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Unformatted text preview: PHY 132 Midterm Exam NAME: Tuesday, February 5, 2008 Directions: You have 75 minutes. Support your answers. Correct answers
with no or unsatisfactory explanation, or supporting calculations (whatever is
applicable) will not receive any credit. You are allowed to use one page (front
and back) formula sheet, and a calculator. Solve the questions on the same
page. If necessary, you can use the back of the page as well. 0.1 Pressure in a ﬂuid at rest expression P = P0 + pgh (l)
0.2 Bernoulli Eqn P + pgh + gm}2 = constant (2) 0.3 Mass—spring system with no friction
dga: cit2
Where w = (I i, and $(t) 2 mm” sin(wt + ¢) Mg (4) 0.5 Wavelength and frequency
v = A f (5) 1)=\/T/# (5) +w211: = 0 (3) 0.4 Simple pendulum 1 Water level and weight[15 pts] Two cups are ﬁlled to the same level with water. One of the two cups has plastic balls ﬂoating in it. If the density of the plastic balls is less than that of
ice, which of the two cups weighs more? > Figure 1: , 2 An irrigation system [15 pts] Water ﬂows through the pipes shown in the ﬁgure. The water’s speed through the lower pipe is 5.0 m/ S and a pressure gauge reads 75 kPa. What is the reading : ” j}
of the pressure gauge on the upper pipe? (1 Pa=1 N/m2) «/ [ OQQ L6 /W\
Prim/k“ 3 A person swings on a swing [15 pts] A person swings on a swing. When the person sits still, the swing oscillates
back and forth at its natural frequency. (a) If, instead, two people sit on the swing, how does the natural frequency
change? (b) If, instead, the person stands on the swing, how does the natural fre—
quency change? ((3) If someone on the ground pushes the person on the swing at almost the same frequency with the natural frequency, what do you expect to observe?
Explain. 4 Measuring mass on the Moon [20 pts] You have been asked to evaluate the design for a simple device to measure the
mass of small rocks on the Moon. The rock is attached to the free end of a
lightweight spring which is horizontal. The surface on Which the rock slides is
almost frictionless. You are worried that the kinetic energy of the rock may
make this device dangerous in some situations. The device speciﬁcations state
that a 150 gram rock will execute harmonic motion, with a frequency of 0.32 Hz, described by 11:05) 2 Asin(bt — 35°) When the rock has an initial speed of
1.2 cm/s. What is the max kinetic energy of the mass? —> Fixed end Figure 2: . 5 Pulses moving on strings [20 pts] A pulse is moving to the right on a long thin Wire. (The left end of the wire is
not shown, which extends at least 50 meters to the left of 55:0) Another thick
wire, ﬁxed at the right end, is attached to the thin wire. The diameter of the
thick wire is 2.2 times that of the thin one. Both wires are made of the same
material. We know that the pulse reaches the junction of the two wires in 1.50 r
seconds. QM rﬁ QULTFEJW‘S‘
(a) What will be the speed of the pulse on the thick wire?(pm3~ W/g) ()0 e (b) Pulse is at X20 at t=0. Draw the pulses (main and reﬂected) at t=4.00
E‘seconds. Indicate the direction of motion for each pulse. 6 Mathematical description of a wave[15 pts] A traveling wave moving along a string is described by y(m, t) 2 (1.OO><10—2 cos(1.20m+
10.5t). All quantities are given in SI units. (a) What is the wavelength of the wave? (b) What is the frequency of the wave? (c) What is the speed of the wave? (d) What direction is the wave moving?
) (e Draw the the snapshot of the wave at t=1.00 second. (Plot y(x,l.00) vs
X) (A) break/icy (lax +59 2U . a '
k” if :11 (Z //" /'O A Figure 3: . 7 Force on a dam[Emtra Credit: 20 pts] As the reservoir behind a dam is ﬁlled with water, the pressure that the water
exerts on the darn increases. Eventually, the force on the dam becomes sub
stantial, and it could cause the dam to collapse. To study this phenomenon,
consider the simple model of a dam depicted in the diagram. View the ﬁgure:
the reservoir of water (density p) behind the dam is ﬁlled to a height h. Assume
that the width of the dam (the dimension pointing into the screen) is L. (a) Consider a horizontal layer of the dam wall of thickness dx located a distance it above the reservoir ﬂoor. What is the magnitude dF of the force on.) 7:, r .. I this layer due to the water in the reservoir? _
(b) The force of the water produces a torque on the dam. In a simple model,
if the torque due to the water were enough to cause the dam to break free
from its foundation, the dam would pivot about its base (point P). What is the ’
magnitude ’7' of the torque about the point P due to the water in the reservoir? dz: JFK ...
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 Fall '07
 Rainey
 Physics, Energy, Frequency, Wavelength, Dam

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