2.7 Kinetic and Static Friction

Learning objectives

2.7A—Describe kinetic friction between two surfacesDescribe kinetic friction between two surfaces• Kinetic friction occurs when two surfaces in contact move relative to each other.- i. The kinetic friction force is exerted in a direction opposite to the motion of each surface relative to the other surface.- ii. The force of friction between two surfaces does not depend on the size of the surface area of contact.• The magnitude of the kinetic friction force exerted on an object is the product of the normal force the surface exerts on the object and the coefficient of kinetic friction. R - -- - µ=FFfk k n, elevant equation:- i. The coefficient of kinetic friction depends on the material properties of the surfaces that are in contact.- ii. Normal force is the perpendicular component of the force exerted on an object by the surface with which it is in contact; it is directed away from the surface.2.7B—Describe static friction between two surfacesDescribe static friction between two surfaces.• Static friction may occur between the contacting surfaces of two objects that are not moving relative to each other.• Static friction adopts the value and direction required to prevent an object from slipping or sliding on a surface. Relevant equation:- i. Slipping and sliding refer to situations in which two surfaces are moving relative to each other.- ii. There exists a maximum value for which static friction will prevent an object from slipping on a given surface. Derived equation: µ=FFfs sn,, max• The coefficient of static friction is typically greater than the coefficient of kinetic friction for a given pair of surfaces. AP Physics 1: Algebra-Based Course and Exam Description Force and Translational Dynamics UNIT 2 TOPIC 2.8 Spring Forces | AP Physics 1: Algebra-Based Course and Exam Description

Recognize sliding

Kinetic friction acts when two surfaces in contact slide relative to each other. On each surface, it points opposite that surface's motion relative to the other surface.

Calculate the magnitude

$|\vec F_{f,k}|=\mu_k|\vec F_n|$

Interpret each quantity

Quantity	Meaning
$F_n$	Perpendicular contact-force component, directed away from the surface
$\mu_k$	Dimensionless coefficient set by the material pair
$F_{f,k}$	Friction magnitude; direction is chosen separately from relative sliding

Apply the model

Worked example: a $5.0\,\text{kg}$ block slides on a horizontal surface with $\mu_k=0.20$ . With no vertical acceleration, $F_n=mg=(5.0\,\text{kg})(10\,\text{m/s}^2)=50\,\text{N}$ . Therefore $F_{f,k}=\mu_kF_n=(0.20)(50\,\text{N})=10\,\text{N}$ , opposite the block's motion relative to the surface.

Respect the boundary

In this friction model, the force does not depend on the apparent contact area. Also, $F_n$ is not automatically $mg$ ; determine it from forces perpendicular to the surface and the motion in that direction.

Recognize no sliding

Static friction may act when contacting surfaces are not sliding relative to each other. It points in the direction needed to prevent the impending relative motion.

Use the allowed range

$|\vec F_{f,s}|\leq \mu_s|\vec F_n|$

Separate actual from maximum

Static friction self-adjusts from zero up to a maximum: $F_{f,s,\max}=\mu_sF_n$ . Below the threshold, solve for the friction actually required to prevent sliding; use the maximum only at impending slip.

Test the threshold

Threshold example: a surface has $F_n=50\,\text{N}$ and $\mu_s=0.40$ , so $F_{f,s,\max}=(0.40)(50\,\text{N})=20\,\text{N}$ . A $12\,\text{N}$ horizontal push produces $12\,\text{N}$ of opposing static friction and no slip. A requested $25\,\text{N}$ exceeds the $20\,\text{N}$ limit, so static friction cannot prevent sliding.

Switch models after slip

Static friction is not always $\mu_sF_n$ . Once the surfaces slide, switch to kinetic friction. For a given surface pair, $\mu_s$ is typically greater than $\mu_k$ , so the maximum static friction is typically greater than the kinetic-friction magnitude for the same normal force.

Next Topic

—2.8 Spring ForcesRead