Engr Help

Example involving Friction

For the first case, assume the block tends to slide up the plane and construct a

FBD. Note the directions taken for + x and + y. Then write the equations of

equilibrium.

ΣF_y = 0 N - P sinθ ˗ Q cosθ = 0 (1)

ΣF_x = 0 ˗ F + P cosθ ˗ Q sinθ = 0 (2)

So from eq. 1 N = P sinθ + Q cosθ

The maximum value for friction is F_max = μ_s N

So from eq. 1 F = μ_s [P sinθ + Q cosθ ] (3)

Next put eq. 3 and eq. 2 and solve for P .

P = Q ( sinθ + μ_s cosθ ) / (cosθ ˗ μ_s sinθ )

For the prescribed values for Q, θ, and μ_s gives P = 483 N. (result)

Next consider the possibility that the block slides down the plane.