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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?

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Answer:

μ = .4842

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.

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