$8-142.$ Determine the minimum horizontal force $P$ required to hold the crate from sliding down the plane. The crate has a mass of $50$ kg and the coefficient of static friction between the crate and the plane is ${}_s=0\mathrm{.}25.$

$8-143.$ Determine the minimum force $P$ required to push the crate up the plane. The crate has a mass of $50$ kg and the coefficient of static friction between the crate and the plane is ${}_s=0\mathrm{.}25.$

$*8-144.$ A horizontal force of $P=100N$ is just sufficient to hold the crate from sliding down the plane, and a horizontal force of $P=350N$ is required to just push the crate up the plane. Determine the coefficient of static friction between the plane and the crate, and find the mass of the crate.

Probs. $8-142/143/144$