Physics 2020 Summer 2011 Richard Ingebretsen REVIEW FOR ...

Physics 2020 Summer 2011
Richard Ingebretsen
REVIEW FOR MIDTERM 3
1. A In the year 2100, an astronaut wears an antique, but accurate, “quartz” wristwatch on a journey at a
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speed of 2.0 × 10 m/s. According to mission control in Houston, the trip lasts 12 hours. How
long was the trip as measured on the watch?
(a) 6.7 hr (b) 8.9 hr (c) 12.0 hr (d) 16.1 hr (e) 21.6 hr
B. Which one of the following statements concerning the proper length of a meter stick is true?
(a) The proper length is always one meter.
(b) The proper length depends upon the speed of the observer.
(c) The proper length depends upon the acceleration of the observer.
(d) The proper length depends upon the reference frame in which it is measured.
(e) The proper length is the length measured by an observer who is moving with respect to the
meter stick.
C. A UFO flies directly over a football stadium at a speed of 0.50 c. If the proper length of the field
is 100 yards, what field length is measured by the crew of the UFO?
(a) 59 years (b) 75 yards (c) 87 yards (d) 113 yards (e) 121 yards
D. An electron gun inside a computer monitor sends an electron toward the screen at a speed of
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1.20 × 10 m/s. If the mass of the electron is 9.109 × 10 kg, what is the magnitude of its
relativistic momentum?
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(a) 9.88 × 10 kgms
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(d) 1.41 × 10 kgms
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(b) 1.09 × 10 kgms
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(e) 3.25 × 10 kgms
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(c) 1.19 × 10 kgms
E. How much energy is required to accelerate a golf ball of mass 0.046 kg initially at rest to a speed
of 0.75 C?
(a) 1.2 × 10 J
(b) 2.1 × 10 J
15
(c) 6.3 × 10 J
14 16
(d) 3.6 × 10 J
(e) 7.5 × 10 J
15 16
F. Astronomers on earth, an inertial reference frame, observe Galaxies A and B that are moving away
from the Earth as shown. The speeds indicated are those measured by the astronomers on Earth.
What is the speed of Galaxy B as measured by an observer in Galaxy A?
(a) 0.22 c (b) 0.60 c (c) 0.71 c (d) 0.95 c (e) 1.42 c

2. Given the circuit shown. All capacitors fully charged.
(a)
(b)
(c)
(c)
What is the equivalent capacitance of the entire circuit?
How much charge does the battery deliver to the circuit?
What is the voltage drop across the 5.0 F capacitor?
How much energy is stored by the 2.0 F capacitor?
3. Given the circuit shown.
(a) What is the equivalent resistance of the whole circuit?
(b) How much current does the battery provide to the entire
circuit?
(c) What is the total power dissipated by the entire circuit?
(d) Find the current in the 12 resistor.
(e) Find the voltage drop across the 2 resistor.
(f) Find the power dissipated by the 4 resistor.
(g) Explain how a voltmeter would be hooked up to the
circuit to measure the voltage across the 2 resistor.
(h) Explain how an ammeter would be hooked up to the
circuit to measure the current flowing through the 12
resistor.
4. For the circuit shown, both capacitors are initially uncharged and both switches are initially open.
(a)
(b)
(c)
(d)
(e)
Find the time constant for the circuit.
Now, switch A is closed. How much time
elapses until the capacitors collectively
store 35.0 C?
When both capacitors are completely
charged, switch A is opened and switch B
is closed. The capacitors are used to run
a small motor. How much time has
elapsed when the capacitors have lost 40% of their charge? The equivalent resistance of the motor
is 2 ohms.
The motor is used to raise a 2.0 g mass vertically off the floor. How high does the motor raise the
mass? (Assume 100% efficiency of the motor.)
How long does it take the motor to raise the mass to its maximum height?
5. A A Wookiee spacecraft has a speed of 0.70 c with respect to the earth. The Wookiees measure
29.0 h for the time interval between two events on the earth. What value for the time interval
would they measure if their ship had a speed of 0.96 c with respect to the earth?
B. An electric furnace runs nine hours a day to heat a house during January (31 days). The heating
element has a resistance of 5.5 and carries a current of 25 A. The cost of electricity is
$0.10/kWh. Find the cost of running the furnace for the month of January.
C. For a three-way bulb (45 W, 110 W, 155 W) that is designed to operate at 110 V, find the
resistance of each of the two filaments. A three-way bulb uses one filament, the other filament, or
both filaments to produce the necessary light.
D. Quasars are believed to be the nuclei of galaxies in the early stages of their formation. Suppose a
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quasar radiated electromagnetic energy at the rate of 4.20 × 10 W. How much mass does the
quasar lose as a result of this radiation during one hour?

