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Unformatted text preview: Physics 1 Final Exam (AM) 3!20i2009 Name; K E Ll) , start 1. (This problem is worth 40 points.) A small object of mass m is released from rest at the top
of a frictionless, stationary, semicircular ramp of radius of curvature R. The object then slides
down the ramp. (3) At the instant the object has moved an angle 9 down the ramp as shown, what is the speed of the object? Your anSWer should involve no quantiﬁes other than m, R, 0, and g. (It may or
may not involve all of these.) For full credit, show your work, simplify your answer, and
draw a box around your answer. “QC”; «3: R
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0+ M52 : q—{MV2+M8_(EEsm a) v1: 232mm 8) ‘V=4/2323ma (b) At the instant the object has moved an angle Bdown the ramp as shown, what is the tangential acceleration
of the object? Your answer should involve no quantiﬁes other m, R, 0, and 3. (it may or may not involve
all of these.) For full credit, show your work, sintplify your answer, and draw a box around your answer. Lacie xi ﬁrm (M objec'l': Hat'wa ﬁrm; 9’1, o I So '{wwi : mgksme ) Ema (’7 “‘3
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9306 \x ZFX : mam (90° 6)= W3 case = max 30 «x wﬁ SincexMis is Wbpaﬂtl'f‘ms is ﬁlm: (0) At the instant the object has moved an angle 9 down the ramp as shown, what is the magnitude of the
nomalforce that the ramp exerts on the object? Your answer should involve no quantities other than m, R, 0, and g. (It may or may not involve all of these.) For full credit, draw a freebody diagram of the object at this
instant, label each force and state what object exerts that force, show your work, simplify your answer,
and draw a box amund your answer. a ‘ (ﬂaw Locilr aﬁeld aJQ' an object: _ I
ZFLr :: 77 mg 005(90~6)= Wang Sli/ie: M447 wmrMa wi—Sfeecq V M 0194601? PM 2:
V2. SubsHlmla V=q/2823m6 {30m (30): 01—. masme +33 '23ESIM9= Physics I Final Exam (AM) 3l20/2009 Name: 2. (This problem is worth 40 points.) 1‘ T
A ball of mass m is launched at an angle of 45° 213
from the horizontal toward a large cylindrical
storage tank of diameter D and height 2D. The ball _;A4(§° u is launched from the same level as the base of the i
. . . I<
tank and 1s a distance 6D away. Ignore air
resistance. l 1
Possibly useful information: sin 45° = T , cos 45° 2 — , tan 45° 2 l
2 J5 (a) What are the minimum and maximum launch speeds that will cause the ball to go into the tank? Your
answers should involve no quantities other than m, D, and g. (They may or may not involve all of these.) For
full credit, show your work, simplify your answers, and draw a box around each answer. . _ 1‘” Ba." (3.233155 X= 61)) (1:20
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____L_ _ _.. 20 (b) [NOTE: You can do this part without first having done part (a).] You launch the ball with a speed such that
F it is at the high point of its trajectory when it is directly over the leftmhand side of the storage tank. It turns out the ball is actually a small bomb, and at the high point of its trajectory it explodes into a piece of mass W3 and
a piece of mass 2m/3. The piece of mass m/3 falls straight down and the piece of mass 2111/3 ﬂies horizontally
to the right. How far to the right of the launch point does the piece of mass 2m13 land? Your answer should
involve no quantities other than m, D, and g. (It may or may not involve all of these.) For full credit, show
your work, simplify your answer, and draw a box around your answor. 35L“ LS A'i' WM all». XI‘éD
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M “13%?”an Kamvx = "4;; =4f%' I23!) 2 MW All x~wowuauiwm 6°14 Mia pieces? mass 2.44/3 . SD erM‘féap ._ (Ba—w)sz ‘ ~ ~  D
ctrLA szz—g—‘mgpl' Tth=i1mei~onse~ 54%: £513 = 551; ) So Pieced? (Mags 1442 W our «7? X2 6D‘i‘ KEV Physics 1 Final Exam (AM) 3/20/2009 Name: 3. (This problem is worth 49 points.)
