A bridge, constructed of 11 beams of equal length L and negligible mass, supports an object of mass M as shown (Figure 1). Real bridges of this sort have steel rockers at the ends, these assure that the support forces on the bridge are vertical even when it expands or contracts thermally.

Throughout this problem, use g for the magnitude of the acceleration due to gravity.

A. Find F_P the vertical force that pier P exerts on the left end of the bridge. Express the vertical force at P in terms of M and g.

B. Find F_Q, the vertical force that pier Q exerts on the right end of the bridge. Express the vertical force at Q in terms of M and g.

C. Assuming that the bridge segments are free to pivot at each intersection point, what is the tension T in the horizontal segment directly above the point where the object is attached? (Figure 2) If you find that the horizontal segment directly above the point where the object is attached is being stretched, indicate this with a positive value for T. If the segment is being compressed, indicate this with a negative value for T. Express the tension in terms of M and g.

Figure 1

\fFo P M