Download Physics 271– FINAL EXAM-SOLUTIONS Friday

Physics 271– FINAL EXAM-SOLUTIONS
Friday Dec 23, 2005
Prof. Amitabh Lath
1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to
make entries on the answer sheet. Enter the following id information
now, before the exam starts.
2. In the section labelled NAME, enter your last name, then fill in the
e/mpty circle for a blank, then enter your first name, another blank,
and finally your middle initial.
3. Under STUDENT # enter your 9-digit ID Number.
4. Under COURSE enter 271.
5. Under SECTION enter your recitation section.
6. Under CODE enter the exam code given above.
00
7. During the exam, you may use pencils, a calculator, and TWO 8 12 ×
1100 sheet of paper with formulas and notes.
8. There are 26 multiple-choice questions on the exam. For each question,
mark only one answer on the answer sheet. There is no subtraction of
points for an incorrect answer, so even if you cannot work out the
answer to a question, you should make an educated guess.
9. At the end of the exam, hand in only the answer sheet. Retain this
question paper for reference and study.
1
1. A constant force F is applied to a body of mass m that initially is
headed east at velocity v0 until its velocity becomes −v0 . The total time of
travel is 2t. The total distance the body travels in that time is: (NOT the
total displacement, but the total distance, ie, what would the odometer read?).
code 101
F 2
t
a) 12 m
F 2
b) m t
F 2
c) v0 t − 21 m
t
1F 2
d) v0 t + 2 m t
F 2
e) 2(v0 t + 12 m
t)
code 102
F 2
a) 2(v0 t + 21 m
t)
F 2
b) m t
F 2
c) v0 t − 12 m
t
1F 2
d) v0 t + 2 m t
F 2
e) 21 m
t
Solution
During the first segment of the trip, the body accelerates from v0 to 0 ms
with an acceleration a = −F
.
m
During the second segment, the body accelerates from 0 ms to −v0 with an
.
acceleration a = −F
m
The motions are identical because the magnitude of the changes in velocity are the same and accelerations are identical. The motions are just in
opposite directions.
During the second segment, the body travels a distance x =
−1 F 2
t
2 m
During the first segment, the body goes the same distance, but in the positive direction.
The length of the path (not the displacement) that the body has traveled is
1F 2
F 2
t + 12 m
t
2m
=
F 2
t
m
2
2. In the figure shown, the coefficient of kinetic friction between the block
and the incline is 0.40. The incline is 40 degrees above the horizon. What is
the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley.
code 101
a) 3.4 m/s2
b) 3.7 m/s2
c) 4.2 m/s2
d) 3.9 m/s2
e) 5.4 m/s2
code 102
a) 3.9 m/s2
b) 4.2 m/s2
c) 3.4 m/s2
d) 3.7 m/s2
e) 5.4 m/s2
3
4
3. A 4.0-kg mass on the end of a string rotates in a circular motion on a
horizontal frictionless table. The mass has a constant speed of 2.0 m/s and
the radius of the circle is 0.80 m. What is the magnitude of the resultant
force acting on the mass?
code 101 code 102
a) 39 N a) 30 N
b) 20 N b) 44 N
c) 44 N
c) 0 N
d) 0 N
d) 39 N
e) 30 N
e) 20 N
5
4. A 0.50 kg mass attached to the end of a string swings in a vertical
circle (radius = 2.0 m). When the mass is at the highest point of the circle
the speed of the mass is 8.0 m/s. What is the magnitude of the force of the
string on the mass at this position?
code 101
a) 21 N
b) 11 N
c) 16 N
d) 26 N
e) 36 N
code 102
a) 21 N
b) 16 N
c) 26 N
d) 36 N
e) 11 N
6
5. A block is pushed across a rough horizontal surface from point A to
point B by a force (magnitude P = 5.4 N) as shown in the figure. The
magnitude of the force of friction acting on the block between A and B is 1.2
N and points A and B are 0.5 m apart. If the kinetic energies of the block
at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the
block by the force P between A and B?
code 101
a) 2.7 J
b) 1.0 J
c) 2.2 J
d) 1.6 J
e) 3.2 J
code 102
a) 2.2 J
b) 1.6 J
c) 2.7 J
d) 3.2 J
e) 1.0 J
7
6. Two eggs of equal mass are thrown at a blanket with equal velocity.
Egg B hits the blanket but egg A hits the wall instead. Compare the work
done on the eggs in reducing their velocities to zero.
code 101
a) More work was done on A than on B.
b) More work was done on B than on A.
c) The amount of work is the same for both.
d) It is meaningless to compare the amount of work because the forces were
so different.
e) Work was done on B, but no work was done on A because the wall did
not move.
code 102
a) It is meaningless to compare the amount of work because the forces were
so different.
b) More work was done on A than on B.
c) The amount of work is the same for both.
d) Work was done on B, but no work was done on A because the wall did
not move.
e) More work was done on A than on B.