A block with mass m} is placed on an inclined plane with slope angle or. This block is connected to a second, hanging block with mass m1, mix, I
by a ii ghtweight cord that passes over a small, frictionless pulley that 5 ’ I 1 :1
does not rotate. The coefficient of kinetic friction for the block of  xxx” WT '
mass m] on the inclined plane is ,uk. When the two blocks are reieased, ‘ ' . . the block of mass mI accelerates up the inclined plane and the block of X0! "'2 mass m,_. accelerates downward. (at) During the time that the block of mass m2 deseends a distance d, how much mechanical energy is lost? Your answer should involve no quantities other than m1, m2, 0:, ,uk, 3, and d. (It may or may not involve all of
w these.) For full credit, show your work, simplify your answer, and draw a box around your answer. — positive since \ 5° Wvl/Uk 1/ ’3 ts
rk $58 ﬁ=ﬂwg 603 W / 33 W W W ‘lwﬁﬁlm 5‘! imam" ’de " (b) Find the tension present in the cord while the two blocks are accelerating as described. Your answa should involve no quantities other than m1, mg, or, pk, and 3. (it may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answer. 4% x MW‘SMIMU':
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Wyl‘Mz (wz—ﬂkm’ casM—wlsmor)
Ml+wl { “4‘ng )(lwkcoamsmcr Ml+m7a :Mrtzg Physics 1 Final Exam (AM) 3/20/2009 4. (This problem is worth 40 points.) A block of mass m is connected to two ideal horizontal
springs having force constants k, and k2 as shown. The
system is initially in equilibrium on a horizontal surface. The Name: coefficient of kinetic friction between the block and the
horizontal surface is [1,. Initially neither spring is stretched or compressed. You now push the block a distance d to the right and release it from rest. (a) How much work did you do to push the block a distance d to the right? Your answer should involve no
quantities other than k” 19, m, pk, g, and d. (It may or may not involve all of these.) For full credit, show your
work, simplify your answer, and draw a box around your answer. In Low? 7m, £0: CWCA’WFM emit 73$. 4'? ")7 W3 7* thinning? (b) What is the acceleration of the block just after you release it from rest? Your answer should involve no
quantities other than k,, k1, m, ,uk, 3, and d. (It may or may not involve all of these.) For full credit, show your
work, simplify your answer, and draw a box around your answer. AA “’4 <——"— 23: organza—75,: MK
75
k lg/‘ﬂ‘ﬂwa 50 Hal—PBX “ﬂip/’48 : “Mix ax =3: (so, ) 7%? (c) After several back—and~forth oscillations, the block returns to rest at the position where neither spring is
stretched or compressed. What was the total distance that the block traveled from when you released it from rest? Your answers should involve no quantities other than kl, kg, m, ,uk, 3, and 01. (They may or may not
involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your
answers. 7%3/4?
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Stank?! sire/Maw? E2 :_ 0 (block wade @ rash mm 8,915“? Accident)
Lelﬂzzﬁoﬂishmce Meal (Hg)? l E: wigs
( .— Z KEV Physics 1 Final Exam (AM) 3f20l’2009 Name: 5. MULTIPLE CHOICE. (This problem is worth 40 points.) For each question, draw a circle around the one best answer. Each question is Worth 4 points. There is no
penalty for guessing. U58 the statements and diagram below to answer questions (a), (b), and (e). The diagram is a view from above of a hockey puck sliding, with a constant velocity, from point “a” to point
“b” along a frictionless horizontal surface. When the puck reaches point “b”, it receives an instantaneous horizontal ‘kick’ in the direction of the heavy print arrow. (a) Along which of the frictionless paths below will the hockey puck move after receiving the “kick”? er it receives the “kick” @ (b) The speed of the puck just .
I? (i) equals the speed v0 it had before it received the “kick”. (ii) equals the speed v it acquires from the “kick”, and is independent of the speed v0.
(iii) equals vn + v. (iv is smaller than either 3 eed v or v.
