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Unformatted text preview: Htl—STEK PHYSICS 0174
Fall 2008 — P. Koehler First Hour Examination October 6, 2008 (2:002t50pm) This sheet of equations and a calculator are the only aids
ma in the xamintion. ~_r#vi‘_y_m The followig inforation may be useful in answering thestio: —~bi\/b2 ~4ac 2a Quadratic formula: if ax2 +bx+c = 0 then x = 0 cos 0 = b/c
a sin 0 = a/c
90° 0 tan 0 = a/b
b a2 + b2 = c2
If it = Ax? + ij' + All; and E = Bx? + By} + B212 then:
(Axin)i+(AyiBy)j+(AziBZ)I€ and
B = AXth + AyBy + A23: = [ElElcose 1 51:1
0 A vector it in the xy plane that has magnitude [171‘ and points in a direction that makes an angle 9 with respect to the positive xaxis (measured in the'counterclockwise Whaﬁheﬂbwmg—meenemﬁmmAw—me Ax=‘;1cosl9 and Ay=gllsin6 Equations of Motion with constant acceleration: Equ. (1): v)( = v0X + axt The corresponding equations in the
Equ. (2): x  x0 = voXt + 1/2axt2
y or zdirection may be obtained by
Equ. (3): v3 = v03 + 2ax(x — x0) SUbStitUﬁnQ “Y” or “z” wherever “x”
Equ. X _ X0 = 1/2(VOX + Vx)t appears in the equations given.
Equ' (5)3 X  X0 = vxt  1/2axt2 Magnitude of gravitational acceleration near earth‘s surface: 9 = 9.80 m/s2 = 32.2 ft/s2
et: w = m*g CONTINUED ON BACK OF SHEET Newton’s 1St Law: a = 0 Newton’s 2"‘1 Law: Xi“ = ma 6X1 (If the forces are in two dimensions, this vector equation is equivalent to the component
equations 2(13“, )x = max, Z<IZX,)y = may ) 5 I'd . _
Newton 3 3 Law. FAD” — —FBW v2 Magnitude of centripetal acceleration required for uniform circular motion: are = —
I” Frictional force magnitude: static friction: ﬂ. Slay .N kinetic friction: fk =yk N
Work: W=1306T=,F{{c?}0056 Kinetic energy: K = §mv2 Work — Kinetic Energy Theorem: Wm, = AK = K M, — Kim, Gravitational Potential Energy: Ug = mgh Elastic Potential Energy: Uei = 1/2 kx2 (k = spring constant) +Mechanical Energy: E = U + K HEM.“ The mechanical energy of an object is conserved if only conservative forces act it. TEAR OFF THIS SHEET AND USE FOR REFERENCE DURING THE TEST First Hour Examination
October 6, 2008 Physics 0174 (Koehler)
Fall 2008 Page 1 of 7 Print Your Name: *“IMPORTANT NOTICE*** Before you start the test, print your name on each page. Use the blank space provided after each question to work out the problem. If you need
more space, use the back of the sheet. WRITE NEATLY! No partial credit can be given if your work is illegible. SHOW YOUR WORK! No credit will be given for a numerical answer that is
correct but not accompanied by sufficient written work that shows how you arrived at your result. Be sure to enter your final answer into the marked box whenever such a box is
provided. Express numerical answers with the appropriate number of significant figures
and give units when appropriate. DO NOT WRITE IN THIS BOX! ____.____I______~_
Problem (pornts) Score 1 8516?. ) #1 (25) 5 f
#2 (25)
3 )
) Total Test (100) 5.4 Problem #1 (25 points): (a) Which of the five dashed vectors , l l t i l L i  1
[*T 7—1 ' l ‘1 r
represents most closely the vector __ t ‘ ‘ A—B ’? Circle your choice. (A) Vector I Ni Vector (C) Vector 3 (D) Vector :1 (E) Vector 3 Physics 0174 (Koehler) First Hour Examination Page 2 of 7 Fall 2008 October 6, 2008 Print Your Name: 5 T E (b) The positions of two blocks at successive 0.20second time intervals are represented by the
numbered squares in the figure below. Both blocks are moving to the right. Which of the
statements below correctly describes the accelerations of the two blocks? (Circle your choice.)
l 2 3 4 5 6 7
BIOCk ‘3 I I I I I I I
B] k b I I I I I
0C 1 2 3 4 5 (A) The acceleration of block a is greater than the acceleration of block b.
(B) The acceleration of block a equals the acceleration of block b; both accelerations
are greater than zero. .
(C) The acceleration of block b is greater than the acceleration of block a.
