A 0.40kg pendulum bob is attached to a massless string of length 1.2m. The bob is pulled aside until the string makes an angle of 15∘ with the vertical and is then released from rest. Because of air resistance, mechanical energy is not fully conserved during the motion.
After completing one full swing (from initial release, through the lowest point, to the opposite side, and back to the original side), the maximum angle reached on the return is observed to be 13∘. Assume the average drag force is uniform along the path and acts opposite to the instantaneous velocity. Take g=9.8ms−2.
(a) Determine the mechanical energy of the pendulum bob at the instant of release, relative to the lowest point of the swing.
(b) Calculate the mechanical energy of the bob at the end of the first full swing when it reaches the 13∘ angle on the return.
(c) Using your answers to parts (a) and (b), find the total work done by air resistance during the first full swing.
(d) The arc length of one full swing (out and back) is approximately 2ℓθavg, where ℓ is the length of the string and θavg is the average of the two extreme angles expressed in radians. Using this approximation, compute the magnitude of the average drag force exerted on the bob during the swing.