Question

A 248 kg object moving at 19m/s comes to stop over a distance of 38 m. What is the coefficient of kinetic friction between the surfaces?

Answer 1

μ = .4842

Step-by-step explanation:

Assuming constant acceleration and the object is sliding on a level surface:

Let's start off by finding the acceleration of the object.

• v₀ = 19 m/s
• v = 0 m/s
• Δx = 38 m
• a = ?

v² = v₀² + 2aΔx

• 0² = 19² + 2a(38)
• 0 = 361 + 76a
• -361 = 76a
• a = -4.75 m/s²

Now, we can make a free-body diagram and see that the only force opposing the object's motion is the friction force -- this is the only force in the x-direction.

We can use Newton's 2nd Law: F = ma to solve for the coefficient of friction.

F = ma

• F = friction force = μ * N = μ * mg

Now, we have:

• μ * mg = ma

The mass cancels out and solving for the coefficient of friction gives us:

• μ * g = a
• μ = a/g

We know the acceleration is -4.75 m/s² and g = -9.81 m/s²:

• μ = -4.75/-9.81
• μ = .4842

The coefficient of kinetic friction between the surfaces, assuming constant acceleration and a flat surface, is 0.4842.