board cables 30° hinge canal Figure 3

An old single-leaf drawbridge is made of a thin rectangular board of mass M, width a(into the page) and length bwhich can pivot at oneend. When it is not in use, the span of the bridge is held at a 60ºangle from the horizontal direction. The two ideal cables that holdit at itsfarther end areanchored to the ground so that they forma 30º angle with the horizontal direction, as shown in Fig. 3.The acceleration due to gravity has magnitude g.

a) Set up all the detailed scalar equations (not the general version)expressing the static equilibrium of the drawbridge.

b) Determine the magnitude T of the tension force exerted by each of the two cables on the board.

c)Determine the magnitude Fh of the hinge force exerted on the board and the angle h that the force forms with respect to the horizontal direction.