A crate, heavier than you are, rests on a rough floor. The coefficient of static friction between the crate and the floor is the same as that between the soles of your shoes and the floor. Can you push the crate across the floor?

No the crate can not be pushed across the floor.

Explanation:

The static frictional force () is the product of the coefficient of static friction () and the normal force () produced by the floor on the object. Mathematically,

For static friction the normal force () is balanced by the weight of the object.

So, for the crate the static frictional force () is written as

where '' is the mass of the crate.

and for the person having mass '' the static frictional force () is written as

Comparing bot the equations,

As, so, > .

Therefore it is not possible for the person to push the crate across the floor.