Physics 221: Final Exam, Spring-il
Name:
Section. No:
1. (12 pts) The object is midway between the lens and the mirror which are separated by a distance of
25M cm. The mirror’s radius of curvature is 20 cm, and the lens has a focal length of 167 cm.
Considering only the light that leaves the object and travels first towards the mirror:
a) locate the final image formed by this system
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c) is it upright or inverted?
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d) what is the overall magnification?
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2. (1 0 pts) In a Young’s interference experiment, the two slits are separated by 0.1 50 mm and
the
incident light includes two wavelengths: 2L 540 nni (green) and X
2 450 nm (blue). The overlapping
interference patterns are observed on a screen 1.40 m from the slits. Calculate the minim
um distance
from the center of the screen to a point where a bright fringe of the green light coincides with
the bright
fringe of the blue light.
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3.( 10 pts) Two polarizers are oriented at 480 to each other and plane polarized light is incident upon
them. If only 25% of the light gets through both of them, what was the initial polarization direction of
the incident light?
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4. (10 pts) A pendulum of length L and mass M has a spring of force constant k connected to it a distance
H
below the point of suspension. Find the frequency of vibration of the system for small values of
0. Assume the
vertical suspension rod of length L is rigid, but ignore its mass. Express your answer in terms of
L, k, H, and g.
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5. (12 pts) A block of mass 0.450 kg is attached to one end of a cord of mass 0.00320 kg; the other end of the
cord is attached to a tixed point. The block rotates with constant angular speed in a circle on a horizontal
frictionless table. Through what angle does the block rotate in the time interval during which the transverse
wave travels along the string from the center to the block?
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6. (10 pts) Two ships are moving along a line due east. The trailing vessel has a speed relative to a land based
obseration pomt of 64 0 km/h and thL leading ship has a speed of 45 0 krn!h relative to that point The trailing
ship tiansmits a sonai signal at a hequn of 1200 Hz ‘hat frequen is monitored h thc leading ship’ USL
1 520 rn/s as the speed of sound in ocean water,
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7. (12 pts) The wooden bar on a marimba which sounds the tone when struck vibrates in a transverse
standing wave having three antinodes and two nodes. The lowest frequency note is 87.0 Hz, produced
by a bar 40.0 cm long.
a) What is the speed of transverse waves on the bar?
b) A resonant pipe suspended vertically below the center of the bar enhances the loudness of the emitted
sound. If the pipe is open at the top end only and the speed of sound in air is 340 mIs, what is the length
of the pipe required to resonate with the bar in part a)?
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8. (12 pts) A cylinder containing n moles of an ideal gas undergoes an adiabatic process going from a
state pj, V) to a final state (pr, V.
a)Using the condition pV = const. Compute the work done by the system for this process and express
your answer in terms ofy. pi. V
1 pi, V. \
b) Starting with the 1 law of thermodynamics compute the work in terms of n, Cv, T
, and T.
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c) Show that these two expressions are equivalent to one another.
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9. (12 pts) A system consisting of n moles of an ideal gas undergoes two reversible proces
ses. It starts
with pressure P
. and volume V
1
1 , and expands isothermally, and then contracts adiabatically to reach a
final state with pressure P and volume 3V
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a) First compute the entropy change in going from a to c along the isobar assuming you are given Cp
recalling that dQ nCpdT. Express your answer in terms of n and
b) What is the entropy change for process bc?
c) What is the entropy change for the isothermal process ab using the results already obtained in parts
a)
and b)
Cp.
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