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

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

Step-by-step 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) = (f_(s))/(m\cdot g)` (1)

`\mu_(k) = (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\,(m)/(s^(2))`, then the coefficients of friction are, respectively:

`\mu_(s) = (83\,N)/((31\,kg)\cdot \left(9.807\,(m)/(s^(2)) \right))`

`\mu_(s) = 0.273`

`\mu_(k) = (55\,N)/((31\,kg)\cdot \left(9.807\,(m)/(s^(2)) \right))`

`\mu_(k) = 0.181`

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