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**Unformatted text preview: **First Name: ’ Last Name: Section: I 1 March 21, 2007 Physics 207 EXAM 2 Please print your name and section number (or TA’s name) clearly on all pages. Show all
your work in the space immediately below each problem. Your ﬁnal answer must be placed in the
boxes provided. Problems will be graded on reasoning and intermediate steps as well as on the ﬁnal
answer. Be sure to include units wherever necessary, and the direction of vectors. Each problem is
worth 20 points. Try to be neat! Check your answers to see that they have the correct dimensions
(units) and are the right order of magnitude. You are allowed one sheet of notes (8.5” x 11”, 2 sides),
a calculator, and the constants in this exam booklet. The exam lasts exactly 90 minutes. Constants: Acceleration due to gravity at the earth’s surface: g = 9.81 m/s2
Avogadro’s Number: NA = 6.02 x 1023 molecules/mole 1 metric ton = 1000 kg Radius of the Earth = 6.4 x 106 m 641a (Do not write below)
SCORE: Problem 1: Problem 2: Problem 3: Problem 4: Problem 5: TOTAL: Don't open the exam until you are instructed to start. “Out of clutter, ﬁnd simplicity. From discord, ﬁnd harmony. In the middle of difﬁculty lies
opportunity.” A. Einstein First Name: Last Name:___ _ Section:_ I 2 PROBLEM 1
It’s time for the egg drop at the annual Physics 207 picnic. You are to drop an egg from a bridge.
The egg starts at rest and falls a distance H = 7 m before hitting a spring designed to cushion the
landing.
a.) Given that the maximum force the egg shell can Withstand is 5 N and an egg has a mass of 50 g,
What is the maximum value of the spring constant k that will result in a successful egg drop (1‘. e. no broken eggs)? Neglect air resistance and assume the spring is long enough that it doesn’t compress all
the way to the ground. Mints. )
l ’4’ (a e 5W9, : K: + U; : K -,1 U
99 O at L r L
€5l¢ : 95 , 14/13019le aggggz ELM wwé'l‘y") ”1535/
Fa—é’m‘: K AS :7 A5:““
ms p
, __ --'V'V\ ‘5er L ﬂ
.. ] (1-H mtg—3+ & K K)
spring F ”(L
(relaxed) .2- —- J [HQ "W3 Mt + h: PW b.) What is the magnitude and direction of the impulse of the spring force on the egg between the time
the egg ﬁrst contacts the spring“? and the time that the spring is compressed? WIS.) J: (PL—1P; 3 (ELT‘HJO I? :— IjC-—m1f)
a)“: “trelmf all—b1 €33; ‘1:ka H gyms: aggregate {121,314 53 __ ~l‘ mVj-HJ ; ofbébuzsciﬂﬂt? [35 -l (“£ij First Name: a.) Two particles move perpendicular to each other until they collide. Particle 1 has mass m and
momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p. Suppose that
after the collision, the particles "trade" their momenta, as shown in the ﬁgure. That is, particle 1 now
has magnitude of momentum p, and particle 2 has magnitude of momentum 2p; furthermore, each
particle is now moving in the direction in which the other had been moving. How much kinetic Last Name: Section: I 3 Problem 2 energy, Klost, is lost in the collision? Express your answer in terms of m and p. (12 pts.) I? Before collision »isz: f}
K-a After ccﬂlision Z W‘ Z Z
' 2: @P) L = .1 Z
K‘ 27 1‘ an“) (:43) 5:;
2 67/4
2
n ,, 3.. 92.39 .x P2
f w ”L 2(zW) } ’> 7‘
at“ Z 3./Z_ x. [QC—Va“ = -?. f,
\ Lt m b.) Consider an alternative situation: This time the particles collide completely inelastically. How
much kinetic energy K is lost is lost in this case? Express your answer in terms of m and p. (8 pts.) «Do—(Elba) ‘AWLL "hf/323.41.141.99 Mym‘ium f6 Can/userwv/ 420% 199% axe/g, z—@Z+ if 5 (z i) 72 r zl %* é ’”
ZZS’m) 3"") W W k [7" 7'72
5/; 35k: 72... W First Name: Last Name: Section: I 4 Problem 3 You set out to design a car that stores energy in a spinning ﬂywheel with moment of inertia I.
a.) Suppose your car requires E Joules to travel 100 km. You want to be able to travel 100 km between
“spinning—up” the ﬂywheel. What is the required angular velocity of the wheel when it is “spun—up?” (8 pts.) KL-
if“) “ E 1/1 (355W 22%;]
(,0 __ (2E
— I b.) You use a motor to spin the wheel from rest to its maximum rotation speed in one minute at
constant angular acceleration. How much torque is required from your motor? (8 pts.) c.) How many revolutions of the wheel occur during the “spin—up” process of part b? Let I = 50 kg-m2
and E = 2 MJ/km. (4pts.) w (215),)” [”559 rwb 0% First Name: Last Name: Section: I 5 Problem 4 —— Multiple Choice a.) Two people standing on ice (with no friction) throw a ball back and forth. After a couple of throws,
they are (ignore friction): (4 pts.)
1. standing where they were initially.
2. standing farther away from each other.
3. standing closer together.
@moving away from each other.
5. moving toward each other. b.) A ladybug sits at the outer edge of a merry-
go-round that is turning and is slowing down. ( i)
The vector expressing her angular velocity is ““— (4 pts.) 2 l. in the +x direction. 2. in the —x direction. {3* 3. in the +y direction. \q /=" 4. in the —y direction.
11 the +2 direction. x o, 1 the —z direction.
7. zero. 0.) What is the net torque exerted by the four forces about the point A? (4 pts.) F1=100 9i F5150 N '——>—-’7 F3=40 hi 5 : Wk 1“ @gngmm F ,— Y Ferny 3. 180N111
4.200Nrn lw00+ Zxél’n3bX/ﬂ0 - 5X71? 7",5 5. None of the above \l First Name: Last Name: Section: I 6 d. Prof. Timbie’s sensible, small car has a mass of 1000 kg and is parked on the street. His neighbor
runs into it with his SUV. The force (in kilo—Newtons) exerted on Prof. Timbie’s econo-car during the
collision is shown below. What is the ﬁnal velocity of the econo-car ? (4 pts.) 1. 10 m/s {H
338%: A72— (FM , .1 zm/iwiw"
4:40m/s ) ’ ;
5.50m/s 7F; v: AP: L0,:/0 va _
203,, t (S)
0.1 e.) A block of mass m is released from the top of the frictionless track shown.
What is its speed v at the top of the loop-the-loop? (4 pts.)
1. Zgh
2. (2gR)“2
3. [2g(h—R)]“2
(gage-2R)?”
_/ First Name: Last Name: Section: I 7 Problem 5 Suppose you are given the following data points for the measurements of the speed v of a ball (dropped
from rest from a height h) when it hits the ground: a) Assuming as usual a product of Gaussian probability distribution functions for the likelihood function (denoted as
symbol L in lecture), what would you estimate for the true value (or mean value) of v (7 pts.)? p
+5, : i— : 72: M57
M [1—) m
f// g [1/ m. b) What would you estimate for the error in each of the measurements of v (7 pts.)? L U
u , I / a
6v: L Ei/(%"v) GE éﬂy’y‘n c) What would you estimate for the error in the mean value of v (6 pts.)? ...

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