The uniform crate has a mass of 140 kg kg . The coefficient of static friction between the crate and the floor is μ s μs = 0.2. The coefficient of static friction between the man's shoes and the floor is μ ′ s μs′ = 0.45. Assume the man exerts only a horizontal force on the crate. Determine the smallest mass of the man so he can move the crate.

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?