Question

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

Answer 1

Answer:

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:

$\mu_{s} = \frac{f_{s}}{m\cdot g}$ (1)

$\mu_{k} = \frac{f_{k}}{m\cdot g}$ (2)

Where:

$\mu_{s}$ - Static coefficient of friction, no unit.

$\mu_{k}$ - Kinetic coefficient of friction, no unit.

$f_{s}$ - Static friction force, in newtons.

$f_{k}$ - Kinetic friction force, in newtons.

$m$ - Mass, in kilograms.

$g$ - Gravitational constant, in meters per square second.

If we know that $f_{s} = 83\,N$, $f_{k} = 55\,N$, $m = 31\,kg$ and $g = 9.807\,\frac{m}{s^{2}}$, then the coefficients of friction are, respectively:

$\mu_{s} = \frac{83\,N}{(31\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}$

$\mu_{s} = 0.273$

$\mu_{k} = \frac{55\,N}{(31\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}$

$\mu_{k} = 0.181$

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