Download Document 8934316

Physics 2220
Third Exam
Summer 2013
(Chs 31-34)
S OL\A"-/o NS
Name:
------~~~---------
Hassan Allami (NS 204)
Circle your Discussion TA:
Monday 22 July
Peter Peroncik (NS 203)
Mei Hui Teh (LCB 225)
You may use your one sheet of notes and formulas, but you must not collaborate with any
other person. Do all four problems, showing your method and working clearly (a correct answer
alone is not necessarily sufficient). Be sure to include correct SI units in your answers where
appropriate. The number of marks for each part is given in square brackets, [ ], to its right.
conducting rod of mass m is free to slide in contact
~
V
1. In a uniform gravitational field g, a horizontal
-0
~
)(
)(
')(
~
~
y
with long, frictionless, parallel, vertical conducting
rails separated by distance h. Connected across the
top end of the rails (at y
=
0) is a resistor R, the rod
\"t\
and the rails having negligible resistance. There is a
)(
X
uniform magnetic field B perpendicular to the plane
of the rails, pointing into the paper as shown in the
sketch at the right. Having been released from rest
at t
=
0, at some later time t the rod is distance y
from the top end of the rails and is moving
downwards at speed v. In terms only of quantities
defined here, derive algebraic expressions for:
X
X
~
~
V
X
X
)(
X
X.
X
;<
X
)(
)(
X 't..
.
:<
~
h
>~
(a) the electric current, I, induced in the rod, also specifying its direction of flow (left or right)
[4]
in the rod;
(b) the magnetic force, F, acting on the moving rod, being sure to give its direction as well as
its magnitude;
[2]
(c) v as a function of t (Use Newton's second law in the form a = (net force) / mass,
remembering that acceleration is a
=
~~.
equation that results, it may help to define a
=
In separating variables to solve the differential
B 2 h2
Rm as a temporary aid.);
[10]
(d) the terminal speed, vT ' of the sliding rod (You can find this even if you were unable to
do part (c), although vT readily follows as a special case of the formula derived there.);
[4]
(e) the rate at which gravity is doing work on the rod when it is moving at speed vT ;
[3]
(f) the rate at which energy is being dissipated as heat in the resistor when the rod is moving
at speed vT .
[3]
(g) Are the answers to (e) and (f) the same or different? Explain briefly why that should be
so physically.
[2]
Name:
1. (cont'd)
cj)
-11«
tt"'......,...,.
e)(j'l-J:.J.-,
.f,., ('l..)
As &
~YM:t~t"'~1 fPte.,t1;..1
1).1
ft. j
lw,:t /'"
~
t:I~J.
(..f) "'.­
.1.0.,./., yoJ. slider
e,'le.;,.,Y /
wL)., reS"'i:<--tPr, .s;".....3A. ;-LIPN S
So Lu-'\ I 0 rJ.s;
Physics 2220, Summer 2013 Name:
Third Exam Circle TA:
2. Two resistors (RI = 1.0 n, R2
an inductor (L
Hassan
Peter
S 2­
= 2.0 n),
·-------'1
5.0 mH), a capacitor (C ;:;;:
0.48 mF), and a battery (E
12 V) of zero internal resistance are connected as shown in
the sketch at the right. Mei Hui
_ ........­
....
.€
(a) Switch S is thrown to position 1 at
time t = O. At what time t will the
instantaneous power supplied by the
[8]
battery be 36 W?
-
C' L
~------------~
~
(b) After S has been in position 1 for a long time, it is switched suddenly to position 2.
(i) What is the initial rate at which electric charge begins to build on the plates of
the capacitor?
[2]
(ii) Just after the switch is moved to position 2, which point (if either) is at higher
[2]
electrical potential: a or b? Give a briefreason for your answer.
(iii) What is the earliest time after moving the switch to position 2 that the magnetic
[8]
energy stored in the inductor will be half its maximum value?
(iv) What is the earliest time after moving the switch to position 2 that the electric
charge on the capacitor will be at its maximum, and what is the value of that
maximum charge?
[6]
L R c..1·~:t
--p -:: . E r,)
~rth ~ ~
v.JL
k"pw
'R t
..}
.tJ, Cit-t­
1i!..J... -=- 3.0...n.,
4";
thr-o~~ .fk, j~J.~1Jar
b.(..
ill
~ ~er rp-te~ti~(
t
6.
ht:\v~
( ij;) We.
4(
.>ecltt-
-tJ,.~t1
I
,.A1.
II\Jl- .{;.w~
CD!
-='?f~
:€ :-
J
1 (f L ~'I-~
\
--
":L
fA)""
c,".,....Jt.).
w~~· -tAt.
Y"e..f,,-
Itf
(i:.
"IT'
>W\'t(;~
../Ci\~e.
'1-"
.J('s".,p-y(O;;';XfD -9'
~e. c~ 4."')1L
~~
;1'
(f
<..
