This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **Physics 2101, Third Exam, Spring 2008 March 25, 2003 KEY Name: Signature: Section: (Circle one) 1 (Rupnik, MWF 8:40 AM) 4 (Rupnik, MWF 2:40 PM)
2 (Giammanco, MWF 10:40 AM) 5 (Rupnik, TTh 9:10 AM) 3 (Gonzalez, MWF 12:40 PM) 6 (Sheehy, TTh 12:10 PM) 0 Please be sure to write your name and circle your section above.
I Please turn OFF your cell phone and MP3 player! 0 Feel free to detach, use, and keep the formula sheet. No other reference material is allowed during
the exam. 0 For the questions, no work needs to be shown, and there is no partial credit. 0 For the problems, please write as much as you can explaining to us your reasoning. Lonely right
answers will not receive full credit, lonely wrong answers will receive no credit at all. 0 You may use scientiﬁc or graphing calculators, but you must derive your answer and explain your
work. 0 Please, carry units through your calculations when needed, lack of units will result in a loss of points. a GOOD LUCK! Problem 1 (22 pts) A wheel of radius R = 20 cm, mounted on a frictionless horizontal axle, is used to lift-
a box of mass m = 5.0 kg. When a constant vertical force F" of magnitude 80.0N is
applied to a rope wrapped around the wheel, the box has an upward acceleration a:
of magnitude 0.60 m/sz. The rope does not slip as it passes over the wheel. a=o.eo mis? (a) (5 pts) Draw free-body diagrams for the box and the wheel. Label all the forces. I FM Nd N 09=:{ T; 4w l 6L- ; L I
T __ 2:. . I 2’ -- F x ________ _. (b) (4 pts) Calculate the magnitude of the tension in the left side of the rope.
21a = may
T; -— 4M? : «La, TI'; 49“? +4) =(5'Eg)(‘l.9Z7—+ 0.6 ‘76) z: ‘52.” ‘___,___-—_- (c) (7 pts) Calculate the rotational inertia of the wheel about its axis of rotation (horizontal axle). 23;: Id Mert— d=% M af=41 Rowe-£— exhausts/gs
(t—T,)R=I% F4“, : rig—L I:[F-— M(¢}+a)j [GDU— (511)(‘7.8?;+0-6%)]%1 = l- 37%? at”
I = 137%”? (d) {4 pts) What is the magnitude of the angular momentum of the box, relative to the center of the wheel,
after the force F was applied for 4.05, assuming the motion started from rest. 4r=~3+atzo+(0.5“;{t)(+s)=2.4—~y.s l 1-: 3m+x3=——(m)(9.za)a3+%)£=44%: (1E)? ,r
MIR 1-: I 2 wt 5;; mﬁJ—«dﬁ (e) (2 pts) What is the direction of box’s angular momentum in part ((1)? In
[EIM “Vex; into the _. . - - (~12) out of the page (£2) to the left {—i) to the right (i) upward (j) downward (—j‘) (u) (iii) (iv) (v) we Question 1 (12 pts) A hollow sphere rolls without slipping up a surface inclined at an an-
gle 6' relative to the horizontal. At any moment, Kg represents the
sphere‘s center-of-mass translational kinetic energy and Kr repre-
sents the rotational kinetic energy about the sphere’s center of mass. hollow ’2.—
.. 2. I g
Sphere} ﬁr gdi) 5...... ﬁme (a) (4 pts) During the motion along the incline, the relation between K: and Kr. is Kt>Kr- K“:- ii} Kt : K... top (iii) K: < K... K e {f r a 2-.
iv) Not enough information to answer. m F) ’H‘ 4 k4? let) {5 3
t. 2. 1‘..— 2.
U a. L g .L + 4.05 L {r __
p.12—va +21 as Zuni; 2, at ﬁwimw (Lee)
W’ KMSI-Jh‘ﬁe «l
(b) (4 pts) Which of the following statements is NOT true? i _ At any moment, the speed of the point of the sphere that is in contact with the incline is zero. he
During the motion up the incline, both the gravitational force and the frictional force are doing
negative work. W = O ./
(iii) At any moment, thse speed of the t0p of the sphere (opposite to the contact point), is twice the M6
speed of the sphere’s center-of—mass.
(iv) While angular velocity vector is into the page (clockwise rotation), the sphere’s angular {The
acceleration vector is out of the page (counterclockwise angular acceleration). 94,,
//=’ (c) (4 pts) During the sphere’s smooth rolling up the incline the frictional force points up the incline. if:
' ii) the frictional force points down the incline. -
' -'|-——.._.—...___.
iii) the frictional force points ﬁrst up, then down the incline. 2% fé 0 0'14?
l (
[iv the direction of the frictional force cannot be determined from the data given. Question 2 (12 pts) A bullet of mass m is ﬁred toward a steel block of mass M which is
hanging fmm a thin rod. The rod has length D and rotational inertia
1,, relative to point P. After a very short impact, the bullet bounces
backward with the speed 1:; while the oenter—of—mass of the rod-block system swings up to a height h. The collision is not elastic. Treat both I
the bullet and the block as point particles (point masses). (a) (4 pts) Which of the following formulas relates the speed of the bullet
before the impact (no) to the speed of the bullet (of) after the impact m .30
and to the angular speed of the block-rod system (to) after the impact? ' ‘ ‘ ED—"" (i) mva=—mv,e+Mw+Ipw “but” (i %mv§=%Mw2 mvoD=—mva+(MD2+IP)w I (iv) mvoD = (m + M)D2w _
hm M’Hooh
so em»: = hm? + at? (b) (4 pts) Which quantityfquantities is/ are conserved during the impact for the bullet—rod-block system? (i) Linear momentum and kinetic energy.
