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Physics 1212 Exam #4B (Final) Instructions:

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Physics 1212 Exam #4B (Final) Instructions:
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
Physics 1212
Exam #4B (Final)
Instructions:
This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your
formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet,
except for your name: it must be handed in, signed but clean, with your exam.
There is space after each question to show your work; if you need more space, you may use
the back of the page, or request more paper. Please clearly indicate where your work for
each problem is. Underline or draw a box around your final answer.
The exam consists of six sections. Read all the questions at the start so that you can allocate
your time wisely. Do easy ones first!
You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put away
throughout the exam.
• Do not open the exam until told to begin.
• You have the one entire class period to finish the exam.
• Put your last name on every page of the exam and on the formula sheet.
• You must provide explanations and/or show work legibly to receive full credit for
Sections II and III.
• Make sure that your answers include appropriate units and significant digits. (Note:
For intermediate steps in your calculation, it’s best to carry more significant digits.)
• Fundamental constants and unit prefixes are on the Formula Sheet, last page.
By signing below, you indicate that you understand the instructions for this exam and agree
to abide by them. You also certify that you will personally uphold the university’s standards
of academic honesty for this exam, and will not tolerate any violations of these standards by
others. Unsigned exams will not be graded.
Signature:
UGACard #:
c 2015 University of Georgia. Unauthorized duplication or distribution prohibited.
Copyright Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Section
I
Score
II
/60
Name:
III
/35
/35
IV
/35
V
/35
VI
/10
I: Multiple-Choice Questions (60 points)
For each question below, choose the single best response and write the corresponding
capital letter in the box provided. There is no penalty for guessing the wrong answer.
1. A real object is placed in front of a converging lens, at a distance greater than the focal
length. When the object is moved slightly towards the lens, without crossing the focal
point, in which direction does the image move or change its size?
A.
B.
C.
D.
E.
The image size doesn’t change.
The image moves closer to the lens.
The image (lateral) size shrinks.
The image (lateral) size grows.
Not enough information is given.
2. Two identically shaped solid blocks, S and T , made from two different transparent
materials, are immersed in the same liquid L. A ray of light strikes each block at the
same angle of incidence, as shown. According to the figure below, what is the relative
magnitude of the indices of refraction of the solid blocks, nS and nT , and liquid, nL ?
L
L
S
A.
B.
C.
D.
E.
nT
nS
nL
nS
nT
T
< nS < nL ;
< nL < nT .
< nS < nT ;
< nT < nL ;
< nL < nS ;
c 2015 University of Georgia.
Copyright 2
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
3. Sound waves (including ultrasound) have a speed of wave propagation vAir = 346m/s
in air and vWater = 1497m/s in water. Also, note that sin(13.364o ) = 346/1497 .
A narrow ultrasound beam striking the flat water surface of your swimming pool
A. will undergo total internal reflection if incident from below the water surface
for any angle of incidence greater than 13.364o ;
B. will have an angle of refraction smaller than the angle of incidence if the beam
is incident from below the water surface;
C. will have an angle of refraction greater than the angle of incidence if the beam
is incident from below the water surface.
D. will undergo total internal reflection if incident from below the water surface
with an angle of incidence of 8.5o ;
E. will undergo total internal reflection if incident from above the water surface
with an angle of incidence of 8.5o ;
4. A diffaction grating (in air or vacuum), is illuminated by coherent (laser) light with
wavelength λ and wave oscillation period τ = λ/c. The 2nd order intensity maximum,
to the right of the central intensity maximum M , is located at point Q, as shown in the
figure below. A wave crest A, from slit R, and a wave crest B, from the neighboring
slit S to the right of R, have departed at the same time from their respective slits of
origin. Therefore, at Q,
M
Q
Fig. 2.29
R S
Diffr. Grating
Laser Beam
A.
B.
C.
D.
E.
A
B
B
A
A
and B will arrive at the same time.
will arrive 3 periods before A.
will arrive 2 periods before A.
will arrive 3 periods before B.
will arrive 2 periods before B.
c 2015 University of Georgia.
Copyright 3
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
5. In the figure below, Q1 is a negative and √
Q2 a positve point charge and |Q1 | and |Q2 |
are of comparable magnitude and |Q1 | < 8|Q2 |. The point P and the locations of Q1
and Q2 form the three corners of a square. Which arrow drawn at P could correctly
~ generated by Q1 and Q2 at P ?
represent the electric field vector E
Fig. 2.16
P
(E)
(D)
(B)
(C)
(A)
Q2
Q1
A.
