Answer:
No the crate can not be pushed across the floor.
Explanation:
The static frictional force ([tex]F_{s}[/tex]) is the product of the coefficient of static friction ([tex]\mu_{s}[/tex]) and the normal force ([tex]N[/tex]) produced by the floor on the object. Mathematically,
[tex]F_{s} = \mu_{s}N[/tex]
For static friction the normal force ([tex]N[/tex]) is balanced by the weight of the object.
So, for the crate the static frictional force ([tex]F_{sC}[/tex]) is written as
[tex]F_{sC} = \mu_{s} N_{C} = \mu_{C} Mg[/tex]
where '[tex]M[/tex]' is the mass of the crate.
and for the person having mass '[tex]m[/tex]' the static frictional force ([tex]F_{sP}[/tex]) is written as
[tex]F_{sP} = \mu_{s}N_{P} = \mu_{s}mg[/tex]
Comparing bot the equations,
[tex]\dfrac{F_{sC}}{F_{sP}} = \dfrac{M}{m}[/tex]
As, [tex]M > m[/tex] so, [tex]F_{sC}[/tex] > [tex]F_{sP}[/tex].
Therefore it is not possible for the person to push the crate across the floor.