(ii) Angular momentum and kinetic energy. (iii) Linear momentum, only. Angular mornentum, only. W $5 ~lﬁ€ {S2 Flo-t él‘gic/
(v) Kinetic energy, only. Mtg %’A&= O (“'E’_ (Unglk'é) (c) (4 pts) To ﬁnd the height h, to which the center-of—rnass of the rod-block system swings after the
impact, one would use (i) conservation of linear momentum. (ii) conservation of angular momentum. (iii) conservation of kinetic energy. (iv) conservation of gravitational potential energy. @onservation of mechanical energy. béemuSé 416 0&9:— MW? w‘ork') (ﬂu . j
‘llué san 3 {.9 lo ‘3“! “473/ ? Ema: (MST
W'lM‘gt is P.on ME (ME Problem 2 (20 pts) A uniform beam of mass M is used to hang a load of mass m at its end. The beam is supported by a horizontal cable and a hinge. The beam is at an angle I9 relative to
a vertical wall. (a) (5 pts) Draw a free body diagram for the beam. Label all the forces. ._\
(b) (9 pts) Find the magnitude of the tension in the cable. Express the answer in terms of M , m, 9, g,
and numerical constants as needed. (c) (6 pts) Find the force on the beam from the hinge, in unit vector notation, using the coordinate system
shown in the ﬁgure. Express the answer in terms of M , m, 9, g, and numerical constants as needed. 3%: : K133+m>63 are] .11“ -+[(H+m)ﬂi (*0 Question 3 (12 pts) Three spheres of masses m1, m3, and 1333 are located, at rest, at distances
:1, b, and c meters from each other, as shown in the ﬁgure. Consider only
gravitational forces between the three particles. . mlmz .
(1) G “2 a.
.. 1m: . "121113 A
n G 1. .
( ) “2 b2 3
m m m m
(iii) G 1 26+6 1 33*.
a”l c2 _ mlmg mlms a A mlmg b) ,_
G — G -— .
i a2 + G (:2 i + c2 (c J m m m b m m a C1
(v) [G 1m2+a 1 3(—)]i+G 1 3(—)5. m
a.2 r:2 c c2 c F ) : G, "4! 3 __|g_
*' 3 y a}- c.
(b) (4 pts) The work done by you to assemble this three-sphere system, assuming they are initially at
rest at inﬁnite separation, is o one—"raw W =A'Mr-V -g/j a“ 0.3+bg+1::2 W ? :1 mlmgmg
G
(n) + a + b + c
(iii) +G 1m” +Gl'w'“3
a. c
‘Gmlmg _ amlmg _ Gmgma : 2/
a c b $Jﬁ
(v) _Gm1m2 _ Gmlms ‘— mgms
a2 c2 b3 (c) (4 pts) The gravitational potential energy of sphere m1 due to the other two spheres, assuming that
gravitational potential energy is zero for inﬁnite separation, is (i) _G mrmams
a2+b2+c2 '— GhiuL _- w
(ii) +G———m1m2m3 u 1" .- r r
a + b + c - 9 {2-1 I?)
‘Gmymi2 _ Gmlms " A ‘
a C ‘
(iv) _Gm1m2 _ Gm1ma _ mama Mfr?”
a c b I; '7 a" ‘1’”! f5; C
2/
(v) +G 1:32 + G 1:13 + szms
0. c [:2 Problem 3 (22 pts) You are about to launch a 20.0 kg probe from a crane that has height h = 0.0100RE above the Earth’s
surface. Neglect Earth’s atmOSphere and the rotation of Earth. Use for Earth’s mass M E = 5.98 x 1024 kg
and radius RE = 6.37 x 106 II]. (a) (6 pts) If you drop a cell phone while on the crane (of height h = 0.0100123) what would be the
magnitude of the cell phone’s initial acceleration? a M : ' x u L Wiﬂ’xlozllgt 1; CM, - _
at” €2ng (“7 ’6 %")[Cl0ll(é.s7mc"m]‘ 4%; /
R341 :— Lo I ﬁt at (b) (8 pts) With what minimum initial kinetic energy must the probe be launched
radially from the crane (of height h = 0.0100RE) if it is to escape the gravitational
pull of Earth? Note the ﬁgure is not drawn to scale. (KJFVMZO because Zéor-o Md 12:0
:; K;:wu-:GMH:VMM _.
Us 4' (b) (8 pts) Suppose, instead1 you would like to launch the probe horizontally from the
crane (with height h = 0.0100123). With what speed should you launch the probe so
that it circles (orbits) Earth at that height? Note the ﬁgure is not drawn to scale. )fﬂ; lat We ¢3RE+h=Lol l3?
GM ' Z ' .u-v" ...

View
Full Document