Types of Forces

Why This Matters

Forces are the foundation of everything in mechanics—they're what make objects speed up, slow down, change direction, or stay perfectly still. In Intro to College Physics, you're being tested on your ability to identify forces, draw free-body diagrams, and apply Newton's laws to predict motion. Every problem you encounter, from blocks on inclined planes to satellites in orbit, requires you to recognize which forces are acting and how they combine.

But here's the key insight: forces aren't random. They fall into predictable categories based on what causes them—contact between surfaces, gravitational attraction, electromagnetic interactions, or restoring mechanisms. When you understand the underlying principle behind each force, you can tackle any scenario the exam throws at you. Don't just memorize names and formulas—know what physical mechanism each force represents and when it shows up in problems.

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Contact Forces: When Objects Touch

These forces arise from direct physical contact between objects. They result from electromagnetic interactions at the atomic level, but in introductory physics, we treat them as separate, measurable pushes and pulls at surfaces.

Normal Force

• Always perpendicular to the contact surface—this is the defining characteristic that distinguishes it from friction
• Adjusts automatically to prevent objects from passing through surfaces; it's a response force, not a fixed value
• Critical for inclined plane problems—on a slope at angle $\theta$, the normal force equals $mg\cos\theta$, not simply $mg$

Friction Force

• Opposes relative motion or attempted motion between surfaces in contact; described by $f = \mu N$
• Static friction ($\mu_s$) prevents motion and can vary up to a maximum; kinetic friction ($\mu_k$) acts during sliding and is typically smaller
• Depends on normal force, not surface area—doubling the weight doubles the friction

Applied Force

• Any external push or pull delivered by a person, machine, or another object
• Direction and magnitude are given in problems; this is usually your "known" force in calculations
• Appears in Newton's second law as part of the net force determining acceleration

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Forces Transmitted Through Objects

Some forces travel through connecting materials like ropes, cables, or springs. These forces transfer energy and momentum from one point to another without the objects being in direct contact.

Tension Force

• Pulls equally at both ends of an ideal rope or string; tension is transmitted, not created
• Acts along the length of the connector and always pulls (never pushes)
• In pulley systems, tension redirects force; for ideal pulleys, tension remains constant throughout the rope

Spring Force (Elastic Force)

• Described by Hooke's Law: $F = -kx$, where $k$ is the spring constant and $x$ is displacement from equilibrium
• Always a restoring force—the negative sign indicates it opposes the displacement direction
• Proportional to displacement, making springs ideal for studying simple harmonic motion

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Field Forces: Action at a Distance

These forces act without physical contact, operating through invisible fields that permeate space. They follow inverse-square laws, meaning their strength decreases with the square of the distance.

Gravitational Force

• Attracts any two masses according to Newton's law: $F = G\frac{m_1 m_2}{r^2}$
• Near Earth's surface, simplifies to $F_g = mg$ where $g = 9.8 \text{ m/s}^2$
• Always attractive and responsible for weight, orbital motion, and tides

Electrostatic Force

• Acts between charged objects following Coulomb's law: $F = k\frac{q_1 q_2}{r^2}$
• Can attract or repel—opposite charges attract, like charges repel
• Much stronger than gravity at atomic scales; holds atoms and molecules together

Magnetic Force

• Acts on moving charges or magnetic materials, described by the Lorentz force: $F = qv \times B$
• Perpendicular to both velocity and field—use the right-hand rule to find direction
• Does no work on charged particles because force is always perpendicular to motion

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Resistive Forces: Opposition to Motion

These forces arise when objects move through a medium and always act opposite to the direction of motion. They convert kinetic energy into thermal energy, slowing objects down.

Air Resistance (Drag Force)

• Opposes motion through air and increases with velocity; often modeled as $F_d \propto v^2$
• Depends on shape and cross-sectional area—streamlined objects experience less drag
• Creates terminal velocity when drag equals gravitational force, resulting in zero net force

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Forces That Maintain Circular Motion

Centripetal Force

• Not a new type of force—it's the net force directed toward the center of a circular path
• Provided by other forces: gravity (orbits), tension (swinging objects), friction (cars turning), or normal force (roller coasters)
• Calculated as $F_c = \frac{mv^2}{r} = m\omega^2 r$, where $v$ is speed and $r$ is radius

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Quick Reference Table

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Self-Check Questions

1. Which two forces both follow an inverse-square law, and what key difference determines whether they attract or repel?

2. On an inclined plane, how do normal force and friction force differ in direction, and what determines the magnitude of each?

3. A block hangs from a spring attached to the ceiling. Identify all forces acting on the block and explain which force is responsible for the spring stretching.

4. Compare and contrast static friction and kinetic friction: under what conditions does each apply, and which has the larger coefficient?

5. A car rounds a flat curve at constant speed. What type of force provides the centripetal acceleration, and what would happen if this force were suddenly removed?