(v) is greater than either of the speeds v0 or 12, but smaller than v0 + v.
(e) Along the frictionless path you have chosen, how does the speed of the puck vary after receiving the
“kick”?
(i) No change.
(ii) .on inuously increasing. (iii) Continuously decreasing.
(iv) Increasing for a while, and decreasing thereafter.
(v) Constant for a whiie, and decreasing thereafter. (CONTINUED ON NEXT PAGE) Physics 1 Final Exam (AM) 3/20/2009 Name:
5. (continued) Refer to the drawing on the right when answering questions (d), (e),
and (f). The drawing depicts a block sliding along a frictionless ramp. The eight
numbered arrows in the diagram represent directions to be referred to when
answering the questions. > (d) When the block is at position I, which of the arrows in the diagram best
represents the direction of the net force on the block? . (i) 1
(ii) 2 (iii 3 (v) 5 (vi) 6 (vii) 7 (viii) 8 (ix) None of the arrows, the net force is zero. @ (e) When the block is at position II, which of the arrows in the diagram best represents the direction of the net
I force on the block? (ii) 2 (iii) 3 (iv) 4 (v) 5 (vi) 6 (vii) 7 (viii) 8 (ix) None of the arrows, the net force is zero. @ (f) When the block is at position 111, which of the arrows in the diagram best represents the direction of the net
force on the block? (i) 1
(ii) 2
(iii) 3 (iv) 4
(v1) 6
(Vii) 7
(viii) 8
(ix) None of the arrows, the net force is zero. (CONTINUED ON NEXT PAGE) Physics 1 Final Exam (AM) 3/2012009 Name: 5. (continued) (g) The positions of two blocks at successive 0.20second time intervals are represented by the numbered
squares in the diagram below. The blocks are moving to the right. Do the blocks ever have the same speed? (i) No. (ii) Yes, at instant 2. (iii) Yes, at instant 5. ' Yes at instants 2 and 5.
(v) Yes, at some time during the interval between instants 3 and 4. (h) A ball of mass m, radius R, and moment of inertia 1 begins rolling from rest with constant angular
acceleration down a hill. If it takes a time T for the ball to make the ﬁrst complete revolution, how long will it take the ball to make the second complete revolution? 2 (i)2T _._._‘O(4;
'2. (ii)T«E 9— £41,
(“DT 6:0—5 211: 21r=?'_°<'T '9 T: y
. T
()— 2.
w J5 0:0etlrr: Nitric/Jr: ‘9 “E: «5&1 = 4/2 T %4ﬁmﬁr6:’2r+LiWi5 ﬁT—T=T[4/2ﬁl)
(VDTl—ﬁ] A —.3
q {g (i) The drawing to the right depicts the paths of two colliding steel balls, P and Q. Jipﬁ . PQZ
k? Which of the arrows below best represents the direction of the impulse applied to ball Q ‘\ x'
by ball P during the collision? an if,
(ii) (iii) (iv) (V) I, ‘\
I ‘
/ \ __._.__.. X ‘A (CONTINUED ON NEXT PAGE) ._‘x (22 ‘ Pact ._':.‘ Physics 1 Final Exam (AM) 3/20/2009 Name: 5. (continued) Ls b (j) Consider the vectors :4 = 31° +4} , E :51: +2]; , and C = 2 j— I}. Which statement about the angle 0
~ between the vector 24 X if and the vector (3' is correct? (09:0 f A Q (ii)0<0<90° .3 _. J A A A
(iii)e=9o° AXE: 3 4 o : 8c 4>J “ZOL
(iv) 90° < 0<180° 5 0 2 (v) 9: 180° (vi) not enough information given to decide (reg) . a: (ea—ejazoa), (2ft) ENDOFTHEEXAM : 4242028” <0 0< 6(90 ° ...
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This note was uploaded on 04/24/2011 for the course PHYS 1 taught by Professor Fridluund during the Winter '08 term at UCSB.
 Winter '08
 Fridluund
 Physics

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