Question $2[17$ marks$]$

A slotted arm revolves in the horizontal plane around the fixed vertical axis at O $($i$.$e$."$up$"$ is

out of the page$).$ The $5$ kg slider is drawn toward O along the slot by a motor pulling the cord

S $.$ The slider is accelerating along the slot at a rate of $1\frac{m}{s^2}.$ The coefficient of friction

between the slot and slider is ${}_k=0\mathrm{.}3.$ The motor has an efficiency of $60\%.$ At the instant

for which $r=500mm$ and $r^{}=50m\frac{m}{s},$ the arm is at angle of $15$ to the horizontal, has a

counterclockwise angular velocity $=6ra\frac{d}{s},$ and is slowing down at the rate of

$2\mathrm{.}5ra\frac{d}{s^2}.$ At this instant, determine:

$($a$)$ The normal force exerted on the slider by the sides of the smooth radial slot,

$($b$)$ The tension in the cord; and

$($c$)$ The power supplied to the motor

$.$please answer all the questions and give me clarity on whether the friction is $2$f or just f