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A box of books weighing 215 N moves at a constant velocity across the floor when the box is pushed with a force of 135 N exerted downward at an angle of 30° with the horizontal. Find μk between the box and the floor.

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sqdancefan

Answer:

  μk ≈ 0.414

Explanation:

The normal force at the box/floor interface is the sum of the weight and the vertical component of the applied force:

  normal force = 215 N + (135 N)sin(30°) = 282.5 N

The tangential force is the horizontal component of the applied force:

  tangential force = (135 N)cos(30°) ≈ 116.91 N

Then the coefficient of friction is ...

  μk = (tangential force)/(normal force) = (116.91 N)/(282.5 N)

  μk ≈ 0.414

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