B.
C.
D.
E.
6. A positron is a sub-atomic particle with the same mass, but the opposite charge as an
electron. If an positron is initially placed at a finite distance d from a negative point
charge, Q, the positron must be given a certain minimum initial speed, vmin , in order
to be able to travel away, to a very large (infinite) distance from the point charge Q.
0
What would be the value of this minimum required speed, vmin
, if instead the positron
0
were placed at a distance d = 6d from another negative point charge, Q0 = 10Q?
0
A. vmin
=
0
B. vmin
=
0
C. vmin =
0
D. vmin
=
0
E. vmin
=
√
√ 6 vmin
10
3
v
5 min
3
v
10 min
10
vmin
6
√
√5 vmin
3
c 2015 University of Georgia.
Copyright 4
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
7. In an electric generator, a single, square-shaped metallic wire loop, of 6cm sidelength,
~ at 2400RPM which produces a maximum
is spinning in a uniform magnetic field B
induced electromotoric force (EMF) of 12mV in the loop. What is the maximum
~
induced EMF in a loop of 18cm sidelength, spinning at 600RPM in the same B-field?
A.
B.
C.
D.
E.
27mV
9mV
6.75mV
5.33mV
16mV
8. A very thin circular ring with radius R = 8cm is centered at the coordinate origin
O ≡ (0, 0, 0), as shown below. The ring lies in the x − z-plane with current I1 flowing
around the ring in the direction indicated in panel (B) below.
(A)
(B)
y
Fig. 3.35
z
I2
I2
I1
x
y
y
z
x-y-Plane View
z
x
x
y
y-z-Plane View
An infinitely long straight wire carries a current I2 = π × 30A parallel to the z-axis and
crosses the y-axis at y = +12cm, as also shown in Fig. 3.34. The net magnetic field,
~ generated by I1 and I2 , is zero at the center of the ring. What is the magnitude of
B,
I1 and the direction of I2 ?
A.
B.
C.
D.
E.
I1
I1
I1
I1
I1
= 40A, I2 in +z-direction;
= π × 40A, I2 in −z-direction;
= 20A, I2 in −z-direction;
= 40A, I2 in −z-direction;
= 20A, I2 in +z-direction;
c 2015 University of Georgia.
Copyright 5
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
II: A Candle in the Mirror (35 points)
A burning candle, 16cm tall, is placed 25cm from a spherical mirror which produces an erect
image of the candle, 32cm tall.
It is critically important that you make drawings of the positioning of the various elements
(optical axis, mirror, candle, focal point, mirror’s center, screen), as needed, in each of the
three parts of this problem
(a) What is the mirror’s focal length and what is the radius of the mirror’s spherical
surface? Is this a convergent (=concave) or a divergent (=convex) mirror? Is the
candle’s image virtual or real?
Hint: Find d0 from d and m, then f from d and d0 .
(b) At what distance from the mirror would the candle’s position on the optical axis
coincide with that of its image?
A candle’s flame is always pointing upward. Would
the candle’s image at that location show a flame pointing upward or downward? Is the
image real or vitual?
(c) A projection screen is now placed at some distance from the same mirror and the same
candle is placed somewhere between the mirror and the screen. The mirror projects a
sharp image of the candle onto the screen and this image is inverted and 64cm tall in
absolute height. How far from the mirror is the screen and how far from the screen is
the candle?
Hint: Get d0 and d from m and f .
c 2015 University of Georgia.
Copyright 6
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
Work and Drawing Space for Problem II:
c 2015 University of Georgia.
Copyright 7
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
III: A Capacitor, a Point Charge, and then an Electron (35 points)
A planar capacitor of unknown size, location and orientation, stores unknown charges +QC
and −QC , respectively, on its two opposing parallel capacitor plates. It produces an electric
~ C ≡ [EC,x , EC,y , EC,z ] with components EC,x = −7N/C, EC,y = −10N/C, EC,z = 0, at
field E
an observation point, P ≡ (xP , 0, 0) with xP = −6m, on the x-axis, both P and the origin
O ≡ (0, 0, 0) being enclosed between the two capacitor plates.
A point charge, Qo = −50nC, is now added, placed at the origin, O, and the capacitor
~ = [Ex , Ey , Ez ].
and the point charge combined, then jointly produce a net electric field, E
~ C , produced by the capacitor in the presence of Qo is the
Assume that the elecric field, E
same as in the absence of Qo .