6. A. A light bulb is wired in series with a 130 resistor, and they are connected across a 134.0 V
source. The power delivered to the light bulb is 22.6 W. What are the two possible resistances of
the light bulb?
B. Two cylindrical rods, one copper and the other iron, are identical in lengths and cross-sectional
areas. They are joined, end to end, to form one long rod. A 12 V battery is connected across the
free ends of the copper-iron rod. What is the voltage between the ends of the copper rod?
8
8
= 1.72 × 10 m; = 9.7 × 10 m
copper
iron
C. Three identical capacitors are connected with a resistor in two different ways.
When they are connected as shown in drawing, the time constant to charge up
this circuit is 0.33 s. What is the time constant when they are connected with
the same resistor as in Fig. 2?
7. A. A battery has an internal resistance of 0.5 . A number of identical lightbulbs, each with a
resistance of 12 , are connected in parallel across the battery terminals. The terminal voltage of
the battery is observed to be one-fourth the emf of the battery. How many light bulbs are
connected?.
B. Examine the circuit shown. The power dissipated by the 12
resistor is 192 W.
(a) Calculate the current flowing through the 3 resistor?
(b) What is V?
8. A. A rectangular plate of glass, measured at rest, has sides 30.0 cm and 60.0 cm.
(a) As measured in a reference frame moving parallel to the 60.0 cm edge at a speed of 0.4c
with respect to the glass, what is the area of the glass?
(b) How fast would a reference frame have to move in the same direction so that the plate of
glass viewed in that frame is a square? (Answer in terms of c.)
B. Six identical capacitors are arranged as shown. When fully charged,
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the collection of capacitors store 1.0 × 10 J of energy. The battery
has a voltage of 6 volts.
(a) Find the equivalent capacitance of the circuit.
(b) What is the capacitance of each capacitor?
(c) What is the charge stored on the capacitor nearest to the
positive terminal of the battery?
9. A.
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A spacecraft has a nonrelativistic (or classical) momentum whose magnitude is 2.70 × 10 kgm/s.
The spacecraft moves at such a speed that the pilot measures the proper time interval between two
events to be one-eighth the dilated time interval. Find the relativistic momentum of the spacecraft.
5
B. A resistor is connected across the terminals of a 9.0 V battery, which delivers 1.7 10 J of energy
to the resistor in 5 hours. What is the resistance of the resistor?
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C. Suppose one gallon of gasoline produces 1.1 × 10 J of energy, and this energy is sufficient to
operate a particular car for 28 miles. An aspirin tablet has a mass of 265 mg. If the aspirin could
be converted completely into thermal energy, how many miles would this car go on a single tablet?
D. A Wookiee spacecraft has a speed of 0.70 c with respect to the earth. The Wookiees measure
29.0 h for the time interval between two events on the earth. What value for the time interval
would they measure if their ship had a speed of 0.96 c with respect to the earth (in hours)?

