How to Find Acceleration with Kinetic Friction: A Comprehensive Guide

Calculating the acceleration of an object moving on a surface with kinetic friction is a fundamental concept in classical mechanics. This comprehensive guide will walk you through the step-by-step process, provide theoretical explanations, and offer practical examples to help you master this essential skill.

Understanding Kinetic Friction and Acceleration

Kinetic friction is a force that opposes the relative motion between two surfaces in contact. It depends on the normal force between the surfaces and the coefficient of kinetic friction, which is a dimensionless value that varies depending on the materials involved. The net force acting on an object is the difference between the applied force and the force of kinetic friction, and this net force determines the object’s acceleration.

Step-by-Step Approach to Finding Acceleration with Kinetic Friction

1. Identify the Mass of the Object (m): Determine the mass of the object that is being accelerated.
2. Determine the Applied Force (F): Identify the force that is being applied to the object to make it move or accelerate.
3. Find the Coefficient of Kinetic Friction (μk): Obtain the coefficient of kinetic friction, which can be found in tables or measured experimentally.
4. Calculate the Force of Kinetic Friction (Fk): Use the equation Fk = μk * m * g, where g is the acceleration due to gravity (approximately 9.81 m/s²).
5. Calculate the Net Force (Fnet): Subtract the force of kinetic friction from the applied force: Fnet = F - Fk.
6. Calculate the Acceleration (a): Apply Newton’s second law, which states that the acceleration of an object is proportional to the net force and inversely proportional to its mass: a = Fnet / m.

Example Calculations

1. Example 1: Chair on a Floor
2. Given Data:
   • Mass of the chair (m) = 6 kg
   • Applied force (F) = 15 N
   • Coefficient of kinetic friction (μk) = 0.25

3. Calculations:

   • Force of kinetic friction (Fk) = μk * m * g = 0.25 * 6 kg * 9.81 m/s² = 14.72 N
   • Net force (Fnet) = F – Fk = 15 N – 14.72 N = 0.28 N
   • Acceleration (a) = Fnet / m = 0.28 N / 6 kg = 0.0467 m/s²

4. Example 2: Hockey Puck on Ice

5. Given Data:
   • Mass of the puck (m) = 2 kg
   • Applied force (F) = 30 N
   • Coefficient of kinetic friction (μk) = 0.05 (assuming a low friction surface like ice)
6. Calculations:
   • Force of kinetic friction (Fk) = μk * m * g = 0.05 * 2 kg * 9.81 m/s² = 0.98 N
   • Net force (Fnet) = F – Fk = 30 N – 0.98 N = 29.02 N
   • Acceleration (a) = Fnet / m = 29.02 N / 2 kg = 14.51 m/s²

Theoretical Explanation

The force of kinetic friction is a dissipative force that opposes the relative motion between two surfaces in contact. It is proportional to the normal force between the surfaces and the coefficient of kinetic friction. The normal force is the force perpendicular to the surface, which is equal to the weight of the object in the absence of additional downward forces.

The net force acting on the object is the difference between the applied force and the force of kinetic friction. This net force determines the object’s acceleration according to Newton’s second law, which states that the acceleration of an object is proportional to the net force and inversely proportional to its mass.

Physics Formulae

• Force of Kinetic Friction: Fk = μk * m * g
• Net Force: Fnet = F - Fk
• Acceleration: a = Fnet / m

Numerical Problems

1. A box of mass 10 kg is being pulled with a force of 20 N on a surface with a coefficient of kinetic friction of 0.3. Calculate the acceleration of the box.
2. A car of mass 1500 kg is accelerating on a road with a coefficient of kinetic friction of 0.15. If the force applied is 3000 N, what is the acceleration of the car?

Figures and Data Points

Force of Kinetic Friction vs. Normal Force

This graph shows the linear relationship between the force of kinetic friction and the normal force, with the coefficient of kinetic friction as the slope.

Acceleration vs. Applied Force

This graph demonstrates how the acceleration of an object changes as the applied force increases, with the force of kinetic friction subtracted from the applied force.

Measurements and Values

Coefficient of Kinetic Friction

Surface Combination	Coefficient of Kinetic Friction (μk)
Wood on Wood	0.25 – 0.50
Metal on Metal	0.15 – 0.30
Rubber on Concrete	0.45 – 0.75

Acceleration Due to Gravity

The acceleration due to gravity on Earth’s surface is approximately 9.81 m/s².

References

1. Sciencing. (2020). How to Calculate Acceleration With Friction. Retrieved from https://sciencing.com/calculate-acceleration-friction-6245754.html
2. Physics Forums. (2011). Finding acceleration with Kinetic Friction coefficient. Retrieved from https://www.physicsforums.com/threads/finding-acceleration-with-kinetic-friction-coefficient.522631/
3. The Physics Classroom. (n.d.). Finding Acceleration. Retrieved from https://www.physicsclassroom.com/class/newtlaws/Lesson-3/Finding-Acceleration