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A force in the xy plane is given by \vec{F}=\frac{F_{o}}{r}(y\hat{i}-x\hat{j}) where F^{_{o}} is a constant and r=\sqrt{x^2+y^2}.

a.) Find the magnitude of the force.

b.)Show that \vec{F} is perpendicular to \vec{r}=x\hat{i}+y\hat{j}

c.) Find the work done by this force on a particle that moves once around a circle of radius 5 m centered at the origin.

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Answer #1

a) |F| = (Fo/r)*sqrt(y^2+x^2)

= (Fo/sqrt(x^2+y^2)*sqrt(y^2+x^2)

= Fo

b)

F.r = (Fo/r)*(yi - xi).(xi+yj)

F*r*cos(theta) = (Fo/r)*(y*x - x*y)

F*r*cos(theta) = 0

==> theta = 90

so F and r are perpendicular to each other

c) W = 0

because dispalcement is zero.

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