Download Final Exam from spring 2002

Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
This 200-point exam consists of 9 questions, some with several parts each. If you cannot do one
part, move on to the next. Partial credit will be given on all parts of this exam.
This is a closed book exam. You will need a calculator. Please remember to write your name on
every page. Remember to convert to meters and kilograms.
To receive full credit, you must show all of your work or reasoning. At times, you may need to
explain your reasoning in words. When grading I look for quality thinking more than right
answers so do take the time to reason carefully. Please ask if the wording of a question is not
clear to you.
1
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
This page has several unrelated questions. Reasoning is important but you may be brief—just
convince me you did not guess.
1) [10 points] Five particles with identical charges and masses are
held, equally spaced, in the arrangement shown.
1
2
3
4
5
a) [5 points] Which one (if released from rest) will have the greatest velocity when far
away? Explain your reasoning.
b) [5 points] Which one (if released from rest) will have the smallest velocity when far
away? Explain your reasoning.
2) [10 points total] Four charges are arranged at the corners of a square, with
two positive and two negative, as shown. All are of the same magnitude.
a) [5 points] Draw an arrow showing the direction of the E-field at the
center of the square. Explain your reasoning.
+q
+q
X
-q
-q
b) [5 points] Is the potential difference from infinity to the X, V,X, a positive number,
negative number, or zero? Explain your reasoning.
3) [10 points total] A resistor (R2) is added to the circuit as
shown. R2 has much larger resistance than R1.
R1
R1
a) [5 points] Is the equivalent resistance of the new circuit
less than R1, between R1and R2, or greater that R2? Explain your reasoning.
b) [5 points] If the current through the battery in the first circuit is 2A and R2 is four times
as large as R1, what is the current through the battery after R2 is added? Show your
reasoning.
2
R2
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
4) [30 points total] A 0.5m conducting rod with mass 2kg is
pulled along frictionless conducting rails by a rope hung
over a pulley. A 4kg mass is attached to the rope and a
10 resistor connects the rails and a uniform B-field
points up. The rod (and mass) move at constant speed.
a) [5 points] Which direction, left to right, or right to
left, does current flow through the resistor? Explain
your reasoning.
Rod
velocity
B field
points up
b) [10 points] If a current of 5A flows through the resistor, what is the velocity of the rod?
Show your reasoning.
c) [5 points] What is the power dissipated by the resistor? Show your reasoning.
d) [10 points] If the B field were to double, what would the constant velocity of the rod be?
Show your reasoning.
3
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
5) [30 points total] Two lenses are positioned as shown. The first lens focal length is f = 8cm.
The second is f = 16cm. 16cm separate the lenses. The object is 24cm left of the first lens.
a) [10 points] Locate the image (size and position) created by the first lens with a ray
diagram and verify its location and size with math. Show your work and at least two
rays. Each square is 1 cm. A dot or X on the lens helps to keep the focal points straight.
math:
b) [5 points] Is this first image virtual or real? Explain.
c) [10 points] Locate the final image (size and position) with a ray diagram. Verify its
location and size with math. Show your work and at least two rays. A new grid is
provided below.
math:
d) [5 points] Is the final image virtual or real? Explain.
4
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
6) [30 points total] Two radio towers, emitting the same
frequency of 500kHz, are positioned as shown. Observer 1
is the same distance from each speaker and observer 2 is
150m to the right. The velocity of the waves is 3x108m/s.
a) [10 points] Observer 1 has bad reception. Where
should she move to improve her reception? Directly
between the towers or to the side? Explain your reasoning.
towers
300m
150m
2
1
b) [10 points] If 300m separate the towers. How is the reception for observer two? Show
your reasoning.
c) [10 points] Now assume the towers are in phase regardless of your previous answers.
How far apart should they be so that observer 2 hears sound? Show your reasoning.
5
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
7) [20 points total] Draw the reflected and transmitted pulse for each situation shown below.
The left side is the heavy end and has the slower velocity. Locate the reflected pulse directly
beneath the initial (incoming) pulse, then locate and draw the transmitted pulse.
a) [10 points]
v = 4 sq/s
v = 8 sq/s
b) [10 points]
v = 8 sq/s
v = 4 sq/s
8) [15 points total] Trace the ray through the materials. It may
refract or reflect as it comes to a boundary. Find the angles
of incidence and refraction/reflection.
n=1.6
n=1.2
n=1 (Air surrounds
materials on all sides.)
20
6
Final Exam
May 8, 2002
Physics 212 Spring 2002
Name________________________
9) [45 points total] The questions below all refer to the
resistor-capacitor circuit at right. The circuit is in a
steady state.
a) [5 points] Which resistors have current through them
and which do not? Explain.
18V
R1
6
C1
10F
R5
R3
2
R2
2
2
b) [10 points] Find the current through the battery. Show your reasoning.
c) [10 points] Find the energy stored in C1 and the energy stored in C2. Show your
reasoning.
d) [5 points] Find the charge stored on C1 and the charge stored on C2. Show your
reasoning.
e) [8 points] If the wire is cut just above R4, how will the charge on C1 and C2 change?
Explain your reasoning. Consider a steady state after any changes are over.
f)
[7 points] If the wire is cut just above R2, how will the charge on C1 and C2 change?
Explain your reasoning. Consider a steady state after any changes are over.
7
C2
30F
R4
2