Fundamental Forces in Nature

Why This Matters

In AP Physics 1, you're building the foundation for understanding why objects move and interact the way they do. While the full picture of fundamental forces spans all of physics, your exam focuses specifically on gravitational force and how it connects to the broader framework of Newton's laws, free-body diagrams, and conservation principles. Understanding gravity isn't just about memorizing an equation—it's about recognizing how this single force explains everything from why you stay on the ground to how satellites orbit Earth.

The key insight here is that gravitational force follows predictable mathematical rules that let you solve real problems. You'll need to connect Newton's law of universal gravitation to concepts like weight, apparent weight, free fall, and orbital motion. Don't just memorize that $F_g = \frac{Gm_1m_2}{r^2}$—know how this inverse-square relationship affects gravitational field strength at different distances, and how gravity interacts with other forces in systems you'll analyze on the exam.

---

The Gravitational Force: Your AP Physics 1 Focus

Gravity is the force that acts between any two objects with mass, always attractive, and responsible for the large-scale structure of the universe. On the AP exam, you'll apply gravitational concepts to analyze motion, weight, and orbital scenarios.

Newton's Law of Universal Gravitation

• Every mass attracts every other mass—the force is always attractive and acts along the line connecting the objects' centers of mass
• Inverse-square law means the force decreases with the square of the distance: $|F_g| = \frac{Gm_1m_2}{r^2}$, where $G = 6.67 \times 10^{-11} \text{ N·m}^2/\text{kg}^2$
• Gravitational field strength $g = \frac{GM}{r^2}$ gives the force per unit mass at any distance from a massive object—this is why $g \approx 10 \text{ m/s}^2$ near Earth's surface

Gravitational Field Strength

• Field strength varies with distance—as you move farther from a planet's center, $g$ decreases following the inverse-square relationship
• Near Earth's surface, we approximate $g$ as constant ($\approx 9.8 \text{ m/s}^2$ or $10 \text{ N/kg}$) because changes in altitude are negligible compared to Earth's radius
• Units of N/kg and m/s² are equivalent—this connects gravitational field to acceleration, which is why objects in free fall accelerate at $g$

---

Weight and Apparent Weight

Understanding the difference between actual gravitational force and what you feel is crucial for analyzing systems where objects accelerate. This distinction appears frequently in elevator problems and free-fall scenarios.

Weight as Gravitational Force

• Weight equals mass times gravitational field strength—mathematically $W = mg$, representing the actual gravitational pull on an object
• Weight is a force, measured in newtons, and always points toward the center of the attracting mass
• Weight changes with location—an astronaut weighs less on the Moon because $g_{\text{Moon}} < g_{\text{Earth}}$, not because their mass changed

Apparent Weight and Normal Force

• Apparent weight is what you feel—it equals the normal force exerted on you by a surface (like a scale reading)
• In accelerating systems, use $N - mg = ma$ to find apparent weight: accelerating upward increases it, accelerating downward decreases it
• Weightlessness occurs in free fall—when gravity is the only force acting, there's no normal force, so apparent weight is zero (this is why astronauts float in orbit)

The Equivalence Principle

• You cannot distinguish between gravity and acceleration—an observer in a closed box can't tell if they're in a gravitational field or accelerating through space
• Inertial mass equals gravitational mass—this fundamental principle means the $m$ in $F = ma$ is the same as the $m$ in $F_g = mg$
• This explains why all objects fall at the same rate—the $m$ cancels when you set $mg = ma$, giving $a = g$ regardless of mass

---

Forces and Conservation Laws

The gravitational force connects directly to the conservation principles you'll use throughout AP Physics 1. Newton's third law and momentum conservation are essential tools for analyzing gravitational interactions.

Newton's Third Law in Gravitational Systems

• Forces come in pairs—Earth pulls on you with force $F$, and you pull on Earth with equal force $F$ in the opposite direction
• Both objects experience the same magnitude of force—but because $a = F/m$, Earth's acceleration is negligible due to its enormous mass
• This applies to all gravitational interactions—the Moon pulls on Earth just as hard as Earth pulls on the Moon

Conservation of Momentum in Gravitational Systems

• Total momentum is conserved when no external forces act—internal gravitational forces between objects in a system don't change total system momentum
• Center-of-mass velocity remains constant for isolated systems: $v_{cm} = \frac{\Sigma m_i v_i}{\Sigma m_i}$
• Recoil problems use this principle—when a rocket expels fuel, momentum conservation explains the rocket's acceleration even though gravity acts on both

Impulse and Gravitational Force

• Impulse equals change in momentum—$J = \Delta p = F \cdot \Delta t$, connecting force, time, and momentum change
• Gravitational force delivers continuous impulse—a falling object gains momentum at rate $mg$ per second
• Conservation applies to collisions and explosions—even when gravity acts, if the collision time is short enough, we can ignore gravity's impulse during the interaction

---

Beyond AP Physics 1: The Four Fundamental Forces

While AP Physics 1 focuses on gravity, understanding where it fits among nature's forces gives you perspective. You won't be tested on nuclear forces, but this context helps you appreciate why gravity matters.

Overview of All Four Forces

• Gravitational force is the weakest but has infinite range—it dominates at large scales because it's always attractive and mass accumulates
• Electromagnetic force is much stronger than gravity with infinite range—it governs charged particle interactions but cancels out in neutral matter
• Strong nuclear force is the strongest but only acts at femtometer scales—it holds atomic nuclei together against electromagnetic repulsion

Why Gravity Dominates Your World

• Large objects are electrically neutral—positive and negative charges cancel, so electromagnetic forces between planets are negligible
• Gravity never cancels—there's no "negative mass," so gravitational effects always add up
• At human and astronomical scales, gravity is the dominant force shaping motion, orbits, and structure

---

Quick Reference Table

---

Self-Check Questions

1. An astronaut orbiting Earth feels weightless. Is the gravitational force on them zero? Explain using the concepts of weight and apparent weight.

2. Compare how gravitational force and gravitational field strength change as you move from Earth's surface to twice Earth's radius from the center. Which quantity requires knowing the object's mass?

3. A 60 kg person stands on a scale in an elevator. The scale reads 720 N. Is the elevator accelerating upward, downward, or not at all? Calculate the acceleration.

4. Two ice skaters push off each other on frictionless ice. Explain why total momentum is conserved even though gravitational force acts on both skaters.

5. Earth exerts a gravitational force of 800 N on an astronaut. What force does the astronaut exert on Earth, and why don't we notice Earth accelerating toward the astronaut?