2006 Phys 125 Exam 2

2006 Phys 125 Exam 2 - I EXAM #1 PHYS 125 '26 SEPTEMBER...

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Unformatted text preview: I EXAM #1 PHYS 125 '26 SEPTEMBER 2006 Name: iéfifr \VQ. l E «A ‘ (please print legibly) Oi II <5‘if‘1iii‘“ \‘n a Student ID #: Part Score ffiroblemxxaéé 1 oi s ‘M/ ______ Problem #3 Honor Code Exams must be completed within the allotted time and with no outside assistance. Instructors will periodically enter the classroom, and you are permitted to ask questions of them. However, remember that your instructor is limited in the amount of information he can give. There should be no communication with any other persons (verbal, electronic, etc.) other than the instructor. The use of calculators on the exam is permitted, but is limited to numerical calculation. Any other uses (unit conversion, formulas, graphing, symbolic manipulation, etc) are not allowed. V Please Sign the honor code below as confirmation that you have complied with this policy: “On my honor, I have neither given nor received any unauthorized aid on this exam.” PHYS 125 Exam #1 26 September 2006 Short Answer (40 points) Each of the ten questions below is worth 4 points. 1. A car makes a right—hand turn as shown below at a constant speed. Draw the average acceleration vector. If there is no average acceleration, indicate it with the zero vector 6. 2. Two students, Omar and Erika, stand on the edge of Herzstein Hall’s roof to throw their organic chemistry books ofl“. Omar throws his straight down to the ground, and Erika throws hers straight up with the same initial speed. In the absence of air resistance, Whose book experiences the greatest mag- nitude of acceleration immediately after it is released? (a) Omar’s (b) Erika’s @t is the same. 3. A force acts on an object for some amount of time. If the amount of time is doubled, what happens to the acceleration? (a) It is one—quarter of its original value. 5 b It is one-half of its original value. N It remains unchanged. 4 XV“. L. d) It is twice its original value. (e) It is quadruple of its original value. 0 w” 1 (ll PHYS 125 Exam #1 26 September 2006 4, Two objects, A and B, have position vs. time curves as shown below. At what time(s) do the two objects share the same instantaneous velocitx? (a)Os b Is s a d)3s g (e)4s (f) lsandSS (g) ls,2s,and3s (h) Osand4s. time (s) * hree identical balls are simultaneously released down each of the three ' tracks below. The tracks are identical except for the portion in the middle. Which ball will reach the end of the track first? 1 \ (a) 1 2 6 (I 3 (d) 1 and 3 R/ I at the same time. 6. The speed of a wave on a string could conceivably depend on three quan- titieszuthe mass of the string m, the length of the string L, and the tension the string isfundep m. ' h: V Use dimensional analysis to find a prepoitionality relationship for the i i speed of a. wave on a string using some combination of m, L, and IT}. , W", m ,,,,,,,,,,,,,, ,A- , . .1 fix PHYS 125 Exam #1 26 September 2006 7. You jump off a table onto the floor. As you are landing (from the moment your feet touch the floor to the moment you stop), how does the normal force exerted y the level ground cgmpare to your weight? (. \wéc/ ‘1 XVMWNH A _ A” 8. Racing cars often have Wings on them. These Wings are angled sothe wind rushing over them creates a downward force (much greater than the weight of the car). In one sentence, .how does this help keep the car from siding off the track? ..lfil = Iwi ‘ (c) Ifil < WI 5% 056A {\y, LU out. 9. Suppose that your bicycle’s brakes supply a nearly constant acceleration when stopping, regardless of speed. If you doublgour initialm what happens to the time it takes to stop? \Ji (a) It decreases to a quarter of the original time. «, " WC) - - - it a db (b) It decreases to half of the original time. /_‘ / M c) It does not change. Wk " a; It increases to twice the original time. ‘ I [x x e) It increases to quadruple the original time. k» 375' i _ ma what happens to the distance required to stop? (a) It decreases to a quarter of the original distance. _, .l 7 )( (b) It decreases to half of the original distance. i i ll i Z (c) It does not change. (d) It increases to twice the original distance. It increases to quadruple the original distance. 