The slider of mass m moves with negligible friction on a cir

The slider of mass m moves with negligible friction on a circular wire of radius R that lies in the vertical plane. The constant horizontal force Facts on the slider. If the slider starts from rest at A, determine the expression for the smallest F that would enable it to reach B

Solution

From point A to B:

displacement, d = R*sqrt(2)*(cos45 i + sin 45 j)

Now, force, F = F i

So, the work done by force, W = F.d

= F*R*sqrt(2)*cos(45deg)

= FR

Now, this amount of work done must be done agaist gravity

Work done by gravity , Wg = mg*R

So, Work energy principle,

F*R = mgR

So, F = mg <--------answer