Download FINAL EXAM

Physics 2220
Fall 2012
Paolo Gondolo
FINAL EXAM
PLEASE FILL IN THE INFORMATION BELOW
Name (printed):
Name (signed):
Student ID Number
Discussion Instructor:
U __ __ __ __ __ __ __
Chad
Chris
Peter
Physics 2220
Fall 2012
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) = sin a sin 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 b cos a ± sin b
mproton = 1.67 × 10−27 kg
h = 6.64 × 10-34 J· s
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 2009Fall 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A meter stick lies on the bottom of a 50-cm-deep, 100-cm-long tank with
its zero mark against the left edge. You look into the tank at a 30o angle,
with your line of sight just grazing the upper left edge of the tank (see
figure).
(a)
(b)
[8 pts.] What mark do you see on the meter stick if the tank is
empty?
[8 pts.] What mark do you see on the meter stick if the tank is
completely full of water (index of refraction n=1.33)?
Paolo Gondolo
1
Physics2220
2220 Fall 2009
Physics
Fall 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
Two 10-cm-diameter charged disks face each other, 22 cm apart. The left disk is charged
to +60 nC and the right disk is charged to -60 nC.
(a)
(b)

[8 pts.] What is the electric field E at the midpoint between the two disks?
Specify its magnitude (in V/m) and its direction (left or right).

[8 pts.] What is the force F on a -1.0 nC charge placed at the midpoint? Specify
its magnitude (in N) and its direction (left or right).
Paolo Gondolo
2
Physics
Physics2220
220
Fall 2009Fall 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
For the circuit in the figure, find
(a)
(b)
(c)
[8 pts.] the current through the 4 Ω resistor,
[8 pts.] the voltage across the 2 Ω resistor,
[8 pts.] the energy stored in the 40 nF capacitor.
Assume the capacitor in the circuit is fully charged.
Paolo Gondolo
3
Physics
Physics2220
220
Fall 2009Fall 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
The two springs in the figure each have a spring constant k = 10 N/m. They are
compressed by x = 1.0 cm when a current passes through the wire. (Hooke’s law
gives a force F = −k x on each spring.)
(a)
(b)
[8 pts.] How big is the current?
[4 pts.] In which direction is the current? Upward or downward in the
figure?
Paolo Gondolo
4
Physics
Physics2220
220
Fall 2009Fall 2012
Paolo Gondolo
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
5
Show all work!! Report all numbers to three (3) significant figures.

A proton moves in the magnetic field B = 0.44 î T with a speed v = 1.0 × 107 m/s in the directions shown in the figures