2:; j i 1 "’3, M ,2: Kl _. 0.15%? W4 : 4 // MAM I ~ I Z r fii (“’3’ K 5'“ p 5?, lbv‘ifiigr ,M” ‘“ I PHYS 125 26 September 2006 comes to him two plays in a row. He is standing in the exact same spot for both plays and throws the ball with the exact same speed both times. In the first play he throws the ball to home plate following the solid path. In the second play he throws the ball along the dashed path to first base. Which ball takes the least time to travel its path? wow§ \ {M ‘ ‘4 ~ w mt m? té‘i‘we... {eff/(Vii \, n A )9 my ,5 ‘z I an»; in q r HOLCIO‘Li Amp PHYS 125 Exam #1 26 September 2006 Problems (60 points) You must work problem #1, but you may choose to work either problem #2 or problem #3. Please circle the number of the problem you want graded on the front of the exam. If you do not, you Will be penalized 2 points on the problem. 1. A lead ball is dropped into a lake from a diving board 10.0 m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. The ball reaches the bottom 5.0 s after it is released. How deep is the lake? Ms: M Mi 0 ref/WM/AA vi «7 K? / f Q Q (“LA/7. ./ Vf)?’ V7 v ' " " ad/ I 7": \ "er/i“, r f fl, W _ w, g PHYS 125 Exam #1 26 September 2006 W ValSOMV’ 7 2. (30 points) This problem is continued on the next page. You are - 9,7» " volunteering for the Doctors Without Borders organization and have been i \ put in charge of delivering medicine to a remote village. You will drop a \ Well-cushioned crate of medicine from an airplane that cruises at a constant i E altitude of 1.0 km with a. speed of 150 m/s. (a) (10 points) In the absence of air resistance, how much time will it take for the crate of medicine to reach the ground? \j' 1 O giwlxb} thzgmidfl‘ Vi), i I“; bit“ i (Mmem . n. , . / _r~ Mt? .z’\ “ woom dig it 42%;” augjjgm N w A" ’2‘ iv “400 “’ 2L All Urge-200093; , a . “96% (a A? “30 JX ‘ x A [3}: i b if (b) (10 points) In the absence of air resistance, at what horizontal dis- placement from the village should you release the medicine? Be sure to also indicate the direction, i.e. “. . . 7 m before/after you pass over the Village.” Myfitgb W” KO MW Exam #1 PHYS 125 26 September 2006 (c) (10 points) In real life air resistance is not negligible In the following analysis, make sure to include drag. i. (6 points) Draw a free body diagram representing the forces on the crate of medicine at some point shortly after it has been released from the airplane. D ii. (4 points) If air resistance is taken into account, does the time to impact get shorter, longer, or remain constant? This is a conceptual, not a numerical, question. A or mix, 1‘va o<§§ PHYS 125 Exam #1 26 September 2006 3. (30 points) This winter Houston is blessed with a nice snow and ice storm. You decide that you want to tow your friend around on a sled. You use a 3—m long rope and pull on it at an angle of 20° above the horizontal. The coefficients of static and kinetic friction between the sled and snow are 0.15 and 0.10, respectively. You are wearing cleated shoes, so you need not worry about slipping. (a) (10 points) Treat your friend and her sled as one 70—kg object, and draw a free-body diagram for the object as you are pulling the sled. Make sure your axes and forces are clearly labeled. (b) (20 points) What is the minimum force needed to get the sled moving from rest? Equation Sheet PHYS 125 Exam #1 Kinematics: w) = dig) A§(t) = tf17'(t)dt 77an = 52—? Ei(t) : dig) A1705) 2 [an dt am = 2—7: Constant Acceleration: 1 As : vat + §as(At)2 71f“, = vi,s + asAt 2a3As = via -— was Forces: 5 : finet : :1?1 m m ~ a ~ Q ~ a ~ 1 a a lfsl S #slnl lfkl = ,uklnl lfrl = min! ID! 2 ZpairA'UQ w = my Good Things toKnow: ME Mass of Earth 2 6 x 1024 kg Ms Mass of Sun 2 2 x 1030 kg Me Mass of electron 2 9 x 10‘31 kg Mn Mass of proton/neutron 2 (5/3) X 10'27 kg Ce Circumference of Earth 2 4 x 107 m rs/e Sun—Earth separation distance 2 1.5 x 1011 m 98 Grav. acceleration at surface of Earth 2 10 m/s2 2 G Gravitational constant 2 g x 10‘10 Nmz/kg2 yr 1 Year 2 71' x 107 3 pair Density