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'll be 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.

Forces 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. At the atomic level, they result from electromagnetic interactions between surface atoms, 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. You solve for it using Newton's second law; you don't just assume it equals $mg$.
• On inclined planes, the surface tilts, so the normal force tilts with it. For an object 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 (coefficient $\mu_s$) keeps an object from starting to slide. It can take any value from zero up to a maximum of $\mu_s N$. Kinetic friction (coefficient $\mu_k$) acts once sliding begins and has a fixed magnitude of $\mu_k N$. Typically $\mu_s > \mu_k$, which is why it takes more force to start sliding a box than to keep it sliding.
• 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 pushes or pulls from one point to another through the connector itself.

Tension Force

• Pulls at both ends of an ideal (massless) rope or string. The rope transmits the force; it doesn't create it.
• Acts along the length of the connector and always pulls, never pushes. You can't push with a rope.
• In pulley systems, tension redirects force. For an ideal (massless, frictionless) pulley, tension remains the same throughout the entire length of the rope.

Spring Force (Elastic Force)

• Described by Hooke's Law: $F = -kx$, where $k$ is the spring constant (units of N/m) and $x$ is displacement from the spring's natural (equilibrium) length.
• Always a restoring force. The negative sign means the force always points back toward equilibrium, opposing the displacement.
• Proportional to displacement, so doubling the stretch doubles the force. This linear relationship makes 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 fields that extend through space. In this course, the two most important field forces both follow inverse-square laws, meaning their strength decreases with the square of the distance between objects.

Gravitational Force

• Attracts any two masses according to Newton's law of universal gravitation: $F = G\frac{m_1 m_2}{r^2}$, where $G = 6.674 \times 10^{-11} \text{ N·m}^2/\text{kg}^2$.
• Near Earth's surface, the distance to Earth's center barely changes, so this simplifies to $F_g = mg$ where $g \approx 9.8 \text{ m/s}^2$.
• Always attractive. There's no "negative mass," so gravity only pulls. It's responsible for weight, orbital motion, and tides.

Electrostatic Force

• Acts between charged objects following Coulomb's law: $F = k_e\frac{q_1 q_2}{r^2}$, where $k_e \approx 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2$.
• Can attract or repel. Opposite charges attract, like charges repel. The sign of the product $q_1 q_2$ tells you which.
• Much stronger than gravity at atomic scales. The electrostatic force between a proton and electron in a hydrogen atom is roughly $10^{39}$ times stronger than their gravitational attraction. Electromagnetic forces are what actually hold atoms and molecules together.

Magnetic Force

• Acts on moving charges or current-carrying wires in a magnetic field, described by $F = qv B\sin\theta$ (magnitude form of the cross product $F = q\vec{v} \times \vec{B}$).
• Perpendicular to both velocity and field. Use the right-hand rule to find the direction: point your fingers along $\vec{v}$, curl them toward $\vec{B}$, and your thumb points in the force direction (for positive charges).
• Does no work on charged particles because the force is always perpendicular to the velocity. It changes the direction of motion but not the speed.

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Resistive Forces: Opposition to Motion

These forces arise when objects move through a medium (like air or water) 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. At higher speeds it's often modeled as $F_d \propto v^2$.
• Depends on shape and cross-sectional area. Streamlined objects experience less drag, which is why race cars and aircraft are shaped the way they are.
• Creates terminal velocity. As a falling object speeds up, drag increases until it equals the gravitational force. At that point the net force is zero, acceleration is zero, and the object falls at constant speed.

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Forces That Maintain Circular Motion

Centripetal Force

• Not a new type of force. It's the net inward force directed toward the center of a circular path. "Centripetal" describes the role a force plays, not what kind of force it is.
• Provided by real forces: gravity (orbits), tension (swinging a ball on a string), friction (a car turning on a road), or normal force (a roller coaster loop). You need to identify which real force is doing the job in each problem.
• Calculated as $F_c = \frac{mv^2}{r} = m\omega^2 r$, where $v$ is the tangential speed, $r$ is the radius, and $\omega$ is the angular velocity.

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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?