A 31 kg block is initially at rest on a horizontal surface. A horizontal force of 83 N is required to set the block in motion. After it is in motion, a horizontal force of 55 N i required to keep it moving with constant speed. From this information, find the coefficients of static and kinetic friction

The static and kinetic coefficients of friction are 0.273 and 0.181, respectively.

Explanation:

By Newton's Laws of Motion and definition of maximum friction force, we derive the following two formulas for the static and kinetic coefficients of friction:

(1)

(2)

Where:

- Static coefficient of friction, no unit.

- Kinetic coefficient of friction, no unit.

- Static friction force, in newtons.

- Kinetic friction force, in newtons.

- Mass, in kilograms.

- Gravitational constant, in meters per square second.

If we know that , , and , then the coefficients of friction are, respectively:

The static and kinetic coefficients of friction are 0.273 and 0.181, respectively.