Forces on a hinged board used as a lever

AI Thread Summary
A 3 m hinged board with a mass of 4.5 kg is used to lift a 75 kg block positioned 80 cm from the hinge by applying a vertical force F at the opposite end. To solve the problem, the force exerted by the hinge needs to be calculated in components, as well as the magnitude of force F when applied perpendicular to the board at a 30° angle. The discussion emphasizes the importance of demonstrating one's own efforts before seeking assistance. The calculations involve understanding the forces acting on the board and the block, including gravitational forces and torque. Accurate results depend on applying principles of static equilibrium and lever mechanics.
ccitycoop
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I'm having trouble with this one. Any help would be appreciated.

A 3 m board of mass 4.5 kg is hinged at one end. A force F is applied vertically at the other end to lift a 75 kg block, which rests on the board 80 cm from the hinge, as shown in Figure 12-35.

(b) Find the force exerted by the hinge at this angle. (in components)
(c) Find the magnitude of the force F if this force is exerted perpendicular to the board when = 30°.
(d) Find the force exerted by the hinge in this case (in components)
 
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