10. A. A resistor has a resistance R, and a battery has an internal resistance r. When the resistor is
connected across the battery, 13% less power is dissipated in R than would be dissipated if the
battery had no internal resistance. Find the ratio r/R.
B. The circuit in the drawing contains five identical resistors of Resistance R.
The V = 60 V battery delivers 87 W of power to the circuit. What is the
resistance R of each resistor?
C. In a heart pacemaker, a pulse is delivered to the heart 78 times per minute. The capacitor that
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controls this pulsing rate discharges through a resistance of 1.8 10 . One pulse is delivered
every time the fully charged capacitor loses 70.0% of its original charge. What is the capacitance
of the capacitor?
11. A. A light bulb is wired in series with a 137 resistor, and they are connected across a 120 V source.
The power delivered to the light bulb is 22.8 W. What are the two possible resistances of the light
bulb?
B. A portable electric heater uses 18 A of current. The manufacturer recommends that an extension
cord attached to the heater dissipate no more than 1.9 W of power per meter of cord length. What
is the smallest radius of copper wire that can be used in the extension cord? (Note: An extension
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cord contains two wires. Resistivity of copper 1.68 × 10 m.).
12. A. Given the circuit shown. All capacitors are fully charged. How much energy is stored by the
2.0 F capacitor?
B. Examine the circuit shown. What is the power dissipated by the 12
resistor?
13. A. The resistance of a bagel toaster is 16 . To prepare a bagel, the toaster is operated for one minute
from a 120 V outlet. How much energy is delivered to the toaster?
B. A resistor is placed in parallel with a 156 resistor and the equivalent resistance is 117 . What
is the equivalent resistance when these two resistors are in series?
C. The current in a series circuit is 17.0 A. When an additional 19.0 resistor is inserted in series,
the current drops to 11.5 A. What is the voltage applied over the circuit?
D. A Wookie spacecraft has a speed of 0.70 c with respect to the earth. The Wookies measure 10.0 h
for the time interval between two events on the earth. What value for the time interval (in hours)
would they measure if their ship had a speed of 0.96 c with respect to the earth?

14. A. An electric furnace runs nine hours a day to heat a house during January (31 days). The heating
element has a resistance of 5.5 and carries a current of 25 A. The cost of electricity is
$01.0/kWh. Find the cost of running the furnace for the month of January.
B. A resistor has a resistance R, and a battery has an internal resistance r. When the resistor is
connected across the battery, 6% less power is dissipated in R than would be dissipated if the
battery had no internal resistance. Find the ratio r/R.
C. A carpenter on a space station has constructed a 30.0° ramp as
shown in the drawing A rocket moves past the space station with a
relative speed of 0.680 c in a direction parallel to side y. What
does a person aboard the rocket measure for the angle of the ramp?
15. A. A resistor (resistance = R) is connected first in parallel and then in series with a 3.50 resistor. A
battery delivers six times as much current to the parallel combination as it does to the series
combination. Determine the two possible values for R.
B. An extension cord is used with an electric weed trimmer that has a resistance of 17.0 . The
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extension cord is made of copper wire that has a cross-sectional area of 3.10 × 10 m . The
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resistivity of copper is 1.68 × 10 m. The combined length of the two wires in the extension
cord is 80 m. The extension cord is plugged into a 60 V socket. What is the power applied to the
trimmer (the rest of the power is dissipated in the wire)?
16. A. Examine the circuit shown. All capacitors are fully
charged. How much energy is stored by the 2.0 F
capacitor?
B. Examine the circuit shown. What is the power dissipated by
the 12 resistor?
17. B. A heating element in a stove is designed to dissipate 3000.0 W when
connected to 240.0V.
1. Assuming that the resistance is constant, calculate the current in this element if it is
connected to 120.0 V.
2. Calculate the power it dissipates at 120 V.
18 Find the current in the 12.00 resistor.

