EXERCISE $4$

The OAB arm of the crane boom shown in Figure $4$ behaves as a rigid body. The mass of the arm is $320kg$ and the moment of inertia with respect to its center of mass is $I=3680kg-m2.$ If point $O$ is a fixed support and the angular acceleration of the arm with respect to that point, at a given instant, is $0\mathrm{.}6ra\frac{d}{s}2$ counterclockwise, taking into account that the crane starts from rest. Calculate:

$($a$)$ The magnitude of the force exerted by the hydraulic piston BC on the crane arm when it is fully stretched $(1\mathrm{.}25$ pto$).$

b$)$ The magnitude of the reaction forces on the fixed support $0.(1\mathrm{.}25$ pto$)$

Note: Assume as acceleration of gravity $9\mathrm{.}81\frac{m}{s}\mathrm{.}2$