Engr Help

Example involving Friction (continued)

FBD:

Write the equations of equilibrium.

→ ∑ F_x = 0 P cos θ ˗ F = 0 (1)

↑ ∑ F_y = 0 N ˗ W + P sin θ = 0 (2)

Ccw ∑ M_B = 0 W(b/2) ˗ N x ˗ P (cos θ) (3h/4) = 0 (3)

The unknowns include: P, F, N, x (4 unknowns)

Therefore need more information.

Investigate the condition that sliding impends. i.e. F = μN

Use (2): F = μ ( W ˗ P sin θ )

and from equilibrium , (2): F = P cos θ

So P cos θ = μ ( W ˗ P sin θ ) So P = μW / ( cos θ + μ sin θ )

For the data: P = 26.67 lb

Investigate the condition for tipping to impend. i.e. x = 0

Use (3): W(b/2) ˗ P (cos θ) (3h/4) = 0 P = (2W/3cosθ) (b/h)

For the data: P = 50 lb

Result: Sliding impends prior to tipping.