19. A. Determine the equivalent capacitance between A and B for the
circuit shown.
B. A 45.0 and a 75.0 resistor are connected in parallel. When this combination is connected
across a battery, the current delivered by the battery is 0.32 A. When the 45.0 resistor is
disconnected the current from the battery drops to 0.120 A. Determine the emf of the battery.
Neglect the internal resistance of the battery.
20. Find the energy dissipated in the 4 resistor.
21. Calculate the equivalent resistance between A and B.
22. Given the circuit shown.
(a)
(b)
Find the current in the 12.0 resistor.
Find the voltage across either of the 6 resistors.
23. A.
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Consider a series RC circuit for which C = 6.0 F, R = 2.0 × 10 and = 20.0 V. Initially the
charge on the capacitor is zero and the switch is open.
(a) Find the maximum charge on the capacitor after the switch in the circuit is closed.
(b) What is the charge on the capactior 4 seconds after the switch is closed?
B. A lamp (R = 150 ), an electric heater (R = 25 ), and a fan (R = 50 ) are connected in parallel
across a 12.0 V line.
(a) What is the total current flowing in the circuit?
(b) What is the voltage across the fan?
(c) What is the current in the lamp?
(d) What power is expended in the heater?

24. B. A heart pacemaker fires 72 times per minute. The pacemaker fires when a 25.0 nF capacitor that is
in series with a resistor is charged to 0.632 of its full voltage. What is the value of the resistor?
25. Given the circuit shown.
(a) Find the total resistance in the circuit.
(b) What is the total power dissipated in the circuit?
(c) Find the current in R 2.
(d) What is the power dissipated in R 2?
(e) What is the voltage drop from A to B?
(f) What is the voltage drop from A to C?
26. A. The current flowing through the 8.45 resistor in the drawing
is 1.22 A. What is the voltage in the battery?
B. A three-way light bulb has two filaments with resistance R 1 and R2
connected in series. The resistors are connected to three terminals
as shown in the drawing. The light switch determines which two of
the three terminals are connected to a potential difference of 120 V
at any given time. When terminals A and B are connected to the
120 V, the bulb uses 75.0 W of power. When terminal A and C are
connect to the 120 V, the bulb uses 50.0 W of power.
(a) What is the resistance in R 1?
(b) What is the resistance in R 2?
(c) How much power does the bulb use when 120 V is connected to terminals B and C?
27. A 0.22 F capacitor is charged by a 1.5 V battery. After being charged, the capacitor is connected to a
small electric motor. Assume 100% efficiency.
(a)
(b)
To what height can the motor lift a 5.0 g mass?
What initial voltage must the capacitor have if it is to left a 5.0 g mass to a height of 1.0 cm?
28. Given the circuit shown.
(a) What is the current flowing past point A?
(b) Find the power dissipated by the 20 resistor.
(c) Calculate the power dissipated by the entire circuit.
(d) What is the potential difference between points B and C;
points A and G; points C and D; points B and F; points H
and I?
29. Six identical capacitors are arranged as shown. When fully
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charged, the collection of capacitors store 1 × 10 J of energy.
The battery has a voltage of 6 volts.
(a) Find the equivalent capacitance of the circuit.
(b) What is the capacitance of each capacitor?
(c) Calculate the charge on capacitor A.
(d) Determine the voltage drop across capacitor A.

30. The drawing shows a resistor and capacitor connected to a battery. The capacitor is initially uncharged and
the switch is initially open.
(a)
(b)
(c)
(d)
What is the time constant for this RC circuit?
Now the switch is closed. How much charge is on the
plates of the capacitor after 0.1 seconds have elapsed?
When the switch is closed, how long does it take to charge
the capacitor to 95% of its maximum value?
After the switch is fully charged, the switch is opened.
How long does it take for the capacitor to loose 50% of its
charge?
31.. Given the circuit shown.
(a) What is the equivalent resistance of the circuit?
(b) How much energy does the circuit use in 1 minute?
(c) What is the voltage drop between points C and D?
. Using the points shown in the drawing, explain in writing how
you would connect the following:
(d) a voltmeter to get a reading of 12 V,
(e) a voltmeter to get a reading of 0 V,
(f) an ammeter to get the smallest current in the circuit.
32. In the circuit shown all capacitors are fully charged.
(a) What is the equivalent capacitance of this circuit?
(b) Find the energy stored in the circuit.
(c) Calculate the voltage drop between points B and C.
(d) Calculate the voltage drop between points A and C.
(e) What is the charge residing on the 5 F capacitor?
33. Given the circuit shown. All switched are initially open.
(a)
(b)
(c)
Now switches A and B are closed and the others
remain open. How long does it take to the charge the
capacitor to 95% capacity?
Switches A, B and E are now closed and C and D are
opened. When fully charged, how much charge is on
the capacitor?
Now switches A, B and E are opened and C and D are
closed. With the capacitor fully charged, the energy
stored in the capacitor is turned into mechanical
energy by the motor. The motor lifts a 5 gram mass off the floor. What height does the mass
reach?

