$3\mathrm{.}2\mathrm{.}5.[$Level $2]$ A ball of mass $m=2kg$ is attached to

a fixed point $O$ by an elastic cord and is constrained to ro$-$

tate about $O$ in the horizontal plane under the action of

an applied force $F$ that varies with time. Let $r$ denote the

length of cord between $O$ and the mass, and take $$ to be the

angle that the cord makes with the horizontal. At a particu$-$

lar instant, $r=0\mathrm{.}9m,=50,r^{}=1\mathrm{.}2\frac{m}{s},{}^{}=6ra\frac{d}{s},r^{}=0,$

${}^{}=1ra\frac{d}{s^2},$ and $F$ acts on the ball in the negative i direction. If the

surface on which the ball moves has a coefficient of friction

of $=0\mathrm{.}7,$ find the instantaneous value of the applied force

$F$ and the tension $T$ in the cord.

E$3.2\mathrm{.}5$