Practice Final Exam
Physics 1310 - 2002
1. A chemistry student heats a 200 g aluminum rod to 200ºC. The rod is 5.00 cm long. She then
drops the rod into an insulated container holding 500 g of water at 10ºC. When the water and
the aluminum rod come to equilibrium, by how much has the length of the rod changed?
Note: The coefficient of linear expansion for aluminum equals 24x10-6 ºC –1 and the specific heat
of aluminum equals 900 J/kg ºC. The specific heat of water equals 4186 J/kg ºC.
0.900 J/g-C *200 g (200 C – T) = 4.186 J/g-C *500 g *(T-10 C)  T= 25 C
L = 5.00 cm * 24x10-6 ºC –1*(200 C- 25 C) =0.02 cm
2. A physics professor puts 2 moles of nitrogen gas into a container at 300 K. The absolute
pressure inside the container equals 1.00 atmospheres. He then heats the gas by an isochoric
process until the temperature of the gas equals 500K. What is the absolute pressure in the
container now?
PV= nRT  P = nRT/V  P2/P1 = T2/T1 = 500/300  P2 = 1.67 atm
3. A geoscience student puts 2 moles of air into a container at 300 K. She wants to heat the gas
to a temperature so that the rms speed of CO2 equals 500 m/s. To what temperature should she
heat the gas? Note: the molar mass of CO2 equals 44 gm/mol.
v = sqrt( 3 kT / m) = sqrt (3RT/M) 
T = M x v2 / 3R = 44x10-3 kg / mol x 0.25 x106 m2/s2 / 24.9 J/mol-K = 442 K
4. A geology student places 100 g of ice at 0C into a very well insulated container that
contains 4.0 kg of rocks at 20C. The specific heat of these rocks equals 0.75 J/g-ºC. Calculate
the temperature of the rocks when the contents of the container comes to thermal
equilibrium.
100 g *333 J/g + 100 g * 4.186 J/g ºC * T = 4000g * 0.75 J/g ºC * (20ºC – T)
 T = 7.8ºC
5. A field biologist is using an insulated container with dimensions equal to 20 cm x 20 cm x 20
cm. (The total surface area of the exterior container walls equals 0.240 m2.) The thickness of the
container walls equals 3.00 cm. The thermal conductivity of the container material equals
0.040 W/m-K. The temperature outside the container equals 20°C. She places 250 g of ice at 0ºC
inside the container. How long will it take for all the ice in the container to melt? Note: The
specific heat of ice equals 2090 J/kg ºC, the specific heat of water equals 4186 J/kg ºC, and latent
heat of fusion of water equals 333 J/g.
H = 0.040 W/m-K * 0.240 m2 * 20ºC / 0.03 m = 6.4 W
6.4 W * time = 250 g * 333 J/g = 1.67 x105 J  time = 3.6 hours
Practice Final Exam
Physics 1310 - 2002
6. A tungsten filament with surface area equal top 4.0x10-5 m2 and emissivity equal to 0.25 has
temperature equal to 3000K and is in an environment with temperature equal to 300K. How
much power does this filament radiate?
P = 0.25 * 5.67x10-8 W/m2 K4 * 4.0x10-5 m2 * [(3000 K)4 - (300 K)4] = 46 W
7. Consider 2.00 moles of an ideal gas at atmospheric pressure and 300 K. The specific heat at
constant volume of this gas equals 12.5 J/mol ºC. As 418 J of heat enters the gas, it undergoes an
isobaric expansion. Calculate the change in the internal energy of the gas during this
process.
Cp = Cv + R = 20.9 J/mol ºC
Q = 418 J = 2.00 mol * 20.9 J/mol ºC * T  T = 10 ºC
U = 2.00 mol * 12.5 J/mol ºC * 10 ºC = 250 J
8. Consider 2.00 moles of an ideal gas at atmospheric pressure and 300 K. The specific heat at
constant volume of this gas equals 12.5 J/mol ºC. The gas goes through a cycle, returning to the
initial conditions. During this cycle, 450 Joules of heat enters the gas from a reservoir at 600K
and 400 Joules of heat leaves the gas and flows into a reservoir at 300K. Calculate the amount
of work done by the gas in this cycle.
