Physics: 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

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A 31 kg block is initially at rest on a horizontal

Ответ:

savannabroyhill24

30.07.2021

Physics

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.

- Mass, in kilograms.

- 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: