Question

The top view of a table, with weight Wt, is shown in the figure. (Figure 1) The table has lost the leg at (Lx, Ly), 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 Wv at ( X, Y). Denote the magnitudes of the upward forces on the table due to the legs at (0, 0), (Lx, 0), and (0, Ly) as F0, Fx, and Fy, respectively.

Find Fx, the magnitude of the upward force on the table due to the leg at (Lx, 0).

Find Fy, the magnitude of the upward force on the table due to the leg at (0, Ly).

Find F0, the magnitude of the upward force on the table due to the leg at (0, 0). While the host is greeting the guests, the cat (of weight Wc) gets on the table and walks until her position is (x,y)=(Lx,Ly).

Find the maximum weight Wmax of the cat such that the table does not tip over and break the vase.

Answer 1