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:
(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:
![\mu_{s} = \frac{83\,N}{(31\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}](https://tex.z-dn.net/?f=%5Cmu_%7Bs%7D%20%3D%20%5Cfrac%7B83%5C%2CN%7D%7B%2831%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%7D)
![\mu_{s} = 0.273](https://tex.z-dn.net/?f=%5Cmu_%7Bs%7D%20%3D%200.273)
![\mu_{k} = \frac{55\,N}{(31\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}](https://tex.z-dn.net/?f=%5Cmu_%7Bk%7D%20%3D%20%5Cfrac%7B55%5C%2CN%7D%7B%2831%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%7D)
![\mu_{k} = 0.181](https://tex.z-dn.net/?f=%5Cmu_%7Bk%7D%20%3D%200.181)
The static and kinetic coefficients of friction are 0.273 and 0.181, respectively.