34. A. The resistance of a bagel toaster is 16 . To prepare a bagel, the toaster is operated for
one minute from a 120 V outlet. How much energy is delivered to the toaster?
B. A resistor is placed in parallel with a 156 resistor and the equivalent resistance is
117 . What is the equivalent resistance when these two resistors are in series?
C. The current in a series circuit is 17.0 A. When an additional 19.0 resistor is inserted in
series, the current drops to 11.5 A. What is the voltage applied over the circuit?
D. A Wookie spacecraft has a speed of 0.70 c with respect to the earth. The Wookies
measure 10.0 h for the time interval between two events on the earth. What value for the
time interval (in hours) would they measure if their ship had a speed of 0.96 c with
respect to the earth?
35. A. An electric furnace runs nine hours a day to heat a house during January (31 days). The
heating element has a resistance of 5.5 Ω and carries a current of 25 A. The cost of
electricity is $0.10/kWh. Find the cost of running the furnace for the month of January.
B. A resistor has a resistance R, and a battery has an internal resistance r. When the resistor
is connected across the battery, 6% less power is dissipated in R than would be dissipated
if the battery had no internal resistance. Find the ratio r/R.
C. A carpenter on a space station has constructed a 30.0° ramp
as shown in the drawing. A rocket moves past the space
station with a relative speed of 0.680 c in a direction parallel
to side y. What does a person aboard the rocket measure for
the angle of the ramp?
36. A. A resistor (resistance = R) is connected first in parallel and then in series with a
3.50 Ω resistor. A battery delivers six times as much current to the parallel combination
as it does to the series combination. Determine the two possible values for R.
B. An extension cord is used with an electric weed trimmer that has a resistance of 17.0 .
The extension cord is made of copper wire that has a cross-sectional area of
3.10 10 -7 m 2 . The resistivity of copper is 1.68 × 10 -8 m. The combined length of
the two wires in the extension cord is 80 m. The extension cord is plugged into a 60 V
socket. What is the power applied to the trimmer (the rest of the power is dissipated in
the wire)?
37. A. Examine the circuit shown. All capacitors are
fully charged. How much energy is stored by the
2.0 μF capacitor?

B. Examine the circuit shown. What is the power
dissipated by the 12 Ω resistor?
38. A. A comet is on a collision course with Earth and is travelling 2.40 × 10 8 m/s relative to
Earth. An alien race has teleported a rescue team onto the comet in order to save us all.
The comet has a mass of 3.42 × 10 11 kg.
1. NASA calculates that the comet will impact in 40.0 hours. How much time do
the aliens on the comet calculate before impact?
2. What is the difference (A-B) between the classical momentum and the relativistic
momentum of the comet as measured by Earth?
3. The aliens realize that if they can slow the comet to 1.80 × 10 8 m/s (relative to
Earth), the comet will miss Earth. How much energy is required to slow the
comet to this new speed?
B. A parallel plate capacitor has a cross sectional area of 1.0 cm 2 and has a separation
distance of 0.10 cm. It is filled with ethylene glycol. When fully charged with a 12.0 V
battery, the negative plate has an excess of 2.45 × 10 9 electrons. Find the dielectric
constant of the ethylene glycol.
39. A. A new computer sits idle 95% of the time. When it is idle, it draws a current of
I rms = 0.832 A from a V rms = 120 V alternating current outlet. If the price of energy is
$0.10/kWh, and there are 8760 hours in a year, how much money is spent running the
idle computer for one year?
B. [8 pts.] The circuit shown has been operating for a
long time. Find the charge on the positive plate of the
15.0 µF capacitor?
C. An alternating sinusoidal current from a specially designed outlet has a peak current of
14.1 A and delivers an average power of 122 watts. What is the peak electric potential
delivered by the outlet?
D. Two identical resistors in parallel are each 1.0 cm long and have a cross sectional area of
0.10 cm 2 . The equivalent resistance is 2.5 Ω. What is the resistivity of each resistor?
40. A. A light bulb is wired in series with a 160 Ω resistor, and the combination is connected
across a 144.0 V source. The power delivered to the light bulb is 25.6 W. What are the
two possible resistances of the light bulb?

