Challenges

See the figure. A box weighing 50 N rests on a horizontal floor. A weightless round drum is welded to the box. Do a planar analysis (no out of plane motions). A massless inextensible string attached to an immovable fixed point above passes around the drum as shown. The rising part of the string makes an angle θ = 13◦ with the vertical, as shown. The friction coefficient between the box and the ground is 0.05, and that between the string and drum is 0.05 as well. Find the hori

See the figure below. Planar analysis. A half-disk (semicircular shape, uniform mass density) rests on a rigid horizontal plane with Coulomb friction coefficient µ. A force F acts on the right corner as shown, making a constant angle β = 20◦ with horizontal. The disk rolls to the right and is at equilibrium. The force F is slowly increased, maintaining equilibrium, until the roll angle is θ = 30◦. At this configuration, the system is at impending slip. Find µ to 3 significant