Force Types

Why This Matters

Forces explain why objects move, stop, change direction, or stay perfectly still. When you study force types, you're really learning about Newton's laws in action. Every force problem comes down to identifying which forces are present, understanding their directions, and applying the right equations to predict motion.

The key concepts you need to master include contact vs. non-contact forces, action-reaction pairs, equilibrium conditions, and force equations. Don't just memorize that friction opposes motion; know why it matters for calculating net force. Don't just recall that gravity pulls things down; understand how it relates to weight and free fall. You'll be tested on your ability to analyze force diagrams, compare how different forces behave, and apply the correct mathematical relationships.

---

Contact Forces: When Objects Touch

Contact forces only act when two objects are physically touching. At the atomic level, these forces arise from electromagnetic interactions between the atoms and molecules at each surface.

Friction Force

• Opposes relative motion (or attempted motion) between surfaces. Static friction prevents motion from starting, while kinetic friction acts once an object is already sliding.
• Depends on surface type and normal force. The equation is $f = \mu N$, where $\mu$ is the coefficient of friction (a unitless number describing how "grippy" the surfaces are) and $N$ is the normal force.
• Essential for traction. Without friction, walking, driving, and braking would all be impossible.

One detail worth remembering: static friction is not a fixed value. It adjusts to match whatever force is trying to start the motion, up to a maximum of $f_{s,max} = \mu_s N$. So if you gently push a heavy box with 10 N and it doesn't budge, static friction is exactly 10 N, not the maximum value. Kinetic friction, on the other hand, stays roughly constant once sliding begins and is typically smaller than the maximum static friction ($\mu_k < \mu_s$ for the same surfaces).

Normal Force

• Acts perpendicular to the contact surface. It always pushes away from the surface, never parallel to it.
• Equals weight only on flat, horizontal surfaces with no other vertical forces. On an inclined plane, the normal force is $N = mg\cos\theta$, which is less than the object's full weight. If someone pushes down on the object, the normal force increases; if they pull upward, it decreases.
• Directly affects friction. Since $f = \mu N$, any change in the normal force changes the friction force too. This is why pressing harder on a surface makes it harder to slide an object.

Applied Force

• Any push or pull from an external source, whether that's you, a machine, or another object.
• Directly relates to acceleration through Newton's second law: $F_{net} = ma$. The applied force contributes to the net force, but it isn't always equal to the net force because other forces like friction are usually also acting.
• Can act in any direction. Unlike gravity or normal force, applied forces have no fixed orientation.

Tension Force

• Transmitted through ropes, strings, or cables. Tension always pulls; it never pushes.
• Acts along the length of the connector. The direction of tension follows the rope's path toward the pulling source.
• Constant throughout an ideal rope. In problems where the rope is treated as massless and the pulley is frictionless, the tension is the same at every point along it.

Spring Force

• Follows Hooke's Law: $F_s = -kx$, where $k$ is the spring constant (a measure of stiffness, in N/m) and $x$ is displacement from the spring's natural resting position.
• Restoring force. The negative sign means the force always acts back toward equilibrium. Stretch the spring to the right, and it pulls left. Compress it to the left, and it pushes right.
• Proportional to stretch or compression. Double the displacement, double the force. This linear relationship holds as long as you stay within the spring's elastic limit. Beyond that limit, the spring deforms permanently and Hooke's Law no longer applies.

---

Non-Contact Forces: Action at a Distance

Non-contact forces act between objects that aren't touching. These forces are carried by fields (gravitational, electric, or magnetic) that extend through space.

Gravitational Force

• Attracts any two masses. Gravity is always attractive, never repulsive, and acts along the line connecting the objects' centers.
• Governed by Newton's law of universal gravitation: $F = G\frac{m_1 m_2}{r^2}$, where $G = 6.67 \times 10^{-11} \text{ N·m}^2/\text{kg}^2$. Notice the $r^2$ in the denominator: double the distance, and the force drops to one-quarter.
• Creates weight near Earth's surface. When one mass is a planet and you're near the surface (so $r$ is roughly constant), the equation simplifies to $F_g = mg$, where $g \approx 9.8 \text{ m/s}^2$. The quantity $mg$ is what we call weight, and it's a force measured in newtons, not to be confused with mass measured in kilograms.

Electrostatic Force

• Acts between charged objects. Like charges repel, opposite charges attract.
• Follows Coulomb's Law: $F = k\frac{|q_1 q_2|}{r^2}$, where $k = 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2$. The absolute value signs remind you that the equation gives the magnitude of the force; the direction (attract or repel) is determined by the signs of the charges.
• Much stronger than gravity at small scales. A small charged balloon can lift your hair against the pull of the entire Earth. Electrostatic force governs chemical bonding and atomic structure.

Magnetic Force

• Acts on moving charges or magnetic materials. A stationary charge sitting in a magnetic field feels no magnetic force.
• Depends on field strength and particle velocity. For a charge moving through a magnetic field: $F = qvB\sin\theta$, where $\theta$ is the angle between the velocity and the field direction. If the charge moves parallel to the field ($\theta = 0°$), then $\sin 0° = 0$ and the force is zero. Maximum force occurs when the charge moves perpendicular to the field ($\theta = 90°$).
• Powers modern technology. Electric motors, generators, MRI machines, and data storage all rely on magnetic forces.

---

Quick Reference Table

---

Self-Check Questions

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

2. An object rests on a 30° inclined plane. How does the normal force compare to the object's weight, and why does this affect the friction force?

3. Compare tension force and spring force: both transmit force through a physical connector, but how does each force's magnitude behave differently along that connector?

4. A charged particle moves through a region with both electric and magnetic fields. Which force acts on the particle if it's stationary? Which acts if it's moving? Explain why.

5. FRQ-style: A box is pushed across a rough floor at constant velocity. Identify all forces acting on the box, explain why the net force must be zero, and describe what would happen to the friction force if the applied force increased.