Question

A 5kg box slides down an incline of angle 40 with an unknown coefficient of kinetic friction. If the box’s acceleration is measured to be 3.58 m/s2 down the slope, what is the value of the unknown coefficient of kinetic friction?

Answer 1

Answer 2

To determine the coefficient of kinetic friction (μk) in this scenario, we can use Newton's second law of motion and the forces acting on the box.

Given: Mass of the box (m) = 5 kg Angle of the incline (θ) = 40° Acceleration of the box (a) = 3.58 m/s² (down the slope)

The force of gravity acting on the box can be broken down into two components:

1. The component parallel to the incline (mg sinθ), which contributes to the acceleration.

2. The component perpendicular to the incline (mg cosθ), which is balanced by the normal force and does not affect the motion.

The force of kinetic friction (fk) acts opposite to the direction of motion and can be expressed as: fk = μk * N

Since the box is sliding down the incline, the force of kinetic friction opposes the component of gravity parallel to the incline (mg sinθ). Therefore, we can write:

fk = mg sinθ

Using Newton's second law (F = ma), we have:

fk = ma

Substituting the values:

μk * N = m * a

To find N (normal force), we can use the component of gravity perpendicular to the incline:

mg cosθ = N

Substituting this value for N, we have:

μk * mg cosθ = m * a

Now, we can solve for the coefficient of kinetic friction (μk):

μk = (m * a) / (mg cosθ)

Simplifying the equation:

μk = a / (g cosθ)

Substituting the known values:

μk = 3.58 m/s² / (9.8 m/s² * cos 40°)

μk = 3.58 / (9.8 * cos 40°)

μk ≈ 0.235

Therefore, the unknown coefficient of kinetic friction in this scenario is approximately 0.235.