A 13.0 -kg box is released on a 33 degree incline and accelerates down the incline at 0.20 m/s^2

What is the coefficient of kinetic friction?

* If I know the friction force impeding the object motion is 67 N. How do I find the coefficient of kinetic friction?

m•a=m•g•sinα – F(fr)

F(fr) = m•g•sinα –m•a
F(fr) =μ•N =μ•m•g•cosα
m•g•sinα –m•a = μ•m•g•cosα
μ = (g•sinα –a)/ g•cosα

To find the coefficient of kinetic friction, you can use the formula:

coefficient of kinetic friction (μ) = friction force (Ff) / normal force (Fn)

Here's how you can calculate it using the given information:

1. First, calculate the normal force (Fn) acting on the object. The normal force is the perpendicular force exerted by a surface to support the weight of an object. It is equal in magnitude and opposite in direction to the weight of the object. In this case, the normal force can be calculated as:

Fn = mass (m) * gravity (g)

Given:
Mass (m) = 13.0 kg
Gravity (g) = 9.8 m/s^2 (approximately)

Fn = 13.0 kg * 9.8 m/s^2 = 127.4 N

2. Now that you have the normal force, you can use the given friction force (Ff) to find the coefficient of kinetic friction (μ). The equation becomes:

μ = Ff / Fn

Given:
Friction force (Ff) = 67 N
Normal force (Fn) = 127.4 N

μ = 67 N / 127.4 N ≈ 0.525

So, the coefficient of kinetic friction is approximately 0.525.