The expression for the work allows to find the result for the work done by the friction force is:
[tex]W_{total}[/tex] = - 11,178 J
Work is defined by the scalar product of force and displacement.
W = F. d
Where bold indicates vectors, W is work, F is force, and d is displacement.
We can develop the scalar product, remaining
W = F d cos θ
where θ is the angle between the force and the displacement.
The friction force is the macroscopic sum of the interaction between the molecules of the two surfaces and always opposes the movement, it can be represented for solid bodies by the equation.
fr = μ N
.
Where fr is the friction force, μ is the friction coefficient and N is the normal.
Indicate that the normal force is 1.8 N, the displacement is 0.15 m and the coefficient of friction is 0.92.
As the friction opposes the movement, it has an angle of 180º with respect to the displacement, see attached.
We substitute.
W = μ N d cos 180
W = - 0.92 1.8 0.15
W = -0.2484 J
Each time the sandpaper passes, it performs this work, at 45 times the total work is
[tex]W_{total}[/tex] = n W
[tex]W_{total}[/tex] = 45 (-0.2484)
[tex]W_{total}[/tex] = -11,178 J
In conclusion using the expression for work we can find the work of the friction force is:
[tex]W_{total}[/tex] = - 11,178 J
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