Respuesta :
Answer:
58.27 N
Explanation:
the data we have is:
mass: [tex]m=22kg[/tex]
coefficient of friction: [tex]\mu =0.27[/tex]
and we also know the acceleration of gravity is [tex]g=9.81m/s^2[/tex]
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:
- Normal force [tex]N[/tex] (acting up from the object)
- weight: [tex]w=mg[/tex] (acting down from)
so the sum of forces in the vertical axis "y" are:
[tex]F_{y}=N-w\\F_{y}=N-mg[/tex]
from Newton's second Law we know that [tex]F=ma[/tex], so:
[tex]ma_{y}=N-mg[/tex]
and since the object is not accelerating in the vertical direction (the movement is only horizontal) [tex]a_{y}=0[/tex], and:
[tex]0=N-mg\\N=mg[/tex]
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now let's analyze the horizontal forces
- frictional force: [tex]f= \mu N[/tex] and since [tex]N=mg[/tex] --> [tex]f=\mu mg[/tex]
- force to move the object: [tex]F[/tex]
and the two forces just mentioned must be opposite, thus the sum of forces in the "x" axis is:
[tex]F=ma_{x}=F-f\\ma_{x}=F-\mu mg[/tex]
and we are told that the crate moves at a steady speed, thus there is no acceleration: [tex]a_{x}=0[/tex]
and we get:
[tex]0=F-\mu mg\\F=\mu mg[/tex]
substituting known values:
[tex]F=(0.27)(22kg)(9.81m/s^2)\\F=58.27N[/tex]
