Download EXAM 1

Physics 2220
Spring 2014
Paolo Gondolo
EXAM 1
PLEASE FILL IN THE INFORMATION BELOW
Name (printed):
Name (signed):
Student ID Number
Discussion Instructor:
U __ __ __ __ __ __ __
Anthony
KC
Matt
Paul
Peter
Important!
You are not required to answer all questions in this exam. You will receive points
toward your exam points for every question correctly answered. Partial credit is
available, however a minimum amount of work and explanation must be shown to
receive any credit (for example, a mere list of equations with no explanation of their
connection to the problem will not receive credit).
Physics 2220
Spring 2014
Paolo Gondolo
Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes).
1 ft = 12 in (exact)
1 m = 3.28 ft
1 mile = 5280 ft (exact)

x


x 2  a 2 dx 
1
3

x2  a2

3
1 hour = 3600 sec = 60 min (exact)
1 day = 24 hr (exact)
2
2
gearth = 9.80 m/s = 32.2 ft/s
gmoon = 1.67 m/s2 = 5.48 ft/s2






dx
 x2  a2 
3

x
a2 x2  a2
1 year = 365.25 days
  ax
e
dx


1 kg = 0.0685 slug
1 N = 0.225 pound
1 horsepower = 550 ft‫ڄ‬pounds/s (exact)
24
Mearth = 5.98 × 10 kg
Rearth = 6.38 × 103 km






Msun = 1.99 × 1030 kg





Rsun = 6.96 × 108 m
22
Mmoon = 7.35 × 10 kg
Rmoon = 1.74 × 103 km
G = 6.67 × 10-11 N‫ڄ‬m2/kg2
9
2
2
k = 8.99 × 10 N‫ڄ‬m /C





εo = 8.85 × 10-12 C2/(N·m2)
eelectron charge = -1.60 × 10-19 C
melectron = 9.11 × 10-31 kg





μo = 4π × 10-7 T‫ڄ‬m/A (exact)
N(Avogadro's No.) = 6.02 × 1023 atoms/gm‫ڄ‬mole
26
= 6.02 × 10 atoms/kg‫ڄ‬mole
cos(a ± b) = cos a cos b ‫ ט‬a sin b
xdx
 x2  a 
2 3/2
xdx
a2  x2

1
x2  a2
  a2  x2
dx
 n  x  x 2  a 2 


x2  a2
1  a  x 2  a 2
  n
a 
x
x x2  a2

dx
x a





x
x
 sin 1   , or  cos 1  
a
a
a2  x2
xdx
2
2
 x2  a2
dx
sin(a ± b) = sin a cos b ± sin b
mproton = 1.67 × 10−27 kg
h = 6.64 × 10-34 J
π = 3.14
8
c = 3.00 × 10 m/s









1 Tesla = 10,000 gauss (exact)
ρ(H2O) = 1000 kg/m3
1
  eax
a









dx
1
 n  a  bx 
a  bx b
dx
 a  bx 2

1
b  a  bx 
Physics
Physics2220
2220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 1
Show all work!! Report all numbers to three (3) significant figures.
A small sphere of mass m = 7.20 g and charge q1 = 30.8 nC is attached to the end of a string
and hangs vertically as in the figure. A second charge of equal mass and charge q2 = −58.0 nC
is located below the first charge a distance d = 2.00 cm below the first charge as in the figure.
(a)
(b)
[10 pts.] Find the tension in the string.
[10 pts.] If the string can withstand a maximum tension of 0.180 N, what is the
smallest value d can have before the string breaks?
Paolo Gondolo
1
Physics
Physics2220
2220 Fall 2009
Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 1
Show all work!! Report all numbers to three (3) significant figures.
The two charges in the figure are separated by a distance d = 5.00 cm, and
Q = +2.00 nC.
(a)
(b)
(c)
[10 pts.] Find the electric potential at point A.
[10 pts.] Find the electric potential at point B.
[10 pts.] A test charge q = -3.00 pC moves from point A to point B. What is
the change in its electric potential energy UB - UA? Is the test charge moving
faster at point A or at point B?
Paolo Gondolo
2
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Exam 1
Discussion TA: ___________________________
Show all work!! Report all numbers to three (3) significant figures.
A plastic rod with positive linear charge density λ is bent into the quarter circle
shown in the figure. We want to find the electric field at the origin.
(a)
(b)
(c)
[10 pts.] Write expressions for the x- and y-components of the electric
field at the origin due to a small piece of charge at angle θ.
[10 pts.] Write, but do not evaluate, definite integrals for the x- and
y-components of the net electric field at the origin.

