A lightweight, rigid beam 10.0 m long is supported by a cable attached to a spring of force constant k = 8.25 kN/m as shown in Figure P12.38. When no load is hung on the beam (Fg = 0), the length L is equal to 5.00 m.
(a) Find the angle θ in this situation.
(b) Now a load of Fg = 250 N is hung on the end of the beam. Temporarily ignore the extension of the spring and the change in the angle θ. Calculate the tension in the cable with this approximation.
(c) Use the answer to part (b) to calculate the spring elongation and a new value for the angle θ.
(d) With the value of from part (c), find a second approximation for the tension in the cable. (e) Use the answer to part (d) to calculate more precise values for the spring elongation and the angle θ.
(f) To three-digit precision, what is the actual value of θ under load?

L. 4.00 m 3.00 7.00 m Figure P12.38