before" and "after."
2. Write down the "kinetic energy" and "potential energy" at each location.
3. Set up the equation "Before = After" and solve for the missing values!

4. Power

Even if you do the same amount of work, there’s a difference in efficiency between finishing it in one minute versus one hour. The amount of work done per unit of time (1 second) is called "Power."

Formula: \( P = \frac{W}{t} \)
(\( P \): Power [W] Watts, \( W \): Work [J], \( t \): time [s])

【Point】
The "60W" on a light bulb uses this same unit. It represents how much energy is being consumed every second.

5. Heat and Energy Use

Energy can change form. When an object slides across a surface with friction, heat is generated. This is also a form of energy (thermal energy).

■ Specific Heat and Heat Capacity

Calculate the heat required to raise the temperature of a substance:
\( Q = mc \Delta T \)
(\( Q \): heat [J], \( m \): mass [g], \( c \): specific heat [J/(g·K)], \( \Delta T \): change in temperature)

■ Conservation of Energy and Irreversibility

The total energy of the entire world never changes (Law of Conservation of Energy).
However, once energy turns into "heat" and escapes into the air, it is very difficult to turn 100% of it back into kinetic energy. This is called an irreversible process.

■ Energy Conversion Efficiency

The ratio of how much energy was used for the intended purpose compared to the energy put in is called "thermal efficiency (conversion efficiency)."
\( e = \frac{\text{Energy used}}{\text{Energy supplied}} \)
*Efficiency is always less than 1 (100%).

★ Final Summary Points

1. Work = Force × Distance. No movement means zero work!
2. Mechanical Energy = Kinetic Energy + Potential Energy.
3. Without friction, the total mechanical energy stays exactly the same!
4. Energy changes form, but the total amount never increases or decreases.

It might feel tough to memorize the formulas at first, but keep this image in mind: "Things at a height have energy (\( mgh \)), things that are moving have energy (\( \frac{1}{2}mv^2 \)), and the sum of those doesn't change."
If you draw diagrams and map out the changes in energy, you'll be able to solve these like a puzzle! You've got this!