VI'tI\A..~ ',6."'11)('..,.."".,..,
At
M~veJ..
.L :r:-no, 4)(
"fC
wt -::. .J: -- ~ ~ wt- - : : 2L
if
(\\1
1-
:r:~ -;:. {. ::r:...: ~
~:9. -:g,,-t ~~ ~'1
C:::r<~~-t
~d, w~c~
J!~ (we. J,...
dvt- +:L..lej\l'Ih::')
--r
--60
tt\
c.of~l,,!! ~(..rL b~v\.n.. ..(;;.~ c..~~t
~
~ry/~
"" -,t- WQl.F b~~ (fJ.p"",~ (Jowll1v.Ja,.J.r'
4- s-ke+c-h). ...-rAe.rt.~~rn ~...c.st
E
7,...
e.,-P
of.
U1J. ~ J- U$",4)()~
,,_ J- L:C
-;::l:;>
L.c.
SoL-\;\.~l.oNS
Name:
2. (cont'd)
f-
~
J
-to tt)J~t/;" -z..) .
CoJ c.ut
J-.
-::.....y-....
~,,(:)<:
SP
t- -=
[i ~ /.2.
::!:!:- . ,.
<t-w
",..
-1
SO l-U I/OIVS
Physics 2220, Summer 2013 Name:
Second Exam Circle TA:
Hassan
Peter Mei Hui
3. (a) Find Vrms in terms of Vmax for the
'sawtooth' or 'triangle' wave sketched at
the right. . (Hint: Concentrate on anyone
quarter of the full wave - since the area
between the curve and the axis is the same
for each of its four quarters and begin by
finding an equation for Vasa function of
time t for that quarter.)
-'\(';.....,
[10]
.
( b) A certain transformer has N 1 = 500 primary turns and N 2 = 10 secondary turns.
(i) Ifthe secondary voltage V2 is 120V (rms), what is VI (rms)?
[4]
(li) If the secondary is connected to a resistive load R L = 15 fl, what will be the (rms)
currents 12 and II in the secondary and the primary respectively?
[6]
.fk..
..{:j;"st j, victr1;e.... 01. -tk. .' w tIlv~/,"'.,.t;.J,/
1.'.lL· p-.r.teJ -tJ.ro~' -f.4. ~ri.J/~/
{k
~ I1fUd -l,.
...,-; ,ti" J. .V';..ms-
f
\4£t'"
te~ ~ re",;oJ .~
.1''V:~j(.S. l'f-1::1-J.-t
"f
"L .
-
,­
o
~)
('PjO)
,£~ l' ~
)
' .
'.
Itr
sc·
,,-
0
.
(~J
-v;. ~~)~ ~~)(\2-0V) ~~OOOV = Vi].
l" ) 1:'1. -
-:r1. " (
-- --' 2.D V
-A..J;.
'S ..!l­
'RL
...-
~
-:r: "V".
-= 1::z,'V;. ~ ::t:1- -:: 'I-
"\Ii.
~>--: ~.o A!.
-=:
i'!:'
0
A){i-z..o ~
fDooov
~ G1
C.
-:.
'0",'~
0./ (, A ': I
Physics 2220, Summer 2013
Third Exam
Circle TA:
Hassan
Peter
Mei Hui
4. (a) A plane electromagnetic wave, having wavelength 2.00 m, travels in vacuum in the negative x direction with its magnetic field vector B, of amplitude 1.20 jlT, directed along the positive y axis.
.
(i) What is the frequency, f, ofthe wave?
[2]
(li) What are the direction and the amplitude, Emax , of the electric field vector E associated
with the wave?
[4]
(iii) If B
=
B max cos (kx + cot), what are the values of k and co?
[4]
[3]
(iv) Find the intensity of the wave.
(v) If the wave falls perpendicularly on to a perfectly reflecting sheet of area 1.60 m 2, at what rate is momentum delivered to the sheet, and what is the radiation pressure on it?
[8] (b) Making the (admittedly unrealistic) assumption that a 100-W light bulb is perfectly efficient (converting'all the electrical energy it consumes into visible light) and behaves as a point source (radiating uniformly in all directions), calculate the amplitude of the electric field vector, Emax , at a distance of 1.50 m from the bulb.
[5]
1.
k."
Qii)
~~SY\l.1"e. ~ rp ';:.
T ~. ~ -;.
¥ -;:.
2
'1(
';:::.
} 00
4~ 'f7r'
( S'»he... t.)
~ z '3.I~
07/.8.12 . . . J. r5' x
'3.")\. IpS
---------------------------W
.:f,0\lJ.ll!r
=9
<,.$"»\).. .
I J:>
.
..,-0 ;
-'!i )
M2.
0....
-t " 2" (/S x 10 8 ..--~
~ [C4l Z "'.'flo x loB ~ J.
Go> "
2..-
/./S
J.A.
'"
'f(l.
f