2.7 Kinetic and Static Friction

Friction is a contact force between two surfaces. Kinetic friction acts when surfaces slide and has a fixed magnitude of $F_{f,k} = \mu_k F_n$. Static friction acts when surfaces are not sliding and can adjust up to a maximum value.

Why This Matters for the AP Physics 1 Exam

Friction shows up constantly in force and dynamics problems, so getting comfortable with it pays off across the exam. You need to connect friction to free-body diagrams, normal force, and Newton's second law, then translate between a written scenario, a diagram, and the math that describes it.

This kind of translation between words, pictures, and equations is exactly the reasoning the exam rewards, especially on the Qualitative/Quantitative Translation question, where you first make a claim with reasoning and then back it up with derived equations. Friction also appears later when you analyze objects on banked curves in circular motion, so building solid habits here helps you in Unit 2 and beyond.

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Key Takeaways

• Kinetic friction acts opposite the relative sliding motion between two surfaces and has magnitude $|\vec{F}_{f,k}| = \mu_k |\vec{F}_n|$.
• Static friction is adjustable: it takes whatever value is needed to prevent sliding, up to a maximum of $\mu_s F_n$.
• The static friction relationship is an inequality, $|\vec{F}_{f,s}| \leq \mu_s |\vec{F}_n|$, not a fixed value.
• Friction does not depend on the size of the contact area, only on the surfaces and the normal force.
• The coefficients $\mu_k$ and $\mu_s$ are dimensionless and depend on the material properties of the two surfaces.
• For the same pair of surfaces, $\mu_s$ is usually greater than $\mu_k$, so it takes more force to start sliding than to keep it going.

Kinetic Friction Between Surfaces

Kinetic friction acts when two surfaces in contact slide against each other. It points opposite the relative motion of the surfaces. For each surface, the friction force from the other surface points opposite that surface's motion relative to the other.

• When you slide a book across a table, friction acts backward against the book's motion relative to the table.
• This opposing force slows and stops the object unless another force keeps pushing it.

The magnitude of kinetic friction does not depend on the size of the contact area. A larger area has more contact points, but the force at each point is smaller, so the overall friction force stays the same.

• A brick experiences the same friction whether it rests on its wide face or narrow edge, assuming equal normal force.

The kinetic friction force is found using:

$|\vec{F}_{f,k}| = |\mu_k \vec{F}_n|$

Where:

• $|\vec{F}_{f,k}|$ is the kinetic friction force (in newtons)
• $\mu_k$ is the coefficient of kinetic friction (dimensionless)
• $|\vec{F}_n|$ is the normal force (in newtons)

The normal force, $F_n$, is the perpendicular component of the force a surface exerts on an object, directed away from the surface. On a horizontal surface with no other vertical forces, the normal force equals the object's weight in magnitude, so $F_n = mg$.

The coefficient of kinetic friction depends on the material properties of the two surfaces in contact. Some typical values:

• Rubber on concrete: roughly 0.8 (high friction)
• Wood on wood: roughly 0.3 (moderate friction)
• Ice on ice: roughly 0.03 (very low friction)

Static Friction Between Surfaces

Static friction can act between surfaces that are pressed together but not moving relative to each other. It is what keeps an object from starting to slide when a force is applied.

Static friction is an adjustable force. It points in whatever direction along the surface is needed to prevent slipping, and it grows to match the applied force up to its maximum value.

• If you push lightly on a heavy box, static friction pushes back with an equal force, so the box stays put.
• The box does not move until you push hard enough to exceed the maximum static friction.

Slipping or sliding begins once the applied force exceeds the maximum static friction force. At that point the surfaces start moving relative to each other and kinetic friction takes over. This switch is what causes the jerky start when you push a heavy object slowly.

The maximum static friction force is:

$F_{f,s,max} = \mu_s F_n$

And the general relationship is an inequality:

$|\vec{F}_{f,s}| \leq |\mu_s \vec{F}_n|$

Where:

• $|\vec{F}_{f,s}|$ is the static friction force (in newtons)
• $F_{f,s,max}$ is the maximum static friction force (in newtons)
• $\mu_s$ is the coefficient of static friction (dimensionless)
• $|\vec{F}_n|$ is the normal force (in newtons)

The coefficient of static friction $\mu_s$ is usually greater than the coefficient of kinetic friction $\mu_k$ for the same pair of surfaces.

• This is why it is harder to start pushing an object than to keep it moving.
• A crate might need 100 N to start moving but only 80 N to keep sliding.

How to Use This on the AP Physics 1 Exam

Problem Solving

• Always find the normal force first. On a flat surface with only gravity acting vertically, $F_n = mg$. On an incline or when another force has a vertical component, the normal force changes, so check the perpendicular direction carefully.
• For sliding objects, plug straight into $|\vec{F}_{f,k}| = \mu_k F_n$ since kinetic friction has a definite value.
• For objects that are not sliding, do not assume friction equals $\mu_s F_n$. Use Newton's second law to find the actual static friction first, then compare it to the maximum $\mu_s F_n$ to decide whether the object moves.

Free Response

• When asked to explain in words, state that kinetic friction opposes relative sliding and that static friction adjusts to prevent slipping up to a maximum.
• When deriving equations, set up a free-body diagram and write the net force equation along the direction of motion. Tie the friction term back to the normal force.
• Connect your verbal claim to your math. If you argued an object stays still, your derived inequality should show the applied force is below $\mu_s F_n$.

Common Trap

• The static friction equation is an inequality. Treating $\mu_s F_n$ as the actual static friction in every problem is a frequent mistake.

Common Misconceptions

• Friction depends on contact area. It does not. Only the normal force and the surface materials matter.
• Static friction always equals $\mu_s F_n$. Static friction takes whatever value is needed to prevent sliding, up to that maximum. Below the threshold it is smaller.
• Kinetic friction depends on speed. In this course, kinetic friction is modeled with a constant coefficient, so it does not change with how fast the object slides.
• Friction always opposes an object's motion. Friction opposes relative motion or attempted relative motion between surfaces. Static friction can even point in the direction an object moves, such as the friction that pushes you forward when you walk.
• Normal force always equals weight. That is only true on a flat surface with no other vertical forces. On an incline or with an applied vertical force, you must solve for the normal force.

Related AP Physics 1 Guides

• 2.1 Systems and Center of Mass
• 2.2 Forces and Free-Body Diagrams
• 2.3 Newton's Third Law
• 2.4 Newton's First Law
• 2.5 Newton's Second Law
• 2.6 Gravitational Force