below. For each, what is the magnetic force F on the proton? Give your answers in vector form using the unit vectors î ,
ĵ and k̂ .
(a)
[8 pts.]
(b)
[8 pts.]
Physics
Physics2220
220
Fall 2009Fall 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
6
Show all work!! Report all numbers to three (3) significant figures.
An electron is confined in a one-dimensional box of length L = 0.82 nm.
(a)
(b)
[8 pts.] What are the energies of the first three energy levels (n = 1,2,3) of the electron?
[8 pts.] Suppose that the electron moves from n = 3 level to the n = 1 level by emitting a photon of light. If
energy is conserved, what is the photon’s wavelength in nm?
I'h~"k"
22211 50 I \.t t
Name:
Unid:
"0 r1
----------~-------------
Discussion TA:
Paolo (;olldolo
hlll21112
1
Final Exam
---=~~~----------
Show all work!! Report all numbers to three (3) significant figures.
A meter stick lies on the bottom of a 50-em-deep, tOO-em-long tank with
its zero mark against the left edge. You look into the tank at a 30° angle,
with your line of sight just grazing the upper left edge of the tank (see
figure).
(a) (b) ~OfSight
30°
50 em
[8 pIS'] What mark do you see on the meter stick if the tank is
empty?
[8 pts.] What mark do you see on the meter stick if the tank is
completely full of water (index of refraction n= 1.33)7
Zero
Meter stick
100em
1;-)"3'0-­
L = (SOc.v'V')
SOc:~ eO'
11------.;:11,--1­
-tOf\
GOb
~
-L-­
•
(\.
S'I\ G,
-
S il\ 60°
--
--
-
vI'Z.-
~
v •• ~_ • • '~' , ' _ ' .
~~.--~---
5,"" 91­
,1.33
}t
Sin ft,/l.
Ph~ sit's
Name:
22211
Fall 2012
Paolo Goudolo
----------------------------------------------
Unid: ______________________________________________
d
Discussion TA:
2
Final Exam
rl5
~~~~---------------------
Show all work!! Report all numbers to three (3) significant figures.
Two 10-cm-diameter charged disks face each other, 22 cm apart. The left disk is charged to +60 nC and the right disk is charged to -60 ne. (a) (b) [8 pts.] What is the electric field E at the midpoint between the two disks? Specify its magnitude (in Vim) and its direction (left or right). [8 pts.} What is the force F on a -1.0 nC charge placed at the midpoint? Specify its magnitude (in N) and its direction (left or right). Bec.o.u.5 e. -Htte $flper-fA..+-~on IS 1D.t-~c.r- t-~I\ ~ JiA.J\1e:f--er:­
we" kb t..\.l~ ~O+- +fiee,..+ +k~$ o..S ().I\ il\t.;,,:+e pcat-Allel p{Q.~ C~ pa. c ".f-o i
I" s,4--eaJ. I -I-ttud-- eo.ch fo.cLe. o..S CA.. f,-I\. I'k - ckla.t'Se.cl J/slc...
-
(£1>;51<.)
'(
.
on-O-'1-1 S
;;
~
l-t..()
[I / + . J:;
l'Z.
(
R'l.
.,
Q: bO~tO c ;
Q
Zf D11 R.
J;:~~J
t [ I
/
R.
POI-r-+- b
F;
'i ~
l-I,07-IO'Y~
-
,------­
(3, '67'1-I0'1)~ (1)
- (3,'br.,. \O~5 ~
.1\
-I
.
.=
OI"5~)
J>h~sks
Name:
Unid:
2211
I-all 2012
Paolo (;011<1010
-----------------------------------~-----------
Discussion TA:
3
Final Exam
--~-=~~---------
Show all work!! Report all numbers to three (3) significant figures.
For the circuit in the figure, find
(a)
(b)
(c)
[8 pts.] the current through the 4 n resistor,
[8 pts.] the voltage across the 2 n resistor,
[8 pts.) the energy stored in the 40 nF capacitor.
-=- 12V
so
40
40nF
Assume the capacitor in the circuit is fully charged.
(0.)
(b)
(C)
Vc
-~
_
-
12. V
4i'L
Vo
----Rz. 1- 1(10
3A
::=
~
12 V
----2Q + 1052­
::: 12. ~:::
/2Q
100
JA
20
Ph~sics
Name:
220
Fall 2012
Paolo Gondolo
------~~~-----------
Unid: _ _ _ _ _ _ _ _ _ _ __
Discussion TA:
4
Final Exam
-----------------
Show all work!! Report all numbers to three (3) significant figures.
The two springs in the figure each have a spring constant k = 10 N/m. They are
compressed by x = 1.0 cm when a current passes through the wire. (Hooke's law
gives a force F = -k x on each spring.)
(a)
(b)
[8 pts.] How big is the current?
[4 pts.] In which direction is the current? Upward or downward in the
figure?
PO-!:'-\­
*
~
r
S~r;~s
Th.ere
o.t't CDM te5Sed-
.
two
IS
....t..
\
I
~"
!Fsp I
FB 1 ::. IFspl
z.. k~
I. L B sin ~OO --
:::-(
l.OO
(o.'LM)(O.ST)
P r-+ b
,._----­
L ' \ - kx I --­
--
"-
L13
--
I
t (loi) (O.OI~)
~~)(
~ --
I
sfr\~5
--:;
F",e.t =-0
F!lor IS +0 +he t-,~h +
~
$0
!l-
M'
'Lk)(
~O0
-­
£).
~
I(",ow
-tho..r
becGllA~~
"J "
B
MUSf
+~Q.
be,
.15
Spt- i~ 5
ou.t - 0+- - pCA~ e.
tltt
--
J..ovJ f\ WlAl"d
LV- t;. e.'" +-"'-e. R. H-. R).
(AI\~
COMpreS5eJ
+0
I
~e-l-
..,J.
Ff'I\
"
}o
IS
S;Iltt
.....
r::
M
+-ke.
~
=:
~
J:L",B /
-"
FM TO
Ie,~+)
PO;I\+-
let+.
Ph~sit:s
2211 [she-tt
Name:
Vnid:
Pl.wlo Gondolo
Fall 21112
5
Final Exam
---------------
Discussion TA: _ _ _ _ _ _ _ __
Show all work!! Report all numbers to three (3) significant figures.
A proton moves in the m~gnetic field
B= 0.44 iT with a speed v 1.0 x 107 mls in the directions shown in the figures
For each, what is the magnetic force F on the proton? Give your answers in vector fonn using the unit vectors i,
below.
~
~
j and k.
[8 pts.]
(a) z
;
[8pts.] (b)
fJ
V
x
\
//
...­
P(). r- -\-
/"'"
B
B
,.,..-''' 0.... ho-s
A prot-ol\
"" c h.o. r- 3e.
1
...I.
-
~v'f-B
..,..
e
~
/'
\]'1..
J
0
B 0
-
=­
1
Vz
(\. 'D 1./0-
11
-'
.s
b
\Fl~ ),,~y.BI
\...--.,-J
f\~~t\ ~ t IA.~ £,
v=
..lo.
\3.-:::.
-- e
1\
\J~ 1
B
f\.
+
01 +-
1
~~ -(O-~.Jl»)) + Ok
0
0
c) (O.4~ r) (lb' MIs)
Y.~ 't> ..,. 10- 13 eMI
~
+e
-- e Bv s I'f\ 45
+ eVa B 3
P~t-+-
,·Y /'",.,
.,.../
,/
~
....
F
/'"
\".,0
/\
..) /'\
J
S;(\ 4S
0
1\
J
Y.'tl6",10
-1'5
N
1
Ve
J
k
X
Ph~sit-s
220
Fall 2012
Paolo Gondolo
Nrune: _________________________
Unid: _ _ _ _ _....-_ _ _ _ _ __
_h-'r~C,...\_~5'-----------
Discussion TA: __--'C}""'<
Final Exam
6
Show all work!! Report all numbers to three (3) significant figures.
An electron is confined in a one-dimensional box oflength L = 0.82 nm.
(a) (b) [8 pts.] What are the energies of the first three energy levels (n = 1,2,3) ofthe electron?
[8 pts.} Suppose that the electron moves from n = 3 level to the n = 1 level by emitting a photon of light. If
energy is conserved, what is the photon's wavelength in nm?
f,;;; If ~ (0 -;J..c> :5
£21';
e2 ::::
'3 (60
~I
{()
xlf) '11
J"
A' (j .-( q ;:r
c::::- ~ V
/) ~ h_"" ;: J, -rl ;</0- 'tn
t:y
- 17?
YI
t11.