TA: Tomoyuki Nakayama
April 12 th – April 13th, 2010
PHY 2048: Physics 1 with Calculus, Spring 2010
Review: Chapter 15.1- 16.13
The purpose of this review is to refresh your memory. Physics is a cumulative subject, so make it
sure that you understand basic concepts and typical problem solving techniques in previous chapters
before moving on to a new chapter.
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A. Simple Harmonic Motion
A 2-kg block on an incline is attached to a spring with a spring constant of 100 N/m . The incline is
frictionless and it makes an angle of 45º to the horizontal. The block is pulled down slightly from the
equilibrium point and released. What is the period of the motion?
B. Pendulums
The pendulum shown below right consists of a uniform disk with radius r = 20.0 cm and mass m =
1.2 kg attached to a uniform rod with length L = 40 cm and mass M = 0.8 kg. What is the period of
the motion?
C . Traveling Waves
A sinusoidal transverse wave of wavelength 20 cm travels along a string in +x direction. The
displacement of the string element at x = 0 is given in the figure on the right, where ys = 5 cm.
Assuming the wave function has a form of y(x,t) = ymsin(kx-ωt+φ), find ym, k, ω, φ and the speed of
the wave.
D. Interference & Standing Waves
A nylon string with mass m = 15 g and length D = 60 cm is under a tension of 200 N. Calculate the
speed, wavelength and frequency of traveling wave which produces the standing pattern shown in
the figure.
TA: Tomoyuki Nakayama
April 12th – April 13th, 2010
PHY 2048: Physics 1 with Calculus, Spring 2010
Practice Exam Problems (Chapter 15.1-16.13)
Working on this problem set is optional, but it is strongly recommended. It is highly likely that some
of these problems will appear in the exams. Do it on a weekly basis. Cramming is tiring and
sometimes it ends up in a disaster.
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1. A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2cos(50t)
where x is in meters and t is in seconds. The spring constant of the spring is: (Simple Harmonic
Motion) a. 1 N/ b. 100 N/m c. 150 N/m d. 7500 N/m e. None of the above
2. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. IF the
oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 ms/ then the
amplitude of the oscillation is: (Energy in SHM) a. 0.13 m b. 0.18 m c. 3.7 m d. 5.2 m e. 13
m
3. A simple pendulum has length L and period T. As it passes through its equilibrium position, the
string is suddenly clamped at its midpoint. The period then becomes: (Simple Pendulum) a. 2T b.
T c. T/2 d. T/4 e. none of these
4. The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is
the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L =
1.0 m this rod will have the same period as a simple pendulum of length: (Physical Pendulum) a.
33 cm b. 50 cm c. 67 cm d. 100 cm e. 150 cm
5. The displacement of a string carrying a traveling sinusoidal wave is given by y(x,t)=
ymsin(kx-ωt-φ). At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive
y direction. The phase constant φ is: (Phase Constant) a. 0º b. 45º c. 90º d. 180º e. 270º
6. The diagrams show three identical strings that
have been put under tension by suspending
blocks of 5 kg each. For which is the wave speed
the greatest? (Wave Speed on Strings) a. 1 b.
2 c. 3 d. 1 and 3 tie e. 2 and 3 tie
7. Two separated sources emit sinusoidal traveling waves that have the same wavelength λ and are in
phase at their respective sources. One travels a distance l1 to get to the observation point while the
other travels a distance l2. The amplitude is a minimum at the observation point if l1-l2 is:
(Interference) a. an odd multiple of λ/2 b. an odd multiple of λ/4 c. a multiple of λ d. an odd
multiple of π/2 e. a multiple of π
8. When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100,
150 and 200 Hz. When the string is also cramped at its midpoint, the lowest four resonant
frequencies are: (Resonance) a. 50, 100, 150 and 200 Hz b. 50, 150, 250 and 300 Hz c. 100,
200, 300 and 400 Hz d. 25, 50, 75 and 100 Hz e. 75, 150, 225 and 300 Hz
Answers: 1-d 2-b 3-e 4-c 5-d 6-d 7-a 8-c