Forces, Motion, and Newton's Laws

Warm-Up: Watch and Observe

Watch this slow-motion collision video:

As you watch, think about and write down your answers to these questions:

1. What happens to the crash test dummy when the car suddenly stops? Why?
2. Which car appears to take more damage — the one that crumples or the one that stays rigid? Which design is actually safer?
3. Where does all the energy of the moving car "go" during the crash?

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Core Lesson: Newton's Three Laws of Motion

A Brief History

Sir Isaac Newton (1643–1727) published his three laws of motion in his masterwork Principia Mathematica. These three simple statements explain nearly all motion you see in everyday life — from a baseball arcing through the air to the orbit of the Moon around Earth.

Newton's First Law: The Law of Inertia

An object at rest stays at rest, and an object in motion stays in motion (at the same speed, in the same direction), unless acted upon by an unbalanced force.

In plain language: things don't change what they're doing unless something makes them change.

Examples of the First Law:

• A hockey puck slides across ice for a long time because there's very little friction to slow it down.
• You lurch forward in a car when the brakes are applied suddenly — your body wants to keep moving.
• A tablecloth can be yanked off a table without disturbing the dishes (if done quickly) — the dishes have inertia.
• Planets keep orbiting the Sun because there's no friction in space to slow them down (gravity curves their path, but doesn't stop them).

Demo idea: Place a coin on a card on top of a glass. Flick the card sideways quickly. The coin drops straight into the glass because its inertia keeps it in place while the card is knocked away.

Newton's Second Law: F = ma

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

The formula version:

F = m × a (Force = Mass × Acceleration)

This is arguably the most important equation in classical physics. Let's unpack it:

• Force (F) is measured in Newtons (N). One Newton is roughly the weight of a small apple.
• Mass (m) is measured in kilograms (kg). Mass is how much "stuff" an object contains.
• Acceleration (a) is measured in meters per second squared (m/s²). It tells you how quickly velocity is changing.

Key insight: The same force on a lighter object produces more acceleration. This is why a tennis ball flies farther than a bowling ball when you throw them both with the same force.

| Scenario | Force | Mass | Acceleration | |---|---|---|---| | Push a shopping cart | 20 N | 10 kg | 2 m/s² | | Push a car | 20 N | 1000 kg | 0.02 m/s² | | Rocket launch | 35,000,000 N | 2,800,000 kg | 12.5 m/s² |

Newton's Third Law: Action and Reaction

For every action, there is an equal and opposite reaction.

When you push on something, it pushes back on you with the exact same force in the opposite direction. Always.

Examples:

• You push against the ground when you walk → the ground pushes you forward.
• A rocket pushes hot gas downward → the gas pushes the rocket upward.
• You push off the wall while sitting in a rolling chair → you roll backward.
• A gun fires a bullet forward → the gun recoils backward.

Free-Body Diagrams

A free-body diagram shows all the forces acting on a single object. It's the most useful tool in physics for understanding motion.

For a book sitting on a table:

         ↑ Normal force (table pushing up)
         |
    +---------+
    |  BOOK   |
    +---------+
         |
         ↓ Gravity (Earth pulling down)

The book is not accelerating, so the forces must be balanced (equal and opposite). The normal force equals the gravitational force.

For a book sliding across a table:

         ↑ Normal
         |
    +---------+
 ←--|  BOOK   |--→ Push (applied force)
    +---------+
         |
         ↓ Gravity
    ←--- Friction (opposes motion)

Now there are horizontal forces too. If the push is greater than friction, the book accelerates to the right (Newton's Second Law).

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Hands-On Lab: Build a Balloon-Powered Car

You're going to engineer a car powered entirely by Newton's Third Law. When air rushes backward out of the balloon (action), it pushes the car forward (reaction).

Materials

Build Instructions

Step 1: Make the chassis. Cut a rectangle of cardboard about 15 cm × 8 cm. This is the body of your car.

Step 2: Make the axles. Tape two straws across the bottom of the cardboard, one near the front edge and one near the back. Thread wooden skewers through the straws. The skewers should extend about 1 cm on each side.

Step 3: Attach the wheels. Press or tape bottle caps onto the ends of the skewers. Make sure the wheels spin freely.

Step 4: Attach the balloon engine. Stretch the opening of the balloon over one end of a straw. Tape the connection tightly so no air can leak. Tape the straw along the top of the car so the open end of the straw points out the BACK of the car.

Step 5: Test it! Blow through the straw to inflate the balloon, pinch the straw closed, set the car on a smooth floor, and let go!

