To glue a strip of laminate to the edge of a circular table, n clamps are evenly spaced ar...

To glue a strip of laminate to the edge of a circular table, n clamps are evenly spaced around the perimeter of the table (the figure shows n = 8). Each clamp has a small pulley, and around all pulleys a cable is wrapped. A turnbuckle is used to tighten the cable, producing a force T. Assuming the diameter of each pulley is small, show that the force R each clamp applies to the edge of the is given by R = 2T cos[(n - 2)180°/(2n)]. Does this expression give expected values when n = 2 and n = ∞? Explain. Hint: The sum of the interior angles of a polygon with m corners is (m − 2)180°.

Figure P3.77