Chapter 11
Conceptual Questions
3. In any periodic motion, unavoidable friction always causes the amplitude to decrease with
time. Does friction also affect the period of the motion? Give a qualitative argument to support
your answer. (Hint: Does the friction affect the kinetic energy? If so, how does this affect the
speed, and therefore the period, of a cycle?)
5. A pendulum is mounted in an elevator that moves upward with constant acceleration. Is the
period greater than, less than, or the same as when the elevator is at rest? Why?
6. At what point in the motion of a simple pendulum is (a) the tension in the string greatest, (b)
the string tension least, (c) the radial acceleration greatest, (d) the angular acceleration least, (e)
the speed greatest?
7. Looking at the molecular structure of matter, discuss why gases are generally more
compressible than liquids and solids.
11. Distinguish clearly between the angular frequency (ω) and I the angular velocity (also ω) of
a pendulum. Which of the two quantities is constant?
14. Would you expect a rubber band to have a larger or a smaller force constant than that of an
iron wire? Why? How would yol think that Young's modulus for these two materials would
compare?
Problems
10. •• Human hair. According to one set of measurements, the tensile strength of hair is 196
MPa, which produces a maximum strain of 0.40 in the hair. The thickness of hair varies
considerably, but let's use a diameter of 50 µm. (a) What is the magnitude of the force giving this
tensile stress? (b) If the length of a strand of the hair is 12 cm at its breaking point, what was its
unstressed length?
14. • Effect of diving on blood. It is reasonable to assume that the bulk modulus of blood is
about the same as that of water (2.2 GPa). As one goes deeper and deeper in the ocean, the pressure increases by 1.0 X 104 Pa for every meter below the surface, (a) If a diver goes down 33 m
(a bit over 100 ft) in the ocean, by how much does each cubic centimeter of her blood change in
volume? (b) How deep must a diver go so that each drop of blood compresses to half its volume
at the surface? Is the ocean deep enough to have this effect on the diver?
21. •• A steel cable with cross-sectional area of 3.00 cm2 has an elastic limit of 2.40 X 10s Pa.
Find the maximum upward acceleration that can be given to a 1200 kg elevator supported by the
cable if the stress is not to exceed one-third of the elastic limit.
26 • The graph shown in Figure 11.36 closely approximates the displacement x of a tuning fork
as a function of time t as it is playing a single note. What are (a) the amplitude, (b) period , (c)
frequency, and (d) angular frequency of this fork's motion?
33. •• A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is
this mass from the equilibrium position of the spring when the elastic potential energy equals the
kinetic energy?
34. •• (a) If a vibrating system has total energy Ea, what will its total energy be (in terms of £0) if
you double the amplitude of vibration? (b) If you want to triple the total energy of a vibrating
system with amplitude A0, what should its new amplitude be (in terms of A0)?
41. •• A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure
11.39 shows a graph of its velocity vx as a function of tune t. Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion, (d) What is the amplitude (in cm), and at
what times does the mass reach this position? (e) Find the maximum acceleration of the mass and
the times at which it occurs, (f) What is the mass m?
48. •• In the laboratory, a student studies a pendulum by graphing ] the angle 9 that the string
makes with the vertical as a function 1 of time t, obtaining the graph shown in Figure 11.40. (a)
What j are the period, frequency, angular frequency, and amplitude of j the pendulum's motion?
(b) How long is the pendulum? (c) Is j it possible to determine the mass of the bob?