Answer:
The friction force exerted by the surface is 490 newtons.
Explanation:
From Physics, we remember that static friction force ([tex]f_{s}[/tex]), measured in newtons, for a particle on a horizontal surface is represented by the following inequation:
[tex]f_{s} \leq \mu_{s}\cdot m \cdot g[/tex] (Eq. 1)
Where:
[tex]\mu_{s}[/tex] - Static coefficient of friction, dimensionless.
[tex]m[/tex] - Mass of the crate, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If [tex]f_{s} = \mu_{s}\cdot m \cdot g[/tex], then crate will experiment an imminent motion. The maximum static friction force is: ([tex]\mu_{s} = 0.6[/tex], [tex]m = 100\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex])
[tex]f_{s} = (0.6)\cdot (100\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]
[tex]f_{s} = 588.42\,N[/tex]
From Newton's Laws we get that current force of friction as reaction to the pulling force done by the worker on the crate is:
[tex]\Sigma F = F-f = 0[/tex]
[tex]f = F[/tex] (Eq. 2)
Where:
[tex]F[/tex] - Horizontal force done by the worker, measured in newtons.
[tex]f[/tex] - Static friction force, measured in newtons.
If [tex]F = 490\,N[/tex], then the static friction force exerted by the surface is:
[tex]f = 490\,N[/tex]
Given that [tex]f < f_{s}[/tex], the crate does not change its state of motion. The friction force exerted by the surface is 490 newtons.
