Energy: The Universe's Currency

Warm-Up: Follow the Energy

Think about your morning: you eat breakfast, walk outside, and break into a sprint.

Where does the energy come from when you eat breakfast and then run?

Trace the energy as far back as you can. Don't stop at "food" — keep going. Where did the food's energy come from? And before that?

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Core Lesson: The Two Faces of Mechanical Energy

What Is Energy?

Energy is the ability to cause change. It comes in many forms — thermal, chemical, electrical, nuclear — but today we focus on the two types of mechanical energy: kinetic and potential.

Kinetic Energy (KE) — Energy of Motion

Anything that's moving has kinetic energy. The faster it moves and the more massive it is, the more kinetic energy it has.

KE = 1/2 × m × v²

Where:

• m = mass (in kilograms)
• v = velocity (in meters per second)

Notice that velocity is squared. This has a huge consequence: if you double your speed, your kinetic energy doesn't just double — it quadruples. This is why car crashes at 60 mph are far more devastating than crashes at 30 mph.

| Object | Mass (kg) | Speed (m/s) | KE (Joules) | |--------|-----------|-------------|-------------| | Walking person | 50 | 1.5 | 56.25 | | Running person | 50 | 8 | 1,600 | | Tennis ball serve | 0.058 | 58 | 97.6 | | Car on highway | 1,500 | 30 | 675,000 |

Potential Energy (PE) — Stored Energy

Gravitational potential energy is the energy an object has because of its height above the ground. The higher it is, the more energy is stored, waiting to be released.

PE = m × g × h

Where:

• m = mass (in kilograms)
• g = acceleration due to gravity (9.8 m/s² on Earth)
• h = height above the ground (in meters)

Conservation of Energy: The Grand Exchange

When a roller coaster climbs to the top of a hill, it's gaining potential energy. As it plunges downward, that potential energy converts into kinetic energy. At the bottom, nearly all the PE has become KE.

At any point: Total Energy = KE + PE = constant

This means if you know the height, you can predict the speed — and vice versa.

At the top of a drop (starting from rest):

• KE = 0 (not moving)
• PE = mgh (maximum)

At the bottom of the drop:

• KE = 1/2 mv² (maximum)
• PE = 0 (ground level)

Setting them equal: mgh = 1/2 mv²

Notice that mass cancels out! Solving for v:

v = sqrt(2 × g × h)

This means the speed at the bottom doesn't depend on mass — a bowling ball and a marble dropped from the same height reach the same speed (ignoring air resistance). Galileo figured this out 400 years ago.

Where Does the Energy "Go"?

In real life, roller coasters slow down. Balls eventually stop rolling. Where does the energy go if it's supposed to be conserved?

It converts to thermal energy (heat) through friction. Rub your hands together — you're converting kinetic energy into heat. The energy isn't destroyed; it's just spread out into a less useful form.

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Hands-On Lab: The Ramp Experiment

Setup

Build a ramp using a flat board (or stiff cardboard) propped up on books. You'll roll objects down the ramp and measure how far they push a lightweight target at the bottom.

Procedure

1. Set up the ramp at a low angle. Place the target object at the base of the ramp.
2. Weigh each rolling object on the kitchen scale. Record in grams and convert to kg.
3. Measure the ramp height from the tabletop to the release point (this is h).
4. Release (don't push!) each object from the top. Measure how far the target slides.
5. Repeat from at least 3 different heights.
6. Record everything in a data table like this:

| Trial | Object | Mass (kg) | Height (m) | Predicted PE (J) | Target Displacement (cm) | |-------|--------|-----------|------------|-------------------|--------------------------| | 1 | | | | | | | 2 | | | | | | | 3 | | | | | |

Analysis Questions

After collecting your data, answer these:

1. When you increase the height, what happens to the target displacement? Why?
2. When you use a heavier object from the same height, what changes? Why?
3. Calculate the predicted PE for each trial using PE = mgh. Does higher PE correspond to greater displacement?
4. Why doesn't 100% of the PE convert to motion of the target? Where does some energy go?

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Challenge: Energy Calculator in Python

Write a Python program that serves as a full energy calculator. It should:

1. Ask the user for mass, velocity, and height
2. Calculate KE, PE, and total mechanical energy
3. Predict the speed an object would reach falling from the given height
4. Display everything in a clean format

Starter Code

import math

print("=" * 40)
print("   ENERGY CALCULATOR")
print("=" * 40)

# Get inputs from the user
mass = float(input("\nMass (kg): "))
velocity = float(input("Velocity (m/s): "))
height = float(input("Height (m): "))

g = 9.8  # acceleration due to gravity (m/s^2)

# Calculate energies
ke = 0.5 * mass * velocity ** 2
pe = mass * g * height
total = ke + pe

# Predict speed from falling the given height (starting from rest)
# Using conservation of energy: mgh = 1/2 mv^2 => v = sqrt(2gh)
predicted_speed = math.sqrt(2 * g * height)

# Display results
print("\n--- RESULTS ---")
print(f"Kinetic Energy:   {ke:,.2f} J")
print(f"Potential Energy:  {pe:,.2f} J")
print(f"Total Mech Energy: {total:,.2f} J")
print(f"\nIf dropped from {height} m, the object would reach {predicted_speed:.2f} m/s")
print(f"That's {predicted_speed * 3.6:.1f} km/h or {predicted_speed * 2.237:.1f} mph!")

Stretch Goal

Extend the program to handle your ramp experiment data:

import math

print("=" * 40)
print("   RAMP EXPERIMENT ANALYZER")
print("=" * 40)

g = 9.8
trials = []

num_trials = int(input("\nHow many trials did you run? "))

for i in range(num_trials):
    print(f"\n--- Trial {i + 1} ---")
    name = input("Object name: ")
    mass = float(input("Mass (kg): "))
    height = float(input("Ramp height (m): "))
    displacement = float(input("Target displacement (cm): "))

    pe = mass * g * height
    predicted_speed = math.sqrt(2 * g * height)

    trials.append({
        "name": name,
        "mass": mass,
        "height": height,
        "pe": pe,
        "speed": predicted_speed,
        "displacement": displacement,
    })

# Print summary table
print("\n" + "=" * 70)
print(f"{'Object':<12} {'Mass':>6} {'Height':>7} {'PE':>10} {'Speed':>8} {'Disp':>8}")
print(f"{'':.<12} {'(kg)':>6} {'(m)':>7} {'(J)':>10} {'(m/s)':>8} {'(cm)':>8}")
print("-" * 70)

for t in trials:
    print(f"{t['name']:<12} {t['mass']:>6.3f} {t['height']:>7.3f} "
          f"{t['pe']:>10.4f} {t['speed']:>8.2f} {t['displacement']:>8.1f}")

# Find the trial with the most displacement
best = max(trials, key=lambda t: t["displacement"])
print(f"\nGreatest displacement: {best['name']} at {best['height']} m "
      f"({best['displacement']} cm)")

# Check correlation between PE and displacement
print("\nDoes more PE generally mean more displacement? Check your table!")

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Resources

• Khan Academy — Kinetic and Potential Energy — full lesson series with practice problems
• PhET Energy Skate Park Simulator — watch energy transform in real time on a virtual skate ramp
• Physics Classroom — Energy — clear explanations with interactive problems
• Python Basics — W3Schools — reference for Python syntax
• Replit — online code editor for running your programs