Problem # $3(10$ Marks$)$:

The slider P $($mass $=5kg)$ can be moved inward by means of the string S $,$ while the slotted arm rotates about point O in the horizontal plane $($effect of gravity is neglected$).$ The angular position of the arm is given by $=0\mathrm{.}8t-\frac{t^2}{20},$ where $$ is in radians and $t$ is in seconds. The radial position is given by $r=1\mathrm{.}6-0\mathrm{.}2t,$ where r is in meters.

When $t=1\mathrm{.}5s,$ determine the tension T in the string S and the magnitude N of the force exerted on the slider P by the sides of the smooth slotted arm. Indicate which side of the slotted arm contacts the slider.