8
9
7. A champion athlete can produce one horsepower (746 W) for a short
period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m
high mountain while expending power at this rate, she would reach the summit in how many seconds?
code 101
a) 1
b) 460
c) 500
d) 1000
e) 35000
code 102
a) 1
b) 460
c) 500
d) 1000
e) 35000
KEi + Wmuscles−on−bike−body−system = KEf + Ug,f
W = mgh
To find the time it will take to do this work:
1s
1s
W ( 746J
) = mgh( 746J
) = 460s
10
8. A 0.04-kg ball is thrown from the top of a 30-m tall building (point
A) at an unknown angle above the horizontal. As shown in the figure, the
ball attains a maximum height of 10 m above the top of the building before
striking the ground at point B. If air resistance is negligible, what is the value
of the kinetic energy of the ball at B minus the kinetic energy of the ball at
A (KB − KA )?
code 101
a) 12 J
b) -12 J
c) 20 J
d) -20 J
e) 32 J
code 102
a) -20 J
b) -12 J
c) 32 J
d) 20 J
e) 12 J
11
12
9. A 1.6-kg ball is attached to the end of a 0.40-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At
the lowest point of its swing, when it is moving horizontally, the ball collides
with a 0.80-kg block initially at rest on a horizontal frictionless surface. The
speed of the block just after the collision is 3.0 m/s. What is the speed of
the ball just after the collision?
code 101
a) 1.7 m/s
b) 1.1 m/s
c) 1.5 m/s
d) 1.3 m/s
e) 2.1 m/s
code 102
a) 2.1 m/s
b) 1.1 m/s
c) 1.3 m/s
d) 1.5 m/s
e) 1.7 m/s
13
14
10. A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg
block initially at rest, as shown. The bullet emerges from the block with a
speed of 400 m/s. To what maximum height will the block rise above its
initial position?
code 101 code 102
a) 78 cm a) 37 cm
b) 66 cm b) 56 cm
c) 56 cm c) 78 cm
d) 46 cm d) 46 cm
e) 37 cm e) 66 cm
15
16
11. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal
axis. A light cord wrapped around the wheel supports a 0.50-kg object, as
shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s2 . What is the moment of inertia of the wheel?
code 101
a) 0.023 kg · m2
b) 0.027 kg · m2
c) 0.016 kg · m2
d) 0.019 kg · m2
e) 0.032 kg · m2
code 102
a) 0.023 kg · m2
b) 0.016 kg · m2
c) 0.032 kg · m2
d) 0.019 kg · m2
e) 0.027 kg · m2
17
18
12. A cylindrical shell rolls without slipping down an incline as shown in
the figure. The linear acceleration of its center of mass is
code 101
a) (5/7)g sin θ
b) (1/2)g sin θ
c) (3/5)g sin θ
d) (2/3)g sin θ
e) (4/5)g sin θ
code 102
a) (5/7)g sin θ
b) (3/5)g sin θ
c) (4/5)g sin θ
d) (1/2)g sin θ
e) (2/3)g sin θ
19
20
13. A solid sphere, spherical shell, solid cylinder and a cylindrical shell
all have the same mass m and radius R. If they are all released from rest at
the same elevation and roll without slipping, which reaches the bottom of an
inclined plane first?
code 101
a) solid sphere
b) spherical shell
c) solid cylinder
d) cylindrical shell
e) all take the same time
code 102
a) all take the same time
b) spherical shell
c) solid cylinder
d) solid sphere
e) cylindrical shell
21
14. An ice skater with rotational inertia Io is spinning with angular speed
ωo . She pulls her arms in, decreasing her rotational inertia to Io /3. Her angular speed becomes:
code 101
a) ωo /3√
b) ωo / 3
c) ω
√o
d) 3ωo
e) 3ωo
code 102
a) ω
√o
b) 3ωo
c) 3ωo
d) ωo /3
√
e) ωo / 3
22
15. A uniform plank is 12 ft long and weighs 20 lb. It is balanced on
a sawhorse at its center. An additional 40 lb weight is now placed on the
left end of the plank. To keep the plank balanced, it must be moved what
distance to the right? ( In English units, g= 32 ft/s2 ).
code 101 code 102
a) 1 ft
a) 4 ft
b) 3 ft
b) 4 ft
c) 2 ft
c) 2 ft
d) 3.43 ft d) 3.43 ft
e) 1 ft
e) 3 ft
23
16. A particle whose mass is 2 kg moves in the xy plane with a constant
speed of 3 m/s in the x-direction along the line y = 5. What is its angular
momentum (in kg ·m2 /s) relative to the origin?