of air at 20°C 2 1.2 kg/m3 0 Speed of light in a vacuum 2 3 X 108 m/s vs Speed of sound in 20° C air 2 340 m/s 6 Fundamental unit of charge 2 1.6 x 10‘19 C 1/471'60 Electrostatic constant 2 9 x 109 Nm2/C2 no Permeability constant 2 47r x 10‘7 Tm/ A BE Magnetic field near Earth’s surface 2 5 x 10”5 T do Approximate nucleon diameter 2 2.4 fm Binomial expansion (1 + as)" 2 1 + me, for x < 1 1 in = 2.54 cm Circumference of a circle 27r R 9 lbs 2 40 N Area of a circle 7T R2 4 9 mph 2 4 m/s Volume of a sphere % R3 1 MeV 2 1‘6 X 10‘13 J Surface area of a sphere 471' R2 1 rad I 0.010 J/kg 1 Ci 3 3.7 x 1010 Bq E 3.7 x1010decays/s Exam #1 Name: RC! 0C» I 'se . 1 PHYS 125 26 September 2006 ID: S 0/0 7 3g 75" Steps Max Score 6 should point down and to the right 4 at 45°. 0 (c) It is the same. 4 LT, (c) It'remains unchanged. 4 (c) At 2 s 4 L (0) Track 3 4 0 v = i/ m 4 '0 oc m 1 [ v (x x/E 1 l 1) cc 1 / fin— 1 1 nothing else 1 I (a) [m > [13' 4 O 3" ":‘g; : gs _ w «'3‘ _ '4 '7 1: Racing cars ‘ ' 4 It increases normal force, 2 I) which increases friction 2 5: Braking on a bicycle 4 i (d) Time doubles 2 2 (e) Distance quadruples 2 (a) Takes longer ' 4 <2) Ojafltal 40 i Exam #1 26 September 2006 Problem Steps 1 PHYS 125 Max Score Find time to hit water 10 Use a. form of As = U3)1At + éasAfi 2 __ Initial velocity is zero 2 Acceleration is :l:g 2 Displacement is :blO m 2 Accurately find time to hit water At] = 2 ___ x/2As/g '1 1.4 s Solve for speed entering water 10 Method #1 Use a form of 2a3As = vi! — vii 2 Initial velocity is zero 2 ,2 Acceleration is :tg 2 - ‘ ,! Displacement is :blO m 2 ' i Accurately solve for final speed 11 = 2 ‘ x/2a333 Method #2 Use a form of v” = 031i + asAt Initial velocity is zero = 14 m/s Acceleration is :l:g Time is from above Accurately solve for final speed 12 asAt = 14 m/s Find depth of water 10 Use a form of A3 = mm + éasAtz 2 Initial velocity is final velocity from above 2 Acceleration is zero 2 2 l, r,» Time is 5.0 3 minus the time from above X, " At2 = Attot — At] 2 3.6 s % Accurately solve for depth A3 = 'uAtg 2 1 50 m Appropriate units of distance I z 7 11/“ Total 30 r Exam #1 Problem Steps 2a 2b 2c Time to reach ground Use a form of A3 = vs,iAt + %asAt2 Initial velocity vertical direction is zero Acceleration in vertical direction is :l:g Displacement in vertical direction is in) km = 1.0 x 103 m , Accurately find time to hit ground At = x/2Ay/g2 14 3 Appropriate units of time Horizontal range Use a form of A3 = 123,1At + éasAt2 Initial velocity horizontal direction is $150 m/s Acceleration in horizontal direction is zero Time is from above Accurately find horizontal displacement Ax = vat 2 2.1 km Appropriate units of distance Before the plane passes over the village With Air Resistance i. FBD Weight must be included Weight must point down Drag must be included Drag must point horizontally or at some angle above the horizontal; it cannot point vertically. There must be no other forces present ii. Time is longer. veal PHYS 125 26 September 2006 Max Score 10 2 2 2 2 )—A tt‘tHVlW” t“hl%%i“ 3O Déltlg btfl“ PHYS 125 Exam #1 26 September 2006 , Problem Steps Max Score 321 FEB 10 Weight must be included 1 Weight must point down 1 Normal must be included 1 Normal must point up 1 Tension must be included 1 Tension must point z 20° above the hor~ 1 1!! WW izontal Friction must be included 1 Friction must point horizontally in the di— 1 rection opposite that of tension There must be no other forces present 2 3b Minimum Force Needed 20 Apply Newton’s 2’” Law in the vertical 2 “ Fget = may COMPONENTS of lfil + [T] sine — 113] = 0 +177} 2 HT; sin 20° 2 —]u'z‘[ 2 ill! Apply Newton ’8 2"”! Law in the horizontal 2 Fifet 2 mail: COMPONENTS of [TI c030 — jf;| = O +|Tl cos 20° 2 __ ~lf§i 2 . Use [flizpsm 1 __ Use pa = 0.15 1 __ Use from y-direction = mg ~ 1 ___ m sin 20° Use HZ! from z-direction [fl] = cos20° 1 _ Find minimum tension “1114/7: 1 “ ,usmg/(cos 20° + ,us sin 20°) If Appropriate units of force V/ 1 a Total 30 __ ...
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2006 Phys 125 Exam 2 - I EXAM #1 PHYS 125 '26 SEPTEMBER...

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