The top view of a table, with weight W_(t), is shown in the figure. (Figure 1) The table has lost the leg at (L_(x),L_(y)), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight W_(v) at (x, y). Denote the magnitudes of the upward forces on the table due to the legs at (0,0), (L_(x),0), and (0,L_(y)) as F_(0), F_(x), and F_(y) respectively.
Find F_(x), the magnitude of the upward force on the table due to the leg at (L_(x),0). Express the force in terms of W_(v), W_(t), x, y, L_(x), and/or L_(y). Note that not all of these quantities may appear in the answer.
Find F_(y), the magnitude of the upward force on the table due to the leg at (0,L_(y)). Express the force in terms of W_(v), W_(t), y, x, L_(y), and/or L_(x). Note that not all of these quantities may appear in the final answer.
Find F_(0), the magnitude of the upward force on the table due to the leg at (0,0). Express the force in terms of W_(v), W_(t), L_(x), L_(y), x, and/or y. Note that not all terms may appear in the answer.
While the host is greeting the guests, the cat (of weight W_(c)) gets on the table and walks until her position is (x,y)=(L_(x),L_(y)). (Figure 2)
Find the maximum weight W_(max) of the cat such that the table does not tip over and break the vase. Express the cat's weight in terms of W_(v), x, y, L_(x), and L_(y).