Friction - - Rigid Bodies in Translation

Example: A rigid block of mass, m = 4 kg, starts at rest on a sloped surface at an angle θ of

30^o from the horizontal. It is subjected to a horizontal force, P = 10 N. The coefficient of

friction, μ = 1.4 and g = 10 m/sec². Determine if the block slides, and if it does, find the

acceleration, a_C, of the block. See the figure below.

The first and most important step is to construct a complete and accurate free body diagram

as shown below.

Case 1: Check for equilibrium. ∑ F_x = 0 ˗ F ˗ mg sinθ + P cosθ = 0 (1)

and ∑ F_y = 0 N ˗ P sinθ ˗ mg cosθ = 0 (2)

From (1) F = ˗ mg sinθ + P cosθ and for the data: F = ˗ 11.339 N

From (2) N = P sinθ + mg cosθ and for the data: N = 39.63 N

Now F_max = μ N = (1/4) N = 9.91 N

Since it takes 11.339 N to hold the block in equilibrium and only 9.91 N is available, |F| > F_max ,

there is insufficient friction to hold the block in equilibrium and the block will slide on the
inclined surface.

Click here to continue with this example.

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