W = QH – QC = 50 J
9. A heat engine takes in 50 kJ of heat from the hot reservoir and transfers 40 kJ of heat into the
cold reservoir. Calculate the efficiency of this engine.
W = 10 kJ
eff = 10 kJ / 50 kJ = 20%
10. A heat engine operates between a hot reservoir at 100ºC and a cold reservoir at 63 ºC.
Calculate the maximum possible theoretical efficiency of this engine.
effcarnot = 37 K / 373 K = 10 %
11. In the diagram, q1 = 5.0 C, q2 = -5.0 C, q3 = 5.0 C, and
d = 30 cm. Calculate the magnitude of the net force that q2
and q1 exert on q3.
F = 9x109 * (25x10-12 /9 x10-2 + 25x10-12 /9 x10-2) N
= 5.0 N (to the left)
d
q2
d
+
q3
+
q1
Practice Final Exam
Physics 1310 - 2002
12. In the diagram, q1 = 0.50 C, q2 = -0.50 C, and d = 3.0 m.
Calculate the magnitude of the electric field at point P.
E = 9x109*(-0.5x10-6 /9 –0.5x10-6 /9)N/C
= 1000 N/C (to the left)
d
d
q2
+
q1
P
13. A small sphere with mass equal to 5.0 g has a charge equal to
6.00x10-6C. The sphere is suspended by a massless string and placed in a
uniform electric field. The equilibrium position of the sphere is shown in the E
figure to the right. Calculate the magnitude of the electric field.
mg / cos(36.9º) = qE / sin(36.9º)  E = (mg /q) tan(36.9º) = 6,1000 N/C
14. In the diagram to the right, the
magnitude of the electric field equals
5,000 N/C. Calculate the change in
electric potential as a positively charged
particle with charge equal to 5.0 C
moves from point A to point B.
V = - E y
= - 5,000 N/C * 0.04 m = - 200 volts
+
36.9
E
8
B
6
y(cm)
E
4
E
E
E
2
A
0
0
2
4
6
8
10
12
x(cm)
15. In the field described in problem 15, a proton (m = 1.67x10-27 kg and q = e =1.60x10-19 C) is
released from rest at point A. What is the kinetic energy of this particle when it hits one of
the plates?
KE = ½ mv2 = q V = e 300 V = 300 eV
16. The resistivity of tungsten equals 5.6x10-8 -m. Calculate the electrical resistance of a
tungsten filament with diameter equal to 0.020 mm and length equal to 40 cm.
R = 5.6x10-8 -m * 0.40 m / [3.14 * (1.0x10-5 m)2] = 72 
14
Practice Final Exam
Physics 1310 - 2002
17. For the circuit,  = 18.4 volts, Rd = 10.0 K , C =10.0 F. The
capacitor is initially fully charged and the switch moves from c to d at
time t = 0.00. Calculate the current flowing through Rd at t = 0.10 s.

Rc

RC = 0.100 sec
c
d
+
sw itc h
+
-
Rd
VC = 18.4 volt * e-1 = 6.77 volt
I = 6.77 volt / 10 k = 0.677 mA
18. A particle is moving in a uniform magnetic field, B. The velocity of the particle, v, is
perpendicular to B. The speed of the particle equals 1000 m/s. The acceleration of the particle
equals 100 m/s2. The mass of the particle equals 2.0x10-10g and the electric charge of the particle
equals 20 µC. Calculate the magnitude of the B-field.
F = qvB = ma  B = ma /qv = 2.0 x10-13 kg*100 m/s2 / (2.0 x 10-5 C*1000 m/s) = 1.0 x10-9 T
19. A long straight wire carries a 20 A
current as shown in the diagram. The
current in this wire produces a magnetic
field at point P, 2.0 cm from the wire.
Calculate the magnitude of the B-field
at P.
P
I
B = 2 x 10-7 *20 / 0.02 T = 200  = 0.200 mT
20. A long straight wire carries a current equal to
50 A. A 5.0 cm long short wire segment that
carries a current of 40 A is suspended 2.0 cm above
the long straight wire by the magnetic force that the
long wire exerts on the short wire segment.
