The **friction equation** establishes a relationship between the friction force (F_{f}), the coefficient of friction (µ), and the normal force (F_{N}). Mathematically, it is represented as F_{f} = µ × F_{N}. 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, F
_{f}= ? - 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/s
^{2}

Applying the formula:

- F
_{f}= µ × F_{N} - F
_{f}= µ × mg (normal force equation, F_{N}= mg) - F
_{f}= 0.09 × 9 × 9.81 - F
_{f}= 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, F
_{f}= ? - 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/s
^{2}

Applying the formula:

- F
_{f}= µ × F_{N} - F
_{f}= µ × mg (normal force equation, F_{N}= mg) - F
_{f}= 0.35 × 12 × 9.81 - F
_{f}= 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, F
_{f}= ? - Coefficient of friction between the book and desk, µ = 0.24
- Assuming gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula:

- F
_{f}= µ × F_{N} - F
_{f}= µ × mg (normal force equation, F_{N}= mg) - F
_{f}= 0.24 × 2 × 9.81 - F
_{f}= 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, F
_{f}= ? - 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/s
^{2}

Applying the formula:

- F
_{f}= µ × F_{N} - F
_{f}= µ × mg (normal force equation, F_{N}= mg) - F
_{f}= 0.75 × 0.5 × 9.81 - F
_{f}= 3.67 N

Therefore, the friction force acting on a knife is **3.67 N**.

## Related

## More topics

- Free fall equation
- Air resistance formula
- Terminal velocity equation
- Gravity equation
- Inertia formula
- Acceleration formula
- Momentum equation
- Mass formula
- Velocity formula
- Pressure equation
- Kinematic equations
**Friction equation**

## 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

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.