Applications involving Friction - - Rigid Bodies in Translation

Key Concepts: Frictional forces always oppose motion or the tendency toward motion (impending

motion). In applications involving friction you need to determine if friction is sufficient to prevent

motion, if friction is just enough that motion impends, or if friction is insufficient to prevent sliding
with the mating surface. So you need to investigate each case and test which case actually occurs.

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

diagram of the body showing all external forces acting on the body noting that the frictional force

always opposes motion or the tendency toward motion. See the figure below. Align the x-coordinate axis along the direction that sliding might occur. In this figure sliding might occur in the x-direction.

The governing equation of motion is:

ΣF = m a_c

where ΣF are the sum of the external forces acting on the body, m is the mass of the body,

and a_c = a_cx i + a_cy j is the acceleration of the body in the x and y-directions.

Note: g is the acceleration of gravity

Examine each case separately.

Case 1: Assume friction is sufficient to prevent sliding and the body starts from rest.

Step 2	Assume vcx = acx = 0
Step 3	Solve for F and for N
Step 4	Calculate Fmax = μN
Test	If |F| ≤ |Fmax| , then friction is sufficient to prevent sliding.

Here F is the frictional force, N is the normal force, and μ is the coefficient of friction.

Cases 2 and 3: Sliding occurs either in the + x-direction or in the ˗ x-direction.

Click here to continue to Cases 2 and 3.

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