[10 pts.] Evaluate the integrals and write E net in component form.
Paolo Gondolo
3
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 1
Paolo Gondolo
4
Show all work!! Report all numbers to three (3) significant figures.
[20 pts.] You have a 2.0 Ω resistor, a 3.0 Ω resistor, a 6.0 Ω resistor, and a 6.0 V battery (neglect its internal resistance).
Draw a diagram of a circuit in which all three resistors are used and the battery delivers 9.0 W of power. (Hint: What
equivalent resistance should the circuit have?)
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 1
Paolo Gondolo
5
Show all work!! Report all numbers to three (3) significant figures.
The circuit in the figure has been connected long enough to fully charge the capacitor.
(a)
(b)
(c)
(d)
[10 pts.] Find the current through the 5.00-Ω resistor at the top, including its direction if non-zero (from c to d, or
from d to c).
[10 pts.] Find the current through the 3.00-Ω resistor, including its direction if non-zero (from c to f, or
from f to c).
[10 pts.] Find the voltage across the capacitor.
[10 pts.] Find the energy stored in the capacitor.
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 1
Paolo Gondolo
6
Show all work!! Report all numbers to three (3) significant figures.
A point charge q = 20.0 nC is located at the center of a uniform ring having linear charge density λ = -10.0 nC/m and
radius a = 0.50 m, as shown in the figure. Determine the total outward electric flux through a sphere centered at the point
charge and having radius R, in the following two cases (do not forget the units):
(a)
(b)
[10 pts.] R < a (illustrated in the figure),
[10 pts.] R > a (not illustrated in the figure).
Ph~sil"S
22211
Paulo Gondulo
Spl"ing 20U
_________________
Name: __~£=~~+~~~
Unid: ____________________________
1
Exam 1
Discussion TA: .~--------------------
Show all work!! Report all numbers to three (3) significant figures.
A small sphere of mass m = 7.20 g and charge ql = 30.S nC is attached to the end of a string
and hangs vertically as in the figure. A second charge of equal mass and charge q2 = -5S.0 nC
is located below the first charge a distance d = 2.00 cm below the first charge as in the figure.
(a)
(b)
{lO pts.] Find the tension in the string.
{lO pts.] If the string can withstand a maximum tension ofO.lS0 N, what is the
smallest value d can have before the string breaks?
Td
~
(a.)
cr\ :
->
0::
• /11 vert Ic",l
F;;ET =
-?
-P
-
T +- G, +
olirec.tio1tt. :
->
k c·
d "'' '1. =
-')
F.,
\ t\}. \
or
IHA ~ - (n'I,
L
if
~
-r:=.
O. II/ I\J
~
Ph~sjl'S
Name:
Unid:
Spl'jng 201.t
22.20 Pau I
-----------------------
Discussion TA: _._________________
Paolo Gon<lolo
n.~51 ~~~o
Exam 1 F7J I
r
Show all work!! Report all numbers to three (3) significant figures. A~
2
_____________ B
The two charges in the figure are separated by a distance d = 5.00 cm, and Q=+2.00nC. (a) (b) (c) [10 pts.} Find the electric potential at pointA.
[10 pts.} Find the electric potential at point B.
[10 pts.} A test charge q = -3.00 pC moves from point A to point B. What is the change in its electric potential energy VB - VA? Is the test charge moving faster at point A or at point B?
d
"­
C .~~.I·------d------~~-~
Q
0) -VC< VQ
;0
~
4
lQa
0.
.J Cl
.- 1I1rfoJ -I- q,,-ft4
n
q~ [tt-J71 ~6"b V I
C')Vti-=­
---
D
2Q
*D~' 2&~oIR
Ph~ ... il''''
220 Spl'ing 2111..t
Paolo Condolo
kc..
Name:
Unid: _ _ _ _ _ _ _ _ _ _ _ _ __
3
Exam 1
Discussion TA:· ,
--------------------
y
Show all work!! Report all numbers to three (3) significant figures. A plastic rod with positive linear charge density .A. is bent into the quarter circle
shown in the figure. We want to find the electric field at the origin.
