A simple pendulum consists of a small bob of mass 0.20kg suspended by a light, inextensible string of length 0.80m. The bob is pulled sideways until the string makes an angle of 25∘ with the vertical and is then released from rest. As it swings toward the lowest point, the bob experiences a resistive force from air of nearly constant magnitude Fd=0.040N that acts opposite its direction of motion along the arc.
Assume the change in height of the bob is small enough that the gravitational field can be treated as uniform.
(a) Treat the bob as the only object in the system and neglect air resistance. Calculate the speed of the bob as it passes through the lowest point.
(b) Still treating the bob as the only object in the system, take into account the average resistive force Fd. The length of the arc between release and the lowest point is s=Lθ with θ in radians. Determine the bob’s speed at the lowest point now that the resistive force acts.
(c) A student suggests redefining the system to include both the bob and the surrounding air through which it moves. For this new system, describe qualitatively how energy is accounted for, and explain whether mechanical energy is conserved within the system.
(d) Using your result from part (b), compute the percentage difference between the speed with resistance and the ideal speed found in part (a).