The acceleration of block a equals the acceleration of block b; both accelerations are ZBFO. (E) Not enough information is given to answerthe question. ~~~—~»_____(.C.)_A.DQLS.€ pullson a wagon with a force of magnitude F, causing the wagon to move fonNard
with increasing speed. Which of the following answers correctly describes the magni u e o the force that the wagon exerts on the horse? (Circle your choice.) A) The magnitude of the force exerted by the wagon on the horse is zero.
) (
(B The magnitude of the force exerted by the wagon on the horse is less than F.
The magnitude of the force exerted by the wagon on the horse is equal to F. D ( ) The magnitude of the force exerted by the wagon on the horse is greater than F.
(E) The force cannot be determined without knowing the wagon’s acceleration. (d) A small steel ball of mass m is suspended from a hook in the ceiling by means of a
(massless) string of length L. After being pulled aside and released, the ball swings back
and forth like a simple pendulum, with a maximum angular deflection Go from the vertical
direction. Which of the expressions below correctly gives the magnitude of the tension T in
the string at the moment when the ball is at its maximum angular deflection 60’? (Circle your choice.) v2 2 (A) szg (B) szg+mf (C) szg—mvf (D) szgsin¢90 @ T=mg00860 3 Physics 0174 (Koehler) First HOUF Examination Page 3 of 7
l Fall 2008 October 6, 2008 ” 1 Print Your Name: ﬂ 5 TE g (e) Three identical balls are launched with identical initial speeds from the edge of a cliff that is
at a height H above a level plane. Ball A is launched at an angle of 25° above the
horizontal, Ball 8 is launched at an angle of 25° below the horizontal, and Ball C is launched
horizontally. lf air resistance is negligible, which ball will hit the plane below last? (Circle
your choice.) Ball A (B) Ball B (C) Ball c (D) None of them; all three balls will hit the plane below at the same time. Problem #2 25 oints : A projectile is fired from the edge of a cliff (point 0 in the diagram) at a height H above the sea.
The projectile’s initial velocity has a magnitude v0 = 150 m/s and makes an angle 60 relative to
the horizontal direction. The projectile passes through its point of maximum height above the sea at time t1 = 6.50 s after it was fired and it strikes the water at point P at time t2 = 15.5 s after
it was fired. Ignore all effects of airfriction. sea level g; =Jm¢k (a) At what angle 80 (in degrees) above the horizontal was the projectile fired? (5 points) V3=Vog+a5t =2) V’303Vog +43%! 3"? V0J=" J‘£(=63v? w/S My answer is: Scum v =V5¢w9 ==>5¢5vt = $11. 63?“Ys_
°<7 ° ° 0 Vo— ways(ms 90:2;[0 <90 = 5w“(0.‘fas) =,ZS.‘{° V (b) From what initial height H above the sea level was the projectile fired? (5 points)
5—3, = v03 d: #24, 9 => Jawsmm +3£a ti
30:3L’Uoth—éqgtLL=H Myansweris:
H: O— 76’}. ‘{+ NH. 2: WOW .\ N Physics 0174 (Koehler) First Hour Examination Page 4 of 7 Fa12008 October 6, 2008
\ Print Your Name: TE 6
(c) What is the maximum height above sea level reached by the projectile during its flight?
(5 points)
 2.
3‘30 'Vog't—‘t' 2.
jl=gmﬁr=#+mJtl+Ja—Q7tl I Myansweris:
= l90+ LfH — 201 =37¥m (d) What is the magnitude of the projectile’s velocity when it strikes the water at time t2?
(5 points) VAX 3V“: 2 VaCWQO = (3.7.8 (la/S
V23 z V0} 7' “I 'tz=63?“7_’5 ~1§L9ﬁ>§= “003.2 “4/; z 2.. l; _ _ ______ My answer is: (e) What is the horizontal distance traveled by the projectile during its flight from point 0 to
point P? (5 points)
7 0 ’70 7..
