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Unformatted text preview: Physics 123 — Analytical Physics
FINAL EXAM Monday, December 20, 2010 9'
Professor RA. Bartynski 10. Answer 5. => ~ c
Your name sticker with exam code. SIGN HERE: The exam will last from 4:00 pm to 7:00 p.111. Use a #2 pencil to
make entries on the answer sheet. Enter the following ID information
now, before the exam starts. In the section labeled NAME (Last, First, M.I.) enter your last name,
then ﬁll in the empty circle for a blank, then enter your ﬁrst name,
another blank, and ﬁnally your middle initial. Under STUDENT # enter your 9digit RUID Number. Enter 123 under COURSE, and your section number (see label above)
under SEC. Under CODE enter the exam code given above. During the exam, you may use pencils, a calculator, and two 8.5 x 11
inch sheets with formulas and notes. There are 30 multiplechoice questions 011 the exam. For each question,
mark only one answer on the answer sheet. There is no deduction of
points for an incorrect answer, so even if you cannot work out the
answer to a question, you should make an educated guess. At the
end of the exam, hand in the answer sheet and the cover
page. Retain this question paper for future reference and study.
When you are asked to open the exam, make sure that your copy
contains all 30 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you
have a question. Please SIGN the cover sheet under your name sticker and have your
student ID ready to Show to the proctor during the exam. If needed, the acceleration due to gravity 011 earth may be take as g 2
9.81 Ill/S2. 1. A student throws a set of keys vertically upward to her sorority sister 4. A pendulum is made by letting a 2.0 kg object swing at the end of in a window 4.0 m above. The keys are caught 1.5 s later by the sister’s a string of length 1.5 111. The maximum angle that the strings makes
outstretched hand. W ith what initial velocity were the keys thrown? with the vertical as the pendulum swings is 300. What is the speed of
a) 894 m/S I Z the object as it goes through the lowest point on its trajectory?
b) 4.47 n1/s ‘3: VHS ' 3 at 4a) 2.0 m/s
c) Cannot be determined 3 “ T b) 1.0 m/s
(1) 3.33 1n/s 4‘0 “3  Z c) 3.5 1n/s
—>e) 10.0 m/s (U. 3+ 3‘51? _ I0 0 Q d) 3.8 m/s
\ 0: t v . A e) 5.4 m/s
2. A force of 11.0 N holds a spring with a 22.0 N/m spring constant in
compression. The potential energy stored in the spring is: 5. Which one of the following statements is correct for an object released
a) 11.0 J F = h 9! W F: “IO N J. R t 22' 0% from rest at a height of 2.3 m? Xi‘F‘lX
) b) 2.75 J :> % z E _ 0 SD m «=9 the average velocity during the ﬁrst second is 4.9 m/s :At l'
c) 5.50 J R _ ' b) during each second the object falls 9.8 m 113, Constant
d 22.0 J 2' ._ : A: c) the acceleration chan<T s by 9.8 m/s every second
e; 5.00 J Usfrlnj : Ji k x : 2'75 J d) the object fallsﬁfgi fang the ﬁrst second of time
e) the acceleration of the object is pro ortional to its weight
3. The horizontal surface on which the 2.0 kg block in the ﬁgure slides is a: 8' WW g w
frictionless. The speed of the block before it touches the spring is 6.0 6. Identical guns ﬁre identical bullets horizontally at the same speed from
m/s. How fast is the block moving at the instant the spring has been the same height above level planes, one on the earth and one on the
compressed 15 cm? The spring constant of the spring is 2.0 kN/m. moon. Which of the following three statements is/ are true?
0 I. The horizontal distance traveled by the bullet is greater for the
+ a) 3.7 m/s moon’
b) 4.4 m/s
c) 4.9 m/s 0 H. The ﬂight time is less for the bullet on the earth.
(1) 5.4 m/s _ .