Calculate the weight of the short wire segment.
B = 500 
F = 40A * 0.05 * 500 mN
5.0 cm
40 A
2.0 cm
50 A
-
C
Practice Final Exam
Physics 1310 - 2002
21. Consider a circular loop of wire that is at rest in a magnetic field. The
area of the circular loop through which current flows is fixed and is equal
to 2.0 m2. The magnetic field points into the page. The magnitude of the
field equals 0.050 T. The magnetic field is decreasing in magnitude at the
rate of 4.0 T/s. The resistance of the loop equals 3.2 ohm. Calculate the
magnitude of the current induced in the loop by this changing
magnetic field.
I * 3.2 ohm = 2.0 m2 4.0 T/s  I = 2.5 A
22. As shown below, a 40 cm x 20 cm rectangular loop of wire is
falling with constant speed into a uniform magnetic field. The
magnetic field is perpendicular to the plane of the loop and goes
through the lower part of the loop. The magnitude of the magnetic
field is 2.5 T. The electric resistance of the loop equals 5.0 ohms.
The induced current in the loop equals 0.60 A. Determine the
direction of the induced current through the part of the loop in
the field.
Current is CCW.
23. An electromagnetic wave has an intensity equal to 400,000 W/m2. Calculate the
magnitudes of the magnetic field associated with this wave.
I = E2 / (2 oc)  E = 17360 N/C
B = E/c = 58 micro Tesla
24. A point source of light emits 2000 watts of visible light. Some of this light strikes, at normal
incidence, a rectangular 2.0 cm by 4.0 cm solar cell. The solar cell is located 2.0 meters from the
light source. Calculate the power of the light that is incident on the solar cell.
I = 2000 W /(4 4.0 m2) and P = 0.020 m x 0.040 m * I  P = 32 mW
25. A uniform beam of laser light with intensity equal to 10,000,000 W/m2 is normally incident
of a flat surface with area equal to 1.0 cm2 and is totally reflected by this surface. Calculate the
force on this surface due to the radiation pressure.
F = p A = 2I/c * A = 2.0 x107 W/m2 / 3.0 x 108 m/s x 1.0 x 10-4 m2 = 6.6  N
26. Indicate the position and orientation of the image of the arrow
formed in the mirror.
Practice Final Exam
Physics 1310 - 2002
27. A light ray in glass (n = 1.50) strikes the interface between glass and air at 45º. Is this ray
totally internal reflected?
sin’ = 1.50 *0.707  TIR
28. A ray of red light strikes a 30-60-90 prism at normal
incidence. The index of refraction of the prism glass for red
light equals 1.5. Calculate the angle of deviation for the light
ray.
30º
1.5 sin(30) = sin()   = 48.6
 deviation = 48.6 –30 = 18.6
60º
29. Would a blue light ray be deviated more or less than the red light ray mentioned in problem
28? more
30. Describe the image of the arrow formed by the converging lens.
virtual, upright, magnified
31. Assume f = +20 cm (converging lens), p = 25 cm, h = 2.0 cm. Calculate h’, the lateral size
of the image. Include the sign of h’.
1/0.25 m +1/q = 1/0.20 m  q = 1.0 m  M = - 4.0  h’ = -8.0 cm
32. A nearsighted student has an uncorrected far point equal to 0.75 meters. Calculate the
power (in diopters) of the lens needed to correct this condition. Include the sign of the
answer.
1/ infinity + 1/(-.75 m) = 1/f  1/f = -1.33 D
33. A student uses a lens with focal length 50 mm to view an insect that has angular size equal to
0.10º when viewed without this magnifying lens and held at the distance of most comfortable
viewing. What is the angular size of the insect when examined with this magnifier?
M = 25 cm / 50 mm = 5X  ’ = 5 x 0.10 º = 0.5º
34. A telescope has an objective lens diameter equal to 25 cm and objective focal length equal to
2.00 m. This telescope is being used to examine a Lunar crater that has angular size equal to
0.0010 degree. The eyepiece being used has focal length equal to 25.0 mm. What is the angular
size of the crater when viewed through the telescope?
