Kinetic and Static Friction - AP Physics 1: Algebra-Based Study Guide

Getting Started

Imagine trying to slide a heavy cardboard box across a wooden floor. At first, you push, but it doesn't budge. You push harder, and suddenly it lurches forward, and it feels slightly easier to keep it sliding than it was to get it started. This common experience reveals the two fundamental types of friction that govern the interaction between surfaces in contact.

What You Should Be Able to Do

After working through this section, you should be able to:

• Describe the conditions under which static and kinetic friction forces act on an object.

• Distinguish between the variable nature of static friction and the constant nature of kinetic friction.

• Calculate the magnitude of the kinetic friction force and the maximum possible static friction force.

• Draw accurate free-body diagrams for systems involving friction on horizontal or inclined surfaces.

• Explain why it is generally more difficult to start an object moving than to keep it in motion.

Key Concepts & Mechanisms

This section explores friction through the lens of Interactions & Conservation, focusing on how the contact interaction between surfaces gives rise to forces that affect an object's motion and energy.

System & Preconditions

• System: Our system is typically a single object of mass m (in kilograms, kg).

• Interaction: The core interaction is the contact between the surface of the object and the surface of its environment (e.g., a floor, a ramp). This interaction can produce two perpendicular contact forces: the normal force and the friction force.

• Preconditions: For a friction force to exist, two surfaces must be pressed together. This means there must be a non-zero normal force (F_N), a contact force acting perpendicular to the surfaces, measured in Newtons (N). Without a normal force, there can be no friction.

• Idealizations: Our model of friction assumes that the surfaces are uniform and that the resistive effects can be characterized by a single, dimensionless value called the coefficient of friction (μ). We also assume this coefficient does not change with the contact area or the relative speed of the surfaces.

Key Steps / Relations

To analyze any situation involving friction, we follow a clear, logical process that connects the physical interaction to a mathematical prediction.

1. Determine the State of Motion: First, observe the system. Are the two surfaces moving relative to each other?

   • If NO, the interaction is governed by static friction.

   • If YES, the interaction is governed by kinetic friction.

2. Draw a Free-Body Diagram: Represent the object as a dot and draw all forces acting on it as arrows. This must include:

   • Force of gravity (F_g or mg) acting straight down.

   • Normal force (F_N) acting perpendicular to the contact surface, pointing away from it.

   • Any applied pushes or pulls.

   • The friction force (f), which always acts parallel to the surface, opposing the direction of motion (for kinetic friction) or impending motion (for static friction).

3. Apply Newton's Second Law (ΣF = ma): Resolve the forces into components parallel (||) and perpendicular (⊥) to the surface.

   • Perpendicular (⊥): The sum of forces perpendicular to the surface is often zero (if the object is not accelerating off the surface). This step is critical for finding the magnitude of the normal force, F_N.

   • Parallel (||): The sum of forces parallel to the surface determines the object's acceleration along that surface. The friction force will be in this equation.

4. Select the Correct Friction Model: Based on Step 1, use the appropriate mathematical relation for the friction force.

   • Static Friction (f_s): This is a responsive, "as-needed" force. It adjusts its magnitude and direction to be exactly equal and opposite to the net applied force parallel to the surface, preventing motion. However, it has a limit.

     • Its magnitude is variable: 0 ≤ f_s ≤ f_{s,max}

     • Its maximum possible value is determined by the coefficient of static friction (μ_s):

     f_{s,max} = μ_s * F_N

     • If the net parallel applied force is greater than f_{s,max}, the object will begin to slide.

   • Kinetic Friction (f_k): This force acts when an object is sliding. It has a constant magnitude for a given situation.

     • Its magnitude is determined by the coefficient of kinetic friction (μ_k):

     f_k = μ_k * F_N

     • Its direction always opposes the object's velocity vector.

Outputs & Effects

• Change in Motion: Friction is a force that contributes to the net force, ΣF. A non-zero net force causes acceleration (a = ΣF / m), changing the object's velocity. Static friction's effect is to maintain zero acceleration, while kinetic friction typically causes an acceleration opposite to the velocity (slowing the object down).

• Energy Dissipation: The work done by kinetic friction is always negative, as the force opposes the displacement. This process converts the system's macroscopic kinetic energy into thermal energy (heat), increasing the internal energy of the object and the surface. Because of this, mechanical energy (kinetic + potential) is not conserved in systems with friction.

Regulation & Limits

• The static friction force f_s is a variable force regulated by the other parallel forces. It cannot exceed its maximum value, μ_s * F_N.