code 101
a) -30 k
b) 30 k
c) -15 k
d) 15 k
e) 45 k
code 102
a) 15 k
b) 45 k
c) -30 k
d) 30 k
e) -15 k
24
17. What is the gravitational force on a 20-kg satellite circling the Earth
(radius = 6.4 ×106 m, mass = 6.0 ×1024 kg) with a period of 5.0 h?
code 101
a) 88 N
b) 55 N
c) 36 N
d) 98 N
e) 18 N
code 102
a) 36 N
b) 88 N
c) 55 N
d) 18 N
e) 98 N
25
18. Five moles of an ideal gas expands isothermally at 100 degrees Celsius
to five times its initial volume. Find the heat flow into the system.
code 101
code 102
4
a) 2.5 ×10 J a) 2.9 ×103 J
b) 1.1 ×104 J b) 6.7 ×103 J
c) 6.7 ×103 J c) 7.0 ×102 J
d) 2.9 ×103 J d) 2.5 ×104 J
e) 7.0 ×102 J e) 1.1 ×104 J
26
27
19. A spaceship of mass m circles a planet (mass = M) in an orbit of
radius R. How much energy is required to transfer the spaceship to a circular
orbit of radius 3R?
code 101
code 102
a) GmM/(2R) a) GmM/(6R)
b) GmM/(3R) b) GmM/(3R)
c) GmM/(4R) c) GmM/(4R)
d) GmM/(6R) d) GmM/(2R)
e) 3GmM/(4R) e) 3GmM/(4R)
28
29
20. Planet Zero has a mass of 4.0 ×1023 kg and a radius of 2.0 ×106 m.
A 10-kg space probe is launched vertically from the surface of Zero with an
initial kinetic energy of 8.0 ×107 J. What maximum distance from the center
of Zero is achieved by the probe?
code 101
code 102
6
a) 3.2 ×10 m a) 6.0 ×106 m
b) 4.0 ×106 m b) 5.0 ×106 m
c) 6.0 ×106 m c) 3.2 ×106 m
d) 5.0 ×106 m d) 2.5 ×106 m
e) 2.5 ×106 m e) 4.0 ×106 m
30
21. A body oscillates with simple harmonic motion along the x axis. Its
displacement varies with time according to the equation x = 5.0 sin (πt + π/3).
The velocity (in m/s) of the body at t = 1.0 s is
code 101
a) +8.0
b) -8.0
c) -14
d) +14
e) -5.0
code 102
a) -5.0
b) -14
c) +14
d) +8.0
e) -8.0
31
22. A clarinet behaves like a tube closed at one end. If its length is 1.0
m, and the velocity of sound is 344 m/s, what is its fundamental frequency
(in Hz)?
code 101
a) 264
b) 140
c) 86
d) 440
e) 172
code 102
a) 140
b) 264
c) 172
d) 86
e) 440
32
23. Organ pipe X (open at one end) is half as long as organ pipe Y (open
at both ends) as shown. The ratio of their fundamental frequencies fX : fY is:
code 101
a) 1:1
b) 1:2
c) 2:1
d) 1:4
e) 4:1
code 102
a) 4:1
b) 1:4
c) 1:2
d) 2:1
e) 1:1
33
24. A mass-spring system is oscillating with amplitude A. The kinetic
energy will equal the potential energy only when the displacement is
code 101
a) zero
b) A/4
√
c) A/ 2
d) A/2
e) anywhere between -A and +A
code 102
a) A/2
b) A/4
c) anywhere between -A and +A
d) zero
√
e) A/ 2
34
25. Two strings are respectively 1.00 m and 2.00 m long. Which of the
following wavelengths, in meters, could represent harmonics present on both
strings?
code 101
code 102
a) 0.800, 0.670, 0.500 a) 4.00, 2.00, 1.00
b) 1.33, 1.00, 0.500
b) 1.33, 1.00, 0.500
c) 0.800, 0.670, 0.500
c) 2.00, 1.00, 0.500
d) 2.00, 1.33, 1.00
d) 2.00, 1.00, 0.500
e) 4.00, 2.00, 1.00
e) 2.00, 1.33, 1.00
When we look at standing waves on a string, the ends of the string which
are tied to a certain position (and hence cannot move) must be nodes of the
standing wave. Similarly, the ends of the string which are free to move must
be antinodes of the standing wave. We must find the 3 standing waves from
the possibilities above that give either nodes or antinodes at the ends of both
of the strings.
35
36
26. A gas expands from A to B as shown in the graph. Calculate the
work (in joules) done by the gas. (1 atm= 1.01 × 105 N/m2 .)
code 101
a) 12
b) 24
c) 1.21 × 106
d) 2.42 × 106
e) 3.64 × 106
code 102
a) 24
b) 2.42 × 106
c) 1.21 × 106
d) 3.64 × 106
e) 12
37