B. Given the circuit shown.
1. Find the current through the battery.
2. Find the power dissipated by the 3.0 Ω
resistor.
41. A. A battery has an internal resistance of 0.5 Ω. A number of identical light bulbs, each
with a resistance of 12 Ω, are connected in parallel across the battery terminals. The
terminal voltage of the battery is observed to be one-fourth the emf of the battery. How
many light bulbs are connected?
B. Given the circuit shown.
1. Find the voltage drop across the 5.0
µF capacitor.
2. Find the energy stored in the
4.0 µF capacitor.
42. A. A space traveler moving at a speed of 0.58c with respect to the earth makes a trip to a
distant star that is stationary relative to the earth. He measures the length of this trip to be
8.3 light-years. What would be the length of this same trip (in light-years) as measured
by a traveler moving at a speed of 0.76c with respect to the earth?
B. The current in a series circuit is 7.0 A. When an additional 7.0 Ω resistor is inserted in
series, the current drops to 3.9 A. What is the resistance in the original circuit?
C. A cigarette lighter in a car is a resistor that, when activated, is connected across the 14 V
battery. Suppose a lighter dissipates 33 W of power. Find the current that the battery
delivers to the lighter.
D. Two capacitors are connected in parallel across the terminals of a battery. One has a
capacitance of 2.0 µF, and the other a capacitance of 3.0 µF. These two capacitors
together store 5.2 × 10 -5 C of charge. What is the voltage of the battery?
43. A. In a heart pacemaker, a pulse is delivered to the heart 78 times per minute. The capacitor
that controls this pulsing rate discharges through a resistance of 1.8 × 10 6 Ω. One pulse is
delivered every time the fully charged capacitor loses 70.0% of its original charge. What
is the capacitance of the capacitor?
B. Quasars are believed to be the nuclei of galaxies in the early stages of their formation.
Suppose a quasar radiated electromagnetic energy at the rate of 4.20 × 10 41 W. How
much mass does the quasar lose as a result of this radiation during one hour?
C. A portable electric heater uses 15 A of current. The manufacturer recommends that an
extension cord attached to the heater dissipate no more than 1.6 W of power per meter of
cord length. What is the smallest radius of copper wire that can be used in the extension
cord? The resistivity of copper is 1.68 × 10 -8 Ω m. (Note: An extension cord contains
two wires.)

44. A. A battery delivering a current of 60.0 A to a circuit has a terminal voltage of 23.4 V. The
electric power being dissipated by the internal resistance of the battery is 34.0 W. Find
the emf of the battery.
B. Given the circuit shown. How much energy is
dissipated by the 2 Ω resistor in 2.0 minutes?
45. A. A carpenter on a space station has constructed a rectangle as shown
in the drawing. A rocket moving past the space station with a
relative speed of 0.800 c in a direction parallel to side y measures
the area of the rectangle to be 1.40 m 2 . What area does a person
moving in a rocket with a relative speed of 0.999 c in a direction
parallel to side x measure?
B. Given the circuit shown. All capacitors are fully
charged. How much energy is stored by the 6.0 μF
capacitor?