• The kinetic friction force f_k is constant for a given normal force and surface pair.

• A crucial experimental finding is that for nearly all pairs of surfaces, the coefficient of static friction is greater than the coefficient of kinetic friction (μ_s > μ_k). This explains why it takes more force to start an object moving (F_{push} > μ_s * F_N) than to keep it moving at a constant velocity (F_{push} = μ_k * F_N).

Key Models & Diagrams

The following matrix shows how to model the friction force in different scenarios for a box on a horizontal floor being pushed by a force F_A.

Key Components & Evidence

• Static Friction Force (f_s): The resistive contact force that prevents relative motion between surfaces. Its magnitude is variable. Units: Newtons (N).

• Kinetic Friction Force (f_k): The resistive contact force that opposes relative motion between surfaces that are sliding. Its magnitude is constant. Units: Newtons (N).

• Normal Force (F_N): The perpendicular component of the contact force between surfaces. It is a prerequisite for friction. Units: Newtons (N).

• Coefficient of Static Friction (μ_s): A dimensionless scalar property of a pair of surfaces that determines the maximum static friction force.

• Coefficient of Kinetic Friction (μ_k): A dimensionless scalar property of a pair of surfaces that determines the kinetic friction force.

• Evidence for μ_s > μ_k: It is consistently observed in labs and daily life that a larger force is required to overcome static friction and initiate motion than is needed to maintain that motion.

• Evidence for f ∝ F_N: If you press down on an object while trying to slide it, increasing F_N, you will find it much harder to move. This supports the direct proportionality between friction and the normal force.

Skill Snapshots

• Causation

  1. The electromagnetic interaction between the atoms of two contacting surfaces causes a friction force that resists sliding.

  2. An applied force parallel to a surface that is less than f_{s,max}causes an equal and opposite static friction force to arise, resulting in zero acceleration.

  3. Relative sliding motion between two surfaces causes a constant kinetic friction force to act, which in turn causes the system's mechanical energy to be converted into thermal energy.

• Comparison

  1. The static friction force is variable and adaptive, while the kinetic friction force is constant in magnitude.

  2. The coefficient of static friction (μ_s) is a multiplier for the maximum possible static force, whereas the coefficient of kinetic friction (μ_k) is a multiplier for the actual kinetic force.

  3. The friction force acts parallel to the surface of contact, while the normal force acts perpendicular to it.

• Change Over Time

  • Baseline: A box is at rest on a floor. The applied horizontal force is zero, and the static friction force is also zero.

  • Change 1: As a person slowly increases their push from zero, the static friction force increases in lockstep, matching the push exactly. The box's velocity remains zero.

  • Change 2: The instant the push exceeds the maximum static friction (μ_s * F_N), the box lurches forward. The friction force immediately drops to the lower, constant kinetic value (μ_k * F_N), and the box accelerates.

  • Continuity: Throughout the entire process, the coefficients μ_s and μ_k are assumed to be constant properties of the box and floor.

Common Misconceptions & Clarifications

1. Misconception: The static friction force is always equal to μ_s * F_N.

   • Clarification: This equation gives the maximum possible static friction. The actual static force is an "as-needed" force that is only as large as it needs to be to prevent motion. If nothing is pushing the object, the static friction is zero.

2. Misconception: The normal force is always equal to an object's weight, mg.

   • Clarification: The normal force is the perpendicular force exerted by a surface. It only equals mg on a horizontal surface with no other vertical forces. If the surface is inclined or if there is an additional vertical push or pull, F_N will be different from mg.

3. Misconception: Friction always opposes an object's motion.

   • Clarification: Friction opposes relative sliding or impending sliding between surfaces. For a person walking, the static friction between their shoe and the ground points forward, pushing them in the direction they are moving. It prevents their foot from slipping backward.

One-Paragraph Summary

Friction is a contact force that opposes relative sliding between surfaces and is categorized into two types: static and kinetic. Static friction acts on objects at rest, is variable in magnitude, and adjusts to prevent motion up to a maximum value defined by the coefficient of static friction (f_{s,max} = μ_s * F_N). Kinetic friction acts on sliding objects, has a constant magnitude defined by the coefficient of kinetic friction (f_k = μ_k * F_N), and always opposes the velocity. Both types of friction are directly proportional to the normal force pressing the surfaces together. A key principle is that the static coefficient is typically greater than the kinetic coefficient (μ_s > μ_k), explaining why it is harder to start an object moving than to keep it sliding.