SHM, Waves, Thermo, E&M Practice Problem Workbook

MECHANICS PRACTICE PROBLEM SETS 10
3. A mass-less spring with spring constant k = 10.0 N/m is attached to an object of mass
m = 0.300 kg. One third of the spring is cut off. What is the frequency of the
oscillations when the "new" spring-mass is set into motion Answer: f = 0.92 Hz
4. Figure 6 below is a plot of the potential energy of a mass-spring system. The total
mechanical energy E T of the system = 0.200 J. Find (a) the potential energy PE and
(b) the kinetic energy KE at x = 0.025 m. Find (c) the spring constant k and (d) the
speed of the particle when x = 0.025 given that the mass of the object m = 0.30 kg.
Find (e) the amplitude of the motion and (f) the maximum velocity of the object.
Answer: PE = 0.050 J, KE = 0.15 J, k = 160 N/m, v = 1 m/s, x m = 0.0500 m, v max = 1.15 m/s
5. The motion of a particle is given by x(t) = 4.0 cm cos(πt - π/6). Find the particle’s
velocity when x = 2.0 cm.
Answer: v = 10.9 cm/s
6. A wave travels along a stretched rope. The wavelength is 2.0 m. The wave period is
0.1 s. What is the speed of this wave Answer: 20 m/s
7. A wave has a frequency of 58 Hz and a speed of 31 m/s. What is the wavelength of
this wave
Answer: 0.53 m
8. A clothesline with a mass of 0.750 kg is 3.00 meters long. How much tension do you
have to apply to produce the observed a wave speed of 12.0 m/s Answer: 36 N
9. Determine the wavelength of a 6000-Hz sound wave traveling along an iron rod.
Answer: 0.60 m
10. A sound wave produced by a clock chime is heard 501 meters away, 1.50 sec later.
a. What is the temperature of the air through which the sound travels
Answer: T = 5°C
b. How long would it take this sound to travel 501 meters away in freshwater
Answer: t = 0.35 s
11. If you clap your hands and hear the echo from a distant wall 0.20 seconds later, how
far away is the wall
Answer: d = 34.3 m
Gamzon & Gregorian-Michaelsen 6/13/12