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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 2: Force & Translational DynamicsKinetic & Static FrictionStatic Friction Force Formula

Static Friction Force Formula (College Board AP® Physics 1: Algebra-Based)

Study Guide

Ann Howell

Written by: Ann Howell

Reviewed by: Caroline Carroll

Static friction force equation

  • The maximum magnitude of the static friction force exerted on an object is the product of the normal force the surface exerts on the object and the coefficient of static friction

  • The possible magnitudes of static friction is given by the inequality:

open vertical bar F with rightwards arrow on top subscript f comma s end subscript close vertical bar space less-than or slanted equal to space open vertical bar mu subscript s F with rightwards arrow on top subscript n close vertical bar

  • Where:

    • open vertical bar F with rightwards arrow on top subscript f comma s end subscript close vertical bar space equals spacemagnitude of static friction, measured in straight N

    • mu subscript s space equals spacecoefficient of static friction

    • F with rightwards arrow on top subscript n space equals spacenormal reaction force between the two contact surfaces, measured in straight N

    • less-than or slanted equal to spacemeans less than or equal to

Coefficient of kinetic vs static friction

  • The coefficient of static friction is typically greater than the coefficient of kinetic friction for a given pair of surfaces

    • As explained in the Static friction study guide, the force of static friction is greater than the force of kinetic friction

    • We can rearrange this inequality to show that the coefficient of static friction is greater

open vertical bar F subscript f comma k end subscript close vertical bar space less than space open vertical bar F subscript f comma s end subscript close vertical bar

open vertical bar mu subscript k F with rightwards arrow on top subscript n close vertical bar less than open vertical bar mu subscript s F with rightwards arrow on top subscript n close vertical bar

open vertical bar mu subscript k down diagonal strike F with rightwards arrow on top subscript n end strike space close vertical bar less than open vertical bar mu subscript s down diagonal strike F with rightwards arrow on top subscript n end strike space close vertical bar

open vertical bar mu subscript k close vertical bar less than open vertical bar mu subscript s close vertical bar

Worked Example

An object of mass 20 space kg is at rest on a rough horizontal surface. When a force of 50 space straight N is applied, the object is on the point of its threshold of motion and will not move, when a force of 40 space straight N is applied, this force is enough to keep it moving at a constant velocity.

Show that for the object open vertical bar mu subscript k close vertical bar less than open vertical bar mu subscript s close vertical bar.

Answer:

Step 1: Draw a free body diagram of the two scenarios

  • When the object is at its threshold of motion, the magnitude of the static frictional force is equal to the magnitude of the applied force

  • When the object is moving at a constant velocity, the kinetic frictional force is equal to the applied force

A block at rest with 50N applied force, and in motion with 40N applied force, depicting static and kinetic friction thresholds.

Step 2: Determine the magnitudes of friction and the normal force in each scenario

  • Normal force is created due to the gravitational force acting on the object

    • The normal force is the same in each scenario

F with rightwards arrow on top subscript g space equals F with rightwards arrow on top subscript n space equals space m g

F with rightwards arrow on top subscript n space equals space 20 space times space 10

F with rightwards arrow on top subscript n space equals space 200 space straight N

  • At the threshold of motion

    • For applied force, F

open vertical bar F close vertical bar space equals space open vertical bar F subscript f comma s end subscript close vertical bar space equals space open vertical bar mu subscript s F with rightwards arrow on top subscript n close vertical bar space equals space 50 space straight N

  • Moving at constant velocity

    • For applied force, F

open vertical bar F close vertical bar space equals space open vertical bar F subscript f comma k end subscript close vertical bar space equals space open vertical bar mu subscript k F with rightwards arrow on top subscript n close vertical bar space equals space 40 space straight N

Step 3: Calculate the magnitude of the kinetic and static friction

  • At the threshold of motion

50 space equals space open vertical bar mu subscript s close vertical bar times space 200

open vertical bar mu subscript s close vertical bar equals space 50 over 200

open vertical bar mu subscript s close vertical bar equals space 0.25

  • Moving at constant velocity

40 space equals space open vertical bar mu subscript k close vertical bar times space 200

open vertical bar mu subscript k close vertical bar equals space 40 over 200

open vertical bar mu subscript k close vertical bar equals space 0.20

Step 4: Compare the magnitudes of the kinetic and static friction

0.25 space greater than space 0.20

open vertical bar mu subscript s close vertical bar space greater than space open vertical bar mu subscript k close vertical bar

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    Author
    Reviewer
    Ann Howell

    Author: Ann Howell

    Expertise: Physics Content Creator

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.