A 31.0 N crate of feeds is resting on a horizontal floor. The coefficients of static and kinetic friction between the crate and the floor are 0.52 and 0.34 respectively. A he-goat is pushing against the crate applying a horizontal force on the crate. Determine the least horizontal force applied by the he-goat to move the crate.

A 36 N pile of books is resting on a horizontal table in a library. The coefficients of static and kinetic friction between the box and the table are 0.36 and 0.22 respectively.  Determine the magnitude of the friction force on the pile when the pile is at rest and horizontal force of magnitude F = 0 N is applied to the pile.

A forklift is loaded with a crate. You want to accelerate the forklift as fast as possible without the crate sliding. The crate is resting on a horizontal area of the fork blade where the coefficients of kinetic friction and static friction between the crate and the blade are 0.239 and 0.458 respectively. Determine the shortest time the forklift can accelerate from rest to 15 m/s without setting the crate in a slide.

Mountain bikes riding along a rough trail will experience a significant coefficient of static friction with the ground. Determine what will be the required coefficient of static friction for a mountain biker to accelerate uniformly and complete a 1.1 km distance in 13s from rest, without tires slipping?

At what angle θ does a small block begin to slide off a dome's curved surface, given the coefficient of static friction (μₛ) is 0.73?