0 III. The veloc1ty of the bullets at impact are the same.
6) 14 m/s
6 T r ..
a) 111 only H \ \ \
+b) Iandllonly /: ,» r»
c) I and 111 only . . < d ’4
d) 11 and In only H _ i. atl :7 t 2 M
e) I, 11, 111 ’ Z a”
d ': 0.1: t 2,0 (4.0;:— 2,0xroag(0.:5)2
2.19 7. 8. —»C ad 48) A particle moves at constant. speed in a circular path. The instanta—
neous velocity and instantaneous acceleration vectors are: a) both tangent to the circular path 1) both perpendicular to the circular path
perpendicular to each other
opposite to each other
none of the above .3
’0’ l l d) __7
l 6 A 3.0—kg and a 2.0—kg cart approach each other on a horizontal air
track in such a way that their center of mass has a speed of 4.0 111/ s.
They collide and stick together. After the collision their total kinetic energy is: a
El El Ya?
I = m m
16J P» (ll 2 CM )
) 2.0.1
) 24.1
)
) a ,—a
U ' P;=PL 7.1 KE£W
1. 2M— 40.] can’t tell from the given data 2 :: 5_.——~*«"0) : 4'0 T
1 You and a friend are sitting opposite each other at a large circular
table in a restaurant. Your friend is in need of a packet of sugar. On
the center of the table is a circular rotating tray (a Lazy Susan) that
is 2.0 m in diameter and its surface has a coefﬁcient of static friction
as = 0.25. You place a packet of sugar on the edge of the rotating tray
and then, starting from rest, give it a constant acceleration, a, such
that the sugar packet overcomes the force of static friction and ﬂies off
the tray just when it reaches your friend. The angular acceleration7
o,(in rad/s2) that you have given the tray is: b) 9.8
a.) K ’W‘ e c) 2.5
d) 0.20
e) 1.3 «mil—z kg} ..— CL): bvvdEé ‘
“I? l 10. 11. 12. A dumbbell consists of two 15kg masses 011 a rod of negligible mass
and length 0.50 m. The moment of inertia for rotation of the dumbbell
around an axis perpendicular to the rod, passing through the center of
mass, is : l3 [(3 ml {.14 0.94 kg m2
3.75 kg 1112 l
A, 1.9 kg in2 R 'm I: 2" m R z
b 7.5 kg in2 m“ ,. 25
cl 175 k0 in2 v z #15 i @' )
) ' O ZR: 0.30mi
) (D A car of mass ml traveling at velocity v passes a car of mass mg parked
at the side of the road. The momentum of the system of two cars is
a) 0. m 0 ab b) min. MP = P' l' PL 2 mar + z '
c) (m1— m2)v. : mm)"
d) mlv _
ml +7112
e) (ml + m2)v.
s s A
Vectors A and B with their magnitudes are
shown. What is the magnitude of a vector C,
if C = A — B? 40
—=’ a) 45
b) 10 60° B
c) 30
d) 78
e) 90 50
—% O 5‘ ' a I )
c : (40mm 1 + +oméo J.
1‘
 50 L
A
A
s — 30 L + 3i; 13. A bicycle wheel, a hollow sphere, and a solid sphere each has the same
mass and radius. They are all rolling straight on a flat horizontal
surface without slipping such that the total kinetic energies are all equal. \Vhich has the greatest magnitude of angular velocity and which has the least? firm < I hound < Ib . a) The wheel has the greatest; the solid sphere has the lea. . b) The wheel has the greatest; the hollow sphere has the least.
c) They all have the same magnitude of angular velocity.
~—§d) The solid sphere has the greatest; the wheel has the least. ) The solid sphere has the greatest; the hollow sphere has the
least. K5. 5 émv’ﬁ. 13:001.; + I ) wz
=> w 2 = (D 7/ 2
A 20g bullet is ﬁred into a 2.0kg bloc ' of woo placed on a horizontal surface. The bullet stops in the block. The impact moves the block
(1— bullet) a distance of 5.0 in before it comes to rest. If the coefficient
of kinetic friction between the block and surface is 0.25, calculate the
speed of the block (+ bullet) system immediately after impact. a) 20111/5 :(m+ M)'\r b 3.5 m s 2.
