Chapter 11, Problem 11.86P

DATA You are to use a long, thin wire to build a pendulum in a science museum. The wire has an unstretched length of 22.0 m and a circular cross section of diameter 0.860 mm; it is made of an alloy that has a large breaking stress. One end of the wire will be attached to the ceiling, and a 9.50-kg metal sphere will be attached to the other end. As the pendulum swings back and forth, the wire’s maximum angular displacement from the vertical will be 36.0°. You must determine the maximum amount the wire will stretch during this motion. So, before you attach the metal sphere, you suspend a test mass (mass m) from the wire’s lower end. You then measure the increase in length Δl of the wire for several different test masses. Figure P11.86, a graph of Δl versus m, shows the results and the straight line that gives the best fit to the data. The equation for this line is Δl = (0.422 mm/kg)m. (a) Assume that g = 9.80 m/s², and use Fig. P11.86 to calculate Young’s modulus Y for this wire, (b) You remove the test masses, attach the 9.50-kg sphere, and release the sphere from rest, with the wire displaced by 36.0°. Calculate the amount the wire will stretch as it swings through the vertical. Ignore air resistance.