~ at P ; its strength, |E|;
~ and its angle, θ, measured from
(a) Calculate the components of E
~
the +x-direction, with θ > 0 if E points above the x-axis, else θ < 0.
~ C;
On the blank page attached, make a big drawing showing: x-axis; y-axis; O; P ; E
~ o , produced by Qo at P ; and E,
~ as the resultant in a vector
the field contribution E
addition parallelogram, all field vectors with their tail ends attached to P .
(b) Assume each capacitor plate has an area of A = 8000m2 and the space between the two
plates is vacuum. What is the absolute amount of charge, |QC |, stored on either plate?
(c) Now the capacitor is removed and an electron is placed, at rest, at point P and then released, to accelerate subject to the electric field produced by Qo . What is the electron’s
speed if it travels infinitely far away from Qo ?
c 2015 University of Georgia.
Copyright 8
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
Work and Drawing Space for Problem III:
c 2015 University of Georgia.
Copyright 9
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
IV: Circuit Analysis (35 points) In the circuit shown below, assume that I1 = 6A,
I4 = 3A, R1 = 2Ω, R2 = 8Ω, R3 = 4Ω, RC = 5Ω, and C = 60 µF. Also assume that the
capacitor is fully charged, by the voltage drop
across it, and there is no current flowing to
Fig. 3.65
or from either capacitor plate.
a
I1
p
E
R2
R1
C
IC
x
e
R3
RC
b
(a) Find the current, IC .
y
f
I4
R4
q
Hint: Use a junction (node).
(b) Find the battery voltage E and the resistance R4 .
another loop to find R4 .
Hint: Use a loop to find E, then
(c) Find the absolute value, |Q|, of the charge stored on either plate of the capacitor C.
c 2015 University of Georgia.
Copyright 10
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
Work Space for Problem IV:
c 2015 University of Georgia.
Copyright 11
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
V: Flux and Induced Current in a Loop (35 points) The infinitely long
straight wire in the x-y-plane, shown below at d = 16cm from the x-axis, carries a constant
~ at the origin, O ≡ (0, 0, 0), with a
current, I. This currrent produces a magnetic field, B,
strength of 1.5mT, pointing in the (+z)-direction. A narrow rectangular wire loop in the
x-y-plane, with sidelengths a = 32cm and b = 0.5cm, is centered at the origin O ≡ (0, 0, 0).
a
y
Fig. 4.18
Loop
b
d
y
x
I
z
x
Straight Wire
(a) Find the current, I, flowing in the straight wire. Is this current flowing in the (+x)or in the (−x)-direction?
~
(b) Calculate the magnetic flux, Φm , through the loop, with the loop’s area vector, A,
defined to point into the plane of the drawing above. Use the given magnetic field
~ at the center of the loop and assume B
~ is approximately uniform across the
vector, B,
loop area.
(c) Suppose the loop is now made to ”spin”, i.e., rotate, around the x-axis, at an angular
speed of ω = 1800radians/s. Find the maximum current value, Imax (≡ current ampli~ assuming
tude), of the oscillating current induced in the loop by the magnetic field, B,
~ is approximately uniform
the loop wire has a resistance of 0.3Ω and, again, that B
across the loop area.
Hint: Think of the loop as a coil of 1 turn in an electrical
generator.
c 2015 University of Georgia.
Copyright 12
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
Work and Drawing Space for Problem V:
c 2015 University of Georgia.
Copyright 13
Physics 1212 Exam #4B (Final)
Tue., 5 May 2015
Name:
VI: Draw a Ray Diagram (Extra Credit: 10 points)
A real object is positioned to the left of a convergent mirror, at a distance from the
mirror which is greater than twice the absolute value of the mirror’s focal length. Use a
ruler to draw a clean ray diagram for the formation of the image, showing at least two of the
principal rays, the mirror and its focal point, the object and the image, all of them clearly
labeled. Also clearly label the incoming and the outgoing side of the mirror. Is the image
real or virtual?
Warning: If you use the C-ray as one of the principal rays, be aware that it does not pass
straight through the mirror, but rather gets reflected at the mirror, subject to the law of
reflection: angle of incidence = angle of reflection, with the optical axis being the normal to
the mirror surface.
c 2015 University of Georgia.
Copyright 14
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