.) / 3L :flka‘l'mg/
oi : 5‘0 14. P g
c) 25 m/s f :1 . d
.)d) 5.0111/8 2Cm+ M) e) 2.2 m/s 2 5., A Yh‘l’m ’U‘: 2.02 15. The speed of a 4.0kg object is given by v 2 (2t) 111/82, where t is in s.
At what rate is the resultant force 011 this object doing work at t = 1 s?
a) 48W Pam/t2?”
1))40W 52 :
C) 32W :®&)"U_) a“ it
d) 56W 7
ﬁe) 16W =4'O‘Z*Z
: it w‘ W Z 16. 17. m 18. A boy launches a rock straight up with an elastic slingshot by pulling it
a certain distance a: from the unstretched position. The rock reaches a
maximum height h above the point of launch; where h is much greater
than :11. If the boy then launches the same rock by stretching the
slingshot by 241?, the maximum height will be nearest
r .— _L.
a) h m3 it ~— 2 la 9&2
b) «2:. X 4 1 x
c) 2h, _L a
’W\ lg .9 k X J
_, (1) 4h, 3 4 i 2 '
e) (need mass of rock7 spring constant of slingshot)
If the coefﬁcient of friction between the blocks and table shown in
the figure is 0.3, and the system is moving with constant velocity, the
tension T] is
T1 T2
a) need to know the other I
masses
m = T
5
b) 2 N fl 3 l
c) 4N O.3X1x‘i,£=T,
Md) 6 N
N
m e) 8 N Tl 1}: 6 The turntable of a record player has an angular velocity of 8.0 rad/s
at the moment when it is turned off. The turntable comes to rest 2.5 s
after. being turned off. Through how many radians does the turntable
rotate after being turned off? Assume constant angular acceleration. a) 12rad a): wo+rxt M
b) 8.0rad O = 3,0 +00: 25 :70(:—'5.Z 3';
9c) 10 rad Z
d) 16 rad I 7 .. l
: ,— O( _.""' 3,2 y 255
e) 6.8 rad G 2 t Z( > < :lO/‘Laa 10. For a particle moving under the inﬂuence of a conservative force, which
of the following is false? a) The net work done by the force on the particle is zero if it follows a closed path. maj— W; o f {‘5‘
+b) The work done 011 the particle in moving from one point to another is always positive.  c) The magnitude of the change in kinetic energy of the particle is
equal to the magnitude of the change in potential energy of the
particle. AE : 19 W 0K15= 450 d) It is possible for the force to do go work 011 the particle during
its motion. I? e) The work done 011 the particle in moving from one point to
another can be positive or negative (or zero). I649», 4’43 20. The horizontal surface on which the objects slide is frictionless. If M
= 2.0 kg, the tension in string 1 is 12 N. Determine F. a) 25 N
h» b) 20 N
c) 12 N F
d) 35 N
e) 24 N Fall: 2 Mo iz—T=ZMQ.} M¢=4 => F=5W¢=20N “Tr/Via, 21. The left 50 cm of a meter stick is made of a uniform plastic of density
p. The other 50 cm is made of a uniform plastic of density 2p. If the
origin of the meter stick is at the left end, how far is the center of mass
of the meter stick from the origin? a) 33 cm
b) 50 cm
)> c) 58 cm
{1) 42 cm e) none of these. PM
Wmaﬁwm 22. A mass of 2.0 kg is moving south with a speed of 4.0 m/s while a mass
of 5.0 kg is moving east at 3.0 in / s. They collide at the origin and stick
together. What is the magnitude of the momentum of the combined
mass (in kg iii/s)? q a?