(a) (b) (c) ------~~~--x
[10 pts,} Write expressions for the x- and y-components of the electric
field at the origin due to a small piece of charge at angle e,
[10 pts.] Write, but do not evaluate, definite integrals for the x- and
y-components of the net electric field at the origin.
[10 pts.] Evaluate the integrals and write E net in component form.
/~
~.
' 0
:, at ::
,~~ .,)
~/
• t-Joy.)
1'6:: IL'
ML-
.l~
\Lt-
Il..~
'f
W)
e
V<~ ~;" Q
J.E,(
le,....~~ ~
elf)' = ~1 £ ~,,81e
'::> Q1 -
--
-
rill
- ~ Si 1tl9
ILl- 1
I={
1(
(
(}
11;..
• ) cA}
~0
~'I\ f)
'
OC1)
\ . ::
Sl" 46 -
~'(\
0
~
/-
0 ~
1
o
o
(tV)
• 1 );1\&
\;)
&1/2­
J-e
~
- ((o~& 10 -:. - (lo'?"h - U»
liL 1
-1Z. 'I--f"\
{
tl<-
.:\
1'\
­ Il '1
~~------------------------------
0)
-:::::
[0- ()
~
1­
~6-
Ph~ sil's
1211
Spring 2UI...
Paolo Gondolo
Name: _----'ML-....k.JCO""'-+'--+--=------_ _ _ _ __
Vnid: ---------------------------Discussion TA:· --------------------.
4
Exam 1
Show all work!! Report all numbers to three (3) significant figures.
[20 pts.] You have a 2.0 n resistor, a 3.0 n resistor, a 6.0 n resistor, and a 6.0 V battery (neglect its internal resistance).
Draw a diagram of a circuit in which all three resistors are used and the battery delivers 9.0 W of power. (Hint: What
equivalent resistance should the circuit have?)
1~1~[
flu..
)0
PDWV .le..I:vere,. J ~y --t~
:-t.
(61) ) ....
\/1.
q...e..t
--
~
:::
--'1~
P
-
p-= v'l..
~","~~Iy (~
--=-1 \.J
R.1,
'{JL
(YOli.
c.",A
o(../So
lit' j
e--I ·h,,'.. /rr} ir'\
f::-:J V tv"'-ue. .t:=
'1fl-~
tV"J, c.. ·fh 114
.
ilk .... lkr
T 1..(
L"
8~ Iy Y11''Ie.c.
-I
e.. J
'lJL
6~-L'8CJL
(Z~
-I'.,.
;s
~ tl-d 4~
(.-1- I)--1
')
oj
(;
pA.rtll/fel
:=.
re-5.'sf.r~
'IlL
.c­
or
LJ2. -t 7.J2. -::
Qe..fr,::
bV
l{ JL
'-{..f}.
(Su':O ')
)
Physics 220
Name:
Paolo Gondolo
Spring 2014
R<:t.1I\
Unid: _ _ _ _ _ _ _ _ _ _ _ __
Discussion T A:
------------------
5
Exam 1
Show all work!! Report all numbers to three (3) siBnificant fiBures. The circuit in the figure has been connected long enough to fully charge the capacitor. (a) (b) (c)
(d)
[10 pts.} Find the current through the 5.00-0 resistor at the top, including its direction if non-zero (from c to d, or
from dto c).
[10 pts.} Find the current through the 3.00-0 resistor, including its direction if non-zero (from c to[, or
from/to c).
[10 pts.} Find the voltage across the capacitor.
flO pts.} Find the energy stored in the capacitor.
4.00 V
T
d
c
h
5.00.n
+
S.OOV
3.00 V
3.00n
+
6.0011F
5.00n
1=0
g
i;:::l ',c--~k 0ff5
IWbP bfJ:
l'*f c; !ef:
.
e". •
I
VI - I%. 12. 1.. - I"3 R3 :::: 0
Vz. -+- 1;.. 'k - T, 'R, :: 0
Xl =II"" ;!rz...
('8;\1) (,.- ~') -r 3 V
~.. 3 52 +'St-!>
S-.fL
e
Ph~,il"
Name:
Spl'ill~
210
Paolo (;ondolo
201-t
~A---,--,,fL/,_f_---,-)_.c_E_Y
_ _ __
Unid: -----------------------------DiscussionTA:' nO~
6
Exam 1
Show all work!! Report all numbers to three (3) significant figures.
A point charge q = 20.0 nC is located at the center of a unifonn ring having linear charge density A. = -10.0 nC/m and
radius a = 0.50 m, as shown in the figure. Detennine the total outward electric flux through a sphere centered at the point
charge and having radius R, in the following two cases (do not forget the units):
(a)
(b)
[10 pts.} R < a (illustrated in the figure),
[10 pts.} R > a (not illustrated in the figure).
Q,'.,
i~
Q;YI
=
p --
'l
fo
Z = '20
=
I"
C
2 o ·(o·!1c
f'.J' )" . 10 -Il ..;;--...
co.
/tI . ...
b.
Af
~
fi
'7 q
rhe
c-h(U)'~
ot
r,'Y/C)-
/-he.
::.
f
,.
~
""Ylp
1-60
Yl0"'""
u
-
;v'"",
t­
c­
7
eY,clos ~cI.
Q
or
2 1rCJ. )..
.r
'- :rc &(
20,(0"
=
I he
WI
1-" i« I
T
hr(,hCC:.
C:t- Zn-{O,f),..)(·lfl.(O-)%,)
,y.?> ,10-
12
- /z
;JO
_ IM
N ·
C
'l./