Provide complete solutions and explain thoroughly. For #2, don't forget to indicate the force's magnitude and direction.

1. A uniform ladder is 10 m long and weighs 200 N. In the gure, the ladder leans against a vertical, frictionless wall at height h = 8.0 m above _T the ground. A horizontal force F is applied to the ladder at distance d = 2.0 m from its base (measured along the ladder). (a) If force magnitude F = 50 N, what is the force of the ground on the ladder, in unit-vector notation? (b) If F = 150 N, what is the force of the ground on the ladder, also in unit-vector notation? (c) Suppose the coefcient of static friction between the ladder and the ground is 0.38; for what minimum value of the force magnitude F will the base of the ladder just barely start to move toward the wall? 2. In the gure, a uniform beam with a weight of 60 N and a length of I- 32 m is hinged at its lower end, and a horizontal force F of magnitude 50 N acts at its upper end. The beam is held vertical by a cable that makes angle 0 = 25 with the ground and is attached to the ' beam at height h = 2.0 111. What are (a) the tension in the cable and l x (b) the magnitude and the direction of the force on the beam from the hinge? 3. Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what . must be its minimum mass so that material on its surface remains in -"'\\0 place during the rapid rotation? ' 4