A dockworker loading crates on a ship finds that a 20 kg crate, initially at rest on a horizontal surface, requires a 70 N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 52 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.

Coefficient of static friction is defined as the proportionality constant for the frictional force between the crate and floor for starting the motion of crate and normal force acting on the crate. As the normal force of the crate is equal to the influence of acceleration due to gravity acting on the mass of the crate, the frictional force for static friction coefficient will be the force applied to move the crate.

Thus, [tex]Static friction force = Coefficient of static friction * Normal force\\\\[/tex]

Since, the static friction force is 70 N, the normal force is equal to [tex]Mass * acceleration due to gravity = 20 * 9.8 = 196 N[/tex]

So normal force is 196 N and static force is 70 N, and the ratio of static friction force to the normal force will give the coefficient of static friction.

[tex]Coefficient of static friction = \frac{Static friction force}{Normal force}\\ \\Coefficient of static friction = \frac{70}{196} = 0.357[/tex]

Similarly, the coefficient of kinetic friction can be determined from the ratio of kinetic friction force to normal force. Here the kinetic friction force will be equal to the force applied on the crate to keep it moving.

[tex]Coefficient of kinetic friction = \frac{Kinetic friction force}{Normal force}\\ \\Coefficient of kinetic friction = \frac{52}{196} = 0.265[/tex]

Thus, the coefficient of static friction is 0.357 and the coefficient of kinetic friction is 0.265.