If the coefficient of kinetic friction between a 22 kg kg crate and the floor is 0.27, what horizontal force is required to move the crate at a steady speed across the floor

58.27 N

Explanation:

the data we have is:

mass:

coefficient of friction:

and we also know the acceleration of gravity is

We need to do an analysis of horizontal and vertical forces acting on the object:

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Vertically the forces acting on the object:

so the sum of forces in the vertical axis "y" are:

from Newton's second Law we know that , so:

and since the object is not accelerating in the vertical direction (the movement is only horizontal) , and:

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now let's analyze the horizontal forces

and the two forces just mentioned must be opposite, thus the sum of forces in the "x" axis is:

and we are told that the crate moves at a steady speed, thus there is no acceleration:

and we get:

substituting known values:

grav potential energy