MULTIPLE CHOICE
Directions: For each multiple choice problem, choose the answer
which is MOST CORRECT. CLEARLY place the letter of your choice in
the space provided.
Q1: When the spring constant of a mass-spring system is changed,
which of the following is LEAST
affected?
A) the resonant frequency B) the damping C) the period D) the
potential energy Answer: ____________
Q2: An object floats with exactly 50% of its volume submerged
when placed in salt water, = 1.06 H2O.
When the same object is placed in pure water, what volume is
submerged?
A) Still exactly 50% submerged B) Less than 50% submered C) More
than 50% submerged D) Cannot be determined without mass Answer:
____________
Q3: A mass-spring oscillator is driven with a periodic force F =
Fo cos (wFt). Which of the following
factors does NOT limit affect the maximum possible amplitude of
the resulting oscillation?
A) the closeness of wF to the natural frequency wo B) the spring
constant k C) mechanical failure of the spring D) the damping
constant = b/2m Answer: ____________
Q4: An undamped mass-spring system has a natural frequency o = 3
rad/sec. A small amount of
friction is added to the system, with a damping constant = b/2m
= 1 rad/sec. The new oscillation frequency will
A) stay the same, but the oscillation amplitude now decays
towards zero B) increase to 4 rad/sec C) slightly increase to 3.2
rad/sec D) slightly decrease to 2.8 rad/sec E) decrease to 2
rad/sec Answer: ____________
The format of the Midterm and Final Exams will be exactly the
same as the discussion quizzes you have had. For each problem, you
will be given a full page for your work.
PROBLEM A: (25 points)A pulse travels from one end to the other
of a long, horizontal string in 0.1 sec. The tension in the string
is provided by passing the string over a pulley to a weight which
has 100 times the mass of the string.
FIND: What is the length L of the string?
PROBLEM B: (25 points)Professor Collins just barely floats into
the sky when tied to 100 large Helium balloons. How many balloons
of the same size would be required if they were filled with Neon
instead of Helium? Take air = 1.3 kg/m3, He = 0.2 kg/m3, Ne = 0.9
kg/m3. (You may assume that Prof. Collins volume is much, much
smaller than the balloons. His mass does not matter, but is
probably close to 70 kg.)
FIND: How many Neon balloons will lift Prof. Collins?
PROBLEM C: (25 points)A pendulum with m = 1.0 kg hangs from the
end of a massless string having L = 1.0 m. Immediately to the left
of its equilibrium point is a spring with spring constant k = 120
N/m. The mass is lifted to an angle = 30o as shown, and then
released at t = 0. The pendulum falls down, compresses the spring,
and bounces back up to its starting point in a periodic motion.
(You may assume that the compression of the spring is approximately
linear along x.)
b) FIND: What is the period T of the oscillation? ( Hint: if
stuck, maybe begin with a sketch of vs time ) Multiple Choice
Solutions: B, C, B, D