A symmetric building has a roof sloping upward at [tex]36.0^\circ[/tex] above the horizontal on each side.
(a) If each side of the uniform roof weighs [tex]1.10\times10^4[/tex]N, find the horizontal force that this roof exerts at the top of the wall, which tends to push out the walls.
(b) Which type of building would be more in danger of collapsing: one with tall walls or one with short walls? Explain.
(c) As you saw in part (a), tall walls are in danger of collapsing from the weight of the roof. This problem plagued the ancient builders of large structures. A solution used in the great Gothic cathedrals during the 1200s was the flying buttress, a stone support running between the walls and the ground that helped to hold in the walls. A Gothic church has a uniform roof weighing a total of [tex]20000[/tex]N and rising at [tex]40.0^\circ[/tex] above the horizontal at each wall. The walls are [tex]40[/tex]m tall, and a flying buttress meets each wall [tex]10[/tex]m below the base of the roof. What horizontal force must this flying buttress apply to the wall?
The Attempt at a Solution
For part (a), I can't see how any force is being applied in the x-direction, rather than just in the y-direction, caused by the force due to gravity. Once this force is recognized, I can solve for the torque about the base of the walls but I don't see how the force applied isn't parallel to the lever arm.
For part (b), it's given and intuitive that tall walls are more subject to falling due to a longer lever arm and, consequently, a greater net torque, driving the system out of equilibrium.
For part (c), I'd choose the axis of rotation to be about one of the walls with a torque in the positive direction caused by the Flying Buttress and a torque in the negative direction applied by the roof. From there, however, I can't seem to see this system in its true, physical light.