Friction Problems - Free Printable

1. Identify the forces acting on the rod: gravity (acting at the center of mass, magnitude Mg), normal force from the wall (horizontal, magnitude N_w), and normal force from the floor (vertical, magnitude N_f).
2. Apply the condition for translational equilibrium: The sum of forces in the horizontal direction is zero (N_w = 0) and the sum of forces in the vertical direction is zero (N_f = Mg).
3. Apply the condition for rotational equilibrium: Choose a pivot point (e.g., the point where the rod touches the floor). The torque due to gravity is Mg * (L/2) * cos(θ), and the torque due to the wall's normal force is N_w * L * sin(θ). Set the net torque to zero.
4. Solve the torque equation: Mg * (L/2) * cos(θ) - N_w * L * sin(θ) = 0. This gives N_w = (Mg / 2) * cot(θ).
5. Combine with the horizontal force equation: Since N_w must be zero for equilibrium (no other horizontal forces), this implies cot(θ) = 0, which is impossible for a finite θ. Therefore, the rod cannot be in static equilibrium without friction or an additional force.