Pi. = P; 2kg 0
l‘ I
a) 11 = 5&5 L " 2*4J i4m/s
—>c) 17 : 15L ’ j s
d) 19 '
L Ski ——>
e) 20 “7:1; W éOfim/s 23. A 2.0—kg mass is projected vertically upward from ground level with
an initial speed of 30 m/s. The mass rises to a maximum height of
35 in above ground level. How much work is done on the mass by air
resistance between the point of projection and the point of maximum height? Wing“;  E H: gal—L
4. a) —0.21 k.] ‘ gm “Ar
1)) +0.21kJ W‘ “ \a: 35
c) —0.42 kJ
(1) +0.42 kJ {WMF my“ ' l“)
e) —O.69 kJ W111 : Wight. _ 551 ‘ m: 24. A baseball outfielder throws a baseball of mass 0.15 kg at a speed of
40 m/s and initial angle of 30° above horizontal. What is the kinetic
I energy of the baseball at the highest point of the trajectory? a) 6.0J ,x'“"“ 240 J /3§°°_ .2 p b) " 9 i are) 90.1  M ’V' '4 d) 5.25.] AtW ‘9 01
e) 120J E‘quif: JiLO‘IS)Q'O 0:030) :90: 25. A 12g bullet is fired into a 3.0—kg ballistic pendulum initially at rest 29. and becomes embedded in it. The pendulum subsequently rises a ver—
tical distance of 12 cm. What was the initial speed of the bullet? n 0.38k1n/s H . b) 0.44 kin/s m M c) 0.50 kin/s .d) 0.54 kin/s
) e 0.024 kin/s m + M 1 Zﬂ(m
NV!)
,1:— ’~ 2 _ 3/
VI. llama—P1,) ’U r i) a)" m
26. A11 escalator is 30 111 long and slants at an angle of 300 relative to the
horizontal. If it moves at 1.0 m/s, at what rate does it do work in lifting a 50 kg man from the bottom to the top of the escalator? am) pm .
a) 49W 5 '
b) 98W Aw mjzgjﬂm gyms
c) 294w =32: at" 5 ..
d) 490W 0 MBO“
A» e) 245W = 50mm?
3 145 4/5 27. A block of mass M is hanging from the middle of a horizontal bar of
length L as shown in the ﬁgure. One end of the bar is held 011 the edge
of a desk and the other end is held up by a rope vertically. What is
the magnitude of the torque exerted by the rope about the edge of the
desk? Assume that the mass of the bar is negligible. a) MgL b) 2MgL “’“e
e? c) MgL/2 I d) MgL/4 c e) The answer depends on
the length of the rope. » M TL
M ’t = O VT}
'G = “1 Q; 1M3
My 7': = 132
28. A torque of 42 N111 gives a large wheel an angular acceleration of
0.78 rad/SQ. What is the moment of inertia in units of (kg In?) of the
wheel? "E: 4L: 3 0.79 1:54 lang a) 32 b) 12 c) 5.1 54 e) 0.98 d)
T 6 —> a) 3.4 iii/s2
b) 4.7 111/s2
c) 4.2 m/s2 A uniform rod of length 2.0 111 is mounted so as to rotate freely about a
horizontal axis that is perpendicular to the rod and that passes through
the rod at a point 0.5 in from one end. If this red is released from rest
in the horizontal position. what is the initial magnitude of angular
acceleration of the rod? The moment of inertia. of a. uniform rod of
mass AI and length L about its center of mass is 11—.2ZUL2. Note7 though, 1 that the ivot )oint is not at the center of massif"
lewﬂw=Q4hH p I
l A a) 8.4 rad/s2 ) 7.4 rad/s2
c) 4.9 rad/s2
d) 6.4 rad/52
e) 3.1 rad/s2 t—Iw In the figure shown, the coefficient of kinetic friction between the block l—LEA
of mass M and the incline is 0.40. What is the magnitude of the
acceleration of the suspended block (of mass 2M) as it falls? Disregard the mass of the pulley and any friction in the pulley. d) 3.9111/52
e) 5.4 m/s2 2M; “araj ~T= 2m =7 T: 21mg”
T— [Answe‘ Mjs’me 2M4
zMgaaL' Mggiwoe + sine):l"lq _ coca sme =30.
Zggjfﬂ" t ) ‘
_ _. 1 Q woe+51na
0“ s ’1 45:2,: 61%
: 3,4 #93:. ...
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