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The friction equation establishes a relationship between the friction force (Ff), the coefficient of friction (µ), and the normal force (FN). Mathematically, it is represented as Ff = µ × FN. This equation enables the determination of the frictional force acting on an object by taking into account the coefficient of friction and the corresponding normal force.
Practice problems
Problem #1
Calculate the friction force acting on a box of mass 9 kg as it is pushed along the floor. The coefficient of friction between the box and the floor is 0.09.
Solution
Given data:
- Friction force acting on a box, Ff = ?
- Mass of a box, m = 9 kg
- Coefficient of friction between the box and floor, µ = 0.09
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- Ff = µ × FN
- Ff = µ × mg (normal force equation, FN = mg)
- Ff = 0.09 × 9 × 9.81
- Ff = 7.94 N
Therefore, the friction force acting on a box is 7.94 N.
Problem #2
Determine the value of the friction force acting on an ice slab of mass 12 kg as it is pulled along a cement floor. The coefficient of friction between the ice slab and the cement floor is 0.35.
Solution
Given data:
- Friction force acting on an ice slab, Ff = ?
- Mass of an ice slab, m = 12 kg
- Coefficient of friction between the ice slab and cement floor, µ = 0.35
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- Ff = µ × FN
- Ff = µ × mg (normal force equation, FN = mg)
- Ff = 0.35 × 12 × 9.81
- Ff = 41.20 N
Therefore, the friction force acting on an ice slab is 41.20 N.
Problem #3
A 2 kg book resting on a desk is pushed with a hand. Calculate the friction force acting on the book, given that the coefficient of friction between the book and the desk is 0.24.
Solution
Given data:
- Mass of a book, m = 2 kg
- Friction force acting on a book, Ff = ?
- Coefficient of friction between the book and desk, µ = 0.24
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- Ff = µ × FN
- Ff = µ × mg (normal force equation, FN = mg)
- Ff = 0.24 × 2 × 9.81
- Ff = 4.70 N
Therefore, the friction force acting on a book is 4.70 N.
Problem #4
Calculate the friction force acting on a 500 gm knife as it is sharpened on a knife sharpening stone. The coefficient of friction between the knife and the knife sharpening stone is 0.75.
Solution
Given data:
- Friction force acting on a knife, Ff = ?
- Mass of a knife, m = 500 gm = 0.5 kg
- Coefficient of friction between a knife and knife sharpening stone, µ = 0.75
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- Ff = µ × FN
- Ff = µ × mg (normal force equation, FN = mg)
- Ff = 0.75 × 0.5 × 9.81
- Ff = 3.67 N
Therefore, the friction force acting on a knife is 3.67 N.
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External links
- Friction Calculator f = μN – Calculator Soup
- Coefficient of friction | Definition & Formula – Britannica
- 6.2 Friction – University Physics Volume 1 – OpenStax
- Friction Equation – Physics This Week
- What is friction? (article) – Khan Academy
- How to Calculate the Force of Friction – Sciencing
- Determining the Coefficient of Friction – National Floor Safety Institute
- 6.5: Friction (Part 2) – Physics LibreTexts
- What is the equation for static friction? – Quora
- Friction – University of Tennessee, Knoxville
- How to Calculate Static Friction | Physics – Study.com
- Friction – Wikipedia
- 6.2 Friction | University Physics Volume 1 – Lumen Learning
- Friction Calculator – Omni Calculator
- Static friction – Boston University
- The formula of friction – Physics Stack Exchange
- Maximum frictional force (Mechanics) – Newcastle University
- Friction Formula – SoftSchools.com
- Friction Static And Kinetic – Force – MCAT Content – Jack Westin
- Standard Friction Equation by Ron Kurtus – Physics Lessons – School for Champions
- How do you get the coefficient of friction – Reddit
- Friction – Isaac Physics
- The equation for the force of friction is f = uN – Chegg
- AP Physics 1 : Force of Friction – Varsity Tutors
- Coefficient of Friction: Equations & Units – Vaia
- Friction (Frictional Force): Definition, Formula, & Examples – Science Facts
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