The Experiment

Now it's time to do real science. Measure and record:

1. Distance traveled on each run (use the ruler/tape measure)
2. Time of travel (use the stopwatch — start when you release, stop when the car stops)
3. Calculate speed: speed = distance / time

Run at least 5 trials and record your data:

| Trial | Distance (cm) | Time (s) | Speed (cm/s) |
|-------|---------------|----------|--------------|
|   1   |               |          |              |
|   2   |               |          |              |
|   3   |               |          |              |
|   4   |               |          |              |
|   5   |               |          |              |
| AVG   |               |          |              |

Engineering Improvements

After your baseline tests, try these modifications one at a time (changing only one variable per test — this is the scientific method!):

• Bigger balloon — does more air mean more distance?
• Wider straw — does a larger nozzle change the speed?
• Lighter chassis — does reducing mass increase acceleration? (F = ma!)
• Smoother surface — test on tile vs carpet. Why does the surface matter?

Data Analysis in Python (Optional)

If you record your data, you can analyze it with code:

# Analyze your balloon car data
trials = [
    {"distance": 120, "time": 2.3},  # Replace with your actual data!
    {"distance": 135, "time": 2.5},
    {"distance": 110, "time": 2.1},
    {"distance": 145, "time": 2.7},
    {"distance": 128, "time": 2.4},
]

print("=== Balloon Car Data Analysis ===\n")
print(f"{'Trial':<8} {'Distance (cm)':<16} {'Time (s)':<12} {'Speed (cm/s)'}")
print("-" * 50)

speeds = []
for i, trial in enumerate(trials, 1):
    speed = trial["distance"] / trial["time"]
    speeds.append(speed)
    print(f"{i:<8} {trial['distance']:<16} {trial['time']:<12} {speed:.1f}")

avg_distance = sum(t["distance"] for t in trials) / len(trials)
avg_time = sum(t["time"] for t in trials) / len(trials)
avg_speed = sum(speeds) / len(speeds)

print("-" * 50)
print(f"{'AVG':<8} {avg_distance:<16.1f} {avg_time:<12.2f} {avg_speed:.1f}")

# Estimate the force!
mass_kg = 0.05  # Estimate your car's mass in kg (50 grams ~ 0.05 kg)
avg_speed_ms = avg_speed / 100  # Convert cm/s to m/s
accel = avg_speed_ms / avg_time  # Rough estimate of acceleration
force = mass_kg * accel

print(f"\n--- Force Estimate ---")
print(f"Car mass: {mass_kg * 1000:.0f} grams")
print(f"Average acceleration: {accel:.3f} m/s²")
print(f"Estimated force: {force:.4f} N")
print(f"That's about the weight of {force / 0.01:.1f} paperclips!")

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Challenge: The Elevator Scale Thought Experiment

Imagine you're standing on a bathroom scale inside an elevator. The scale reads your normal weight: let's say 500 Newtons (that's about 112 pounds, or roughly a 50 kg person on Earth where g ≈ 10 m/s²).

Now think about what happens to the scale reading in each of these scenarios:

1. The elevator is moving upward at a constant speed.
2. The elevator accelerates upward (starts going up).
3. The elevator accelerates downward (starts going down).
4. The elevator cable snaps and it's in free fall.

Bonus: Compute Elevator Forces in Python

# Elevator force calculator
mass = float(input("Enter your mass in kg: "))
g = 9.8  # acceleration due to gravity on Earth, m/s²

print(f"\nYour weight on Earth: {mass * g:.1f} N")
print(f"{'='*50}")

scenarios = [
    ("Standing still / constant velocity", 0),
    ("Elevator accelerating UP at 2 m/s²", 2),
    ("Elevator accelerating UP at 5 m/s²", 5),
    ("Elevator accelerating DOWN at 2 m/s²", -2),
    ("Elevator accelerating DOWN at 5 m/s²", -5),
    ("Free fall (cable snaps!)", -9.8),
]

for name, accel in scenarios:
    apparent_weight = mass * (g + accel)
    pct = (apparent_weight / (mass * g)) * 100
    status = ""
    if apparent_weight <= 0:
        status = " << WEIGHTLESS!"
    elif pct > 100:
        status = f" (feels {pct:.0f}% of normal)"
    else:
        status = f" (feels {pct:.0f}% of normal)"

    print(f"\n{name}")
    print(f"  Scale reads: {max(0, apparent_weight):.1f} N{status}")

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Resources

• Professor Dave: Newton's Laws — clear, concise explanation of all three laws
• PhET Simulations: Forces and Motion — interactive simulation where you can apply forces and watch motion
• Khan Academy: Newton's Laws of Motion — video lessons with practice problems
• Physics Classroom: Newton's Laws — in-depth explanations and problems
• NASA: Newton's Laws of Motion — how NASA applies Newton's Laws to real space missions
• Replit — online code editor