X‘X0=Voxf+éaxt => X;_ 0:V0X.tl—+’3£ kt; L Physics 0174 (Koehler) First Hour Examination
Fall 2008 October 6, 2008 Print Your Name: If! A S I E g Page 5 of7 Problem #3 (25 points): A small metal ball of mass m = 0.750 kg is
suspended from a hook by a very thin wire of length
L = 1.25 m and negligible mass. The ball revolves
at constant tangential speed v in a horizontal circle
of radius R. The wire makes an angle 9 = 20.0°
with the vertical (see adjacent sketch). (a) in the adjacent box draw a freebody __
force diagram for the revolving ball T when it is at the position indicated in
the above sketch. Clearly identify all
forces in your diagram. (5 points) 715 Macaw t'ut Hm WL'Ve _. _. F 1*} = {one 0(‘ffdmutz ‘3
_._._.____. _.__. 3 D I . v u ,gn'uce We. [Mus 3am (QCCe(eraxl'c'ou\ ck m UCv+CLw‘ oliv‘ect Ce“, ‘1'" __F _ 0
7 3 ' 7=Tm6=5=mg 'T= 214?: age/v (c) Determine the tangential speed of the ball. (10 points) ﬂu: (48+ {OVCC 0“ H4; (44.“ l/Zijuéf' be Ha; Cem‘n/efml
\/ érei 0‘( Wui‘chg E: “A? “‘41 At‘lrcoll't‘ouc fﬂéiu'ftlg
+0 Hare C€M+€V 0% Hake. CL'VCM (AI 7. My answer is: E:K:T§ﬁMQ: mv $ V: R'T'5"“9 R m SCuce R: L'5L'k9, {44.65 become; vva' Jr'in‘&
n4 (Note: this problem continues on the next page) V: [.23 “4/; My answer is: Physics 0174 (Koehler) First Hour Examination ‘ Page 6 of 7
Fall 2008 October 6, 2008 ” Print Your Name: TE E (d) Determine the work that is done by the tension in the string on the ball during one
complete revolution around its circular path. (5 points) Wr: w5¢ A Myansweris: ' ﬂ ‘ fag wing m4 at US <9/‘W75 hotwa 1‘17 ﬁe.» circular perith , ¢ 6'5 div/60475 yﬂo. u’Zl’: 0
#0er W1 : 0 ..——— Problem #4 (25 points): Two blocks of masses mA = 1.75 kg and m3 = 3.25 kg are in contact with each other while being pushed along a horizontal table top by a constant force F that is applied to block A. This force
has magnitude F = 37.5 N and is directed at an angle 6 = 27.5° below the horizontal (see the
diagram below). The coefficient of sliding friction between each block and the table surface is
uk = 0.225. There is no friction between the two blocks. (a) In the adjacent box, draw a freebody force
diagram for block A. Clearly label all forces.
(5 points) b) Determine the magnitude of the acceleration of the system of the two blocks. (5 points) (
Tranfie? 7%: Z Hack; {eyeFlier, Hm net force, ha; Components.
@ Z<E~JK= “R ‘72,; “7:” = {W4+w_5)ctx (a 2'? (an), = M ~s M w 5 =0 (Vaftﬁfitiiii’? Frau @1 FAIA’rFA/s ~‘ (“4141‘ “Half + BA (“:4 {(443)34 ngaél geucg I94 1‘ QB r/Cuc[FA/ﬂ +FALB) :ﬂK[(l€1/;+M_3)~j —f— 51.1... Q] a ' ' '7 l = €.22§x66.5: answeriS:
bubslt'+u+t'uj "H485 t'ufo@ {162115 : new: 3'6; M, 0“ MA fwﬁ v 5.00th /5 Physics 0174 (Koehler) First Hour Examination Page 7 of 7
Fall 2008 October 6, 2008 “ Print Your Name: K (c) Determine the magnitude of the contact force Fc between the two blocks while the system is
undergoing the acceleration you found in part (b) above. (5 points) CDMSL'AGI’ bloc/(<3 9‘1 L'+S€({:
my a — e =w<<m>=m
E= WB</(/(K‘g +5L\): {M Myansweris:
‘ E=i9.iA/ (d) Determine the work done by the force F while it pushes the two blocks to the right by a
distance d = 1.25 m. (5 points) WF : ($(.{j(.cd, e: (5?.5N)[l.zsm)cmﬁ5’= 97.63" My answer is: (e) Assume now that the force F is applied to block B
instead, having the same magnitude F and angle 9 as
before but pointing as shown in the adjacent diagram. How will this change affect the magnitude of the contact force Fc between the two blocks? Circle your A/F choice, (5 points)
ms (A) The magnitude of Fc will increase The magnitude of Fc will decrease (C) The magnitude of FC will remain the same. The, mat of‘H/xc 2 Hook system We’ll b: ﬁg Same
{009+ 901441 MA 4 M43 ) The Contact" {one WLW {02/ Smalter. END OF TEST ...
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This note was uploaded on 09/11/2011 for the course PHYS 0174 taught by Professor Kohler during the Spring '08 term at Pittsburgh.
 Spring '08
 KOHLER
 Physics

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