Question

A force of 115.0 N is applied horizontally to a 25.0 kg box to move it across a
horizontal floor. If the box has an acceleration of 3.00 m/s2, find the coefficient of
friction.

Answer 1

So, the coefficient of kinetic friction approximately 0.16.

Introduction

Hi ! Here I will help you to solve the problem of the coefficient of kinetic friction. When an object moving on a rough surface, there will be a frictional force called kinetic friction. Remember that friction is also a force, but reduces the value of the force acting. Kinetic friction force is affected by the normal force (N) and the coefficient of kinetic friction. The greater the value of the normal force (N) and/or the coefficient of friction, the greater the value of the kinetic friction force. The normal force is also affected by the mass and the gravity acceleration [See the attached image to see the direction of the friction force].

Formula Used

For kinetic friction, there are the following equations that you will use in various problem conditions. However, the equation in the box is the formula you use for solve this problem.

$\sf{\sum F = m \cdot a}$

$\sf{F - f_k = m \cdot a}$

$\boxed{\sf{\bold{F - \mu_k \cdot m \cdot g = m \cdot a}}}$

With the following condition:

• $\sf{\sum F}$ = resultant of the force (N)
• F = acting force (N)
• m = mass of the object (kg)
• a = acceleration (m/s²)
• $\sf{f_k}$ = kinetic friction (N)
• g = coefficient of the earth gravity ≈ 9.8 m/s²
• $\sf{\mu_k}$ = coefficient of the kinetic friction

Solution

We know that:

• F = acting force = 115.0 N
• m = mass of the object = 25.0 kg
• a = acceleration = 3 m/s²
• g = coefficient of the earth gravity ≈ 9.8 m/s²

What was asked ?

• $\sf{\mu_k}$ = coefficient of the kinetic friction = ... ?

Step by step:

$\sf{F - \mu_k \cdot m \cdot g = m \cdot a}$

$\sf{115.0 - \mu_k \cdot 25.0 \cdot 9.8 = 25 \cdot 3}$

$\sf{115.0 - \mu_k \cdot 245 = 75.0}$

$\sf{-\mu_k \cdot 245 = 75-115}$

$\sf{-\mu_k \cdot 245 = -40}$

$\sf{\mu_k = \frac{-40}{-245}}$

$\boxed{\sf{\mu_k \approx 0.16}}$

Conclusion

So, the coefficient of kinetic friction approximately 0.16.

Learn More

• After learning about kinetic friction. Are you still remember about static friction? If not, visit https://brainly.com/question/28353910
• Do you want to see another type of the question about finding the coefficient of kinetic friction ? Visit https://brainly.com/question/28353877