Practice Final Exam
Physics 1310 - 2002
M = 200 cm / 2.5 cm = 80 X  ’ = 0.08 º
35. A physics student uses a camera with a 100 mm focal length and an f/2 rating to photograph
an insect that is 2.0 cm long and is located 30 cm from the lens. Calculate the linear size of the
image formed by this lens.
1/30 cm + 1/q = 1/10 cm  q = 15 cm  M = -15cm / 30 cm = -0.5  h’ = -1.0 cm
36. Light from a HeNe laser (wavelength = 632.8 nm) is incident normally on a diffraction
grating. The angular position of the 1st order line in the resultant diffraction pattern occurs at
22.3º from the central maximum. Calculate the grating spacing and express it in units of lines
per mm of the grating.
600 lines/mm
37. Two yellow-breasted sapsuckers are flying 0.80 m apart. They are being observed by a birdwatcher using binoculars with 40 mm diameter objective lenses. Assume  = 550 nm. At what
distance from the birdwatcher will the birds be when the birdwatcher is first able to resolve the
birds as a two distinct objects rather than as a single object? (Express your answer in meters.)
48 km
38. Monochromatic light with wavelength 600 nm in air is traveling through air. It is normally
incident on a lens (n = 1.40) that is coated with a thin film (n = 1.20). There is no reflection of
this light from the coated surface. The thickness of the thin film is somewhere between 50 and
300 nanometers. Calculate the actual thickness of this thin film coating.
125 nm
39. Unpolarized light with intensity equal to 400 W/m2 is incident on an ideal polarizer that has
its transmission axis oriented vertically. Light that passes through this polarizer then passes
through an ideal polarizer with its transmission axis rotated 60 degrees from the vertical.
Calculate the intensity of the light that passes through the second polarizer.
50 W/m2
40. An astronomer on Earth observes Galaxy A moving to the left at 0.81c and Galaxy B moving
to the right at 0.83c. A resident of Galaxy A observes a supernova explosion in Galaxy A that
lasts 4 months.
Galaxy A
Galaxy B
Earth
From the point of view of an observer in Galaxy B, how long does this supernova explosion
last?
20 months
41. The wavelength corresponding to the peak of a UV star’s spectrum equals 362 nm. What is
the temperature of this star’s surface?
8000K
Practice Final Exam
Physics 1310 - 2002
42. An atom is initially in its ground state. It absorbs a photon with wavelength equal to 827 nm
and moves to a metastable excited state. The atom then absorbs a second photon with wavelength
equal to 496 nm to move to a higher energy excited state. The atom then emits a photon and falls
to the ground state. What is the energy of the emitted photon?
4.00 eV
43. A hydrogen atom is initially in its ground state (n = 1). What is the wavelength of the
photon that must be absorbed to move this atom to its first excited state (n = 2)?
122 eV
44. In a container of hydrogen gas at 1982 K, there are 1.00 x 106 atoms in 2s states.
How many hydrogen atoms are in 3s states?
16
45.. Consider the following fission reaction:
n +
238
92U
--->
97
36Kr
+ Y + 3n
Identify the unknown daughter (Y). What is its mass and atomic number?
Ba-139
46. A piece of wood found in the remains of a New England Native American village was
analyzed to determine its approximate age. A 20.0 g sample of carbon from this wood was found
to have carbon-14 activity of 2.50 Bq. A carbon sample from a living tree has a decay rate of
0.250 Bq/g. When did this tree from which the wood originated die?
5730 y
47. For problem 46, what is the ratio of C-14 to C-12 atoms in the ancient sample?
6.5 x 10-13
48. Calculate the energy released by the fissioning of 1 kg of U-235.
208 MeV / nucleus  8.64x1013 J
49. A patient having a chest x-ray receives a dose equivalent of 200 mrem in 0.80 kg of
tissue. Calculate the energy (in joules) absorbed by the patient.
1.6 mJ
50. A nucleus with mass equal 226 u decays by emission of an alpha particle. The energy carried
by the alpha particle equals 4.44 MeV. Calculate the kinetic energy of the daughter nucleus.
80 keV