Name _______________________________________________________________________
Section #
1 M/R 8-10 (Washington, DCC308)
2 M/R 10-12 (Yamaguchi, DCC308)
3 M/R 12-2 (Yamaguchi, DCC308)
5 M/R 2-4 (Eah, DCC318)
9 M/R 4-6 (Eah, DCC318)
6 T/F 10-12 (Malak, DCC324)
7 T/F 12-2 (Wetzel, DCC324)
Questions
Part A
Part B
Part C
Total
Value
40
20
40
100
Score
10 T/F 12-2 (Adams, DCC308)
8 T/F 2-4 (Adams, DCC308)
You may detach the formula sheet, but leave exam pages attached.
Cheating on this exam will result in an F in the course.
1

Name _______________________________________________________________________
Part A – Multiple Choice (4 points each)
Circle the letter of the best answer.
1.
Suitable units for the gravitational constant  are:
A. kg¢m/s
2
B. m/s
2
C. N¢s/m
D. kg¢m/s
E. m
3
/(kg¢s
2
)
2.
Venus has a mass of about 0  0558 times the mass of Earth and a diameter of about 0  381 times the diameter of Earth. The acceleration of an object falling near the surface of Venus is:
A. 0  21m  s
2
B. 1  4m  s
2
C. 2  8m  s
2
D. 3  8m  s
2
E. 25m  s
2
3.
Two particles have charges  and ¡  (equal magnitude and opposite sign). Other than the solution at infinity, for them to exert a net force of zero on a third charge it must be placed:
A. midway between  and ¡ 
B. on the perpendicular bisector of the line joining  and ¡  , but not on that line itself
C. on the line joining  and ¡  , to the side of  opposite ¡ 
D. on the line joining  and ¡  , to the side of ¡  opposite Q
E. at none of the above choices because there is no solution
4.
A 5  0-C charge is 10m from a ¡2  0-C charge. The electrostatic force on the positive charge is:
A. 9  0 £ 10 8 N toward the negative charge
B. 9  0 £ 10 8 N away from the negative charge
C. 9  0 £ 10
9
N toward the negative charge
D. 9  0 £ 10
9
N away from the negative charge
E. none of these
2

Name _______________________________________________________________________
5.
The electric ¯eld at a distance of 10 cm from an isolated point particle with a charge of 2£10 ¡9
C is:
A. 1  8N  C
B. 180N  C
C. 18N  C
D. 1800N  C
E. none of these
6.
The diagram shows a particle with positive charge +  and a particle with negative charge ¡  .
The direction of the electric ¯eld at point P on the perpendicular bisector of the line joining them is:
A. Up on the page.
B. Down on the page.
C. Right on the page.
D. Left on the page.
E. zero
7.
The electric potential in a certain region of space is given by  = ¡7  5  2 + 3  , where  is in volts and  is in meters. In this region the equipotential surfaces are:
A. planes parallel to the  axis
B. planes parallel to the  plane
C. concentric spheres centered at the origin
3

Name _______________________________________________________________________
D. concentric cylinders with the  axis as the cylinder axis
E. unknown unless the charge is given
8.
The potential di®erence between two points is 100V. If a particle with a charge of 2C is transported from one of these points to the other, the magnitude of the work done is:
A. 200 J
B. 100 J
C. 50 J
D. 100 J
E. need more information
9.
Acceptable units for a magnetic ¯eld are:
A. C¢m/s
B. C¢s/m
C. C/kg
D. kg/C¢s
E. N/C¢m
10.
At one instant an electron is moving in the  plane with velocity components 

= 5 £ 10 5 m  s and 

= 3 £ 10 5 m  s. A uniform magnetic ¯eld of 0  8 T is in the positive  direction. At that instant the magnitude of the magnetic force on the electron is:
A. 0
B. 3  8 £ 10 ¡14 N
C. 5  1 £ 10 ¡14 N
D. 6  4 £ 10 ¡14 N
E. 7  5 £ 10 ¡14 N
4

Name _______________________________________________________________________
Part B – (20 points)
Circle the best answer.
1) The sketch shows two charges lying on the x axis, a distance d apart. The charge on the left is positive, and that on the right is negative. The magnitude of the charge on the right is double that of the charge on the left. a) (5%) Where on the x axis, other than an infinite distance from the charges, is the electric field due to the two charges equal to zero? ( Circle more than one if the electric field is zero in more than one region.) to the left of q between q and -2q there are no points on the x axis where E = 0.
to the right of -2q b) (5%) Setting the electric potential to zero at infinity, where else on the x axis is the electric potential due to the two charges equal to zero? (Circle more than one if the electric potential is zero in more than one region.) to the right of -2q to the left of q between q and -2q there are no points on the x axis where V = 0.
c) (5%) Are there any points that are not on the x axis where the electric field due to the two charges is equal to zero, other than an infinite distance from the charges?
Yes No Need more information d) (5%) Are there any points that are not on the x axis where the electric potential due to the two charges is equal to zero, other than an infinite distance from the charges?
Yes No Need more information
5

Name _______________________________________________________________________
Part C – Numerical Problem (40 points)
Circle the correct answer to multiple choice questions. You must show your work on the numerical questions in the space indicated. You will receive zero points if your work does not match your answer!
1) A small charged ball is suspended from a massless string in a region where there is a uniform horizontal electric field, directed as shown. The system is in equilibrium, with

= 45.0°. The mass of the ball is 0.0100 kg, the magnitude of the electric field is 2.00 × 10 6
V/m, and the gravitational acceleration is g = 9.80 m/s². a )(10%) Find the magnitude of the charge on the ball.
q = _________C b) (5%) If the string supporting the ball broke, the ball would fall. The path that it would follow, while in the region of the uniform electric field, would be a:
STRAIGHT LINE PARABOLA CIRCLE SOMETHING ELSE
Suppose the apparatus in the sketch is transported to the top of an enormous tower, where the gravitational acceleration is only g
’ = 9.00 m/s² (No, you can’t build a tower that high!).
E and q remain the same, only g changes. c) (10%) Find the angle that the string will make with the vertical direction when g
’ = 9.00 m/s².

= _________degrees
6

Name _______________________________________________________________________ d) (10%) How tall is the tower? In other words, how far is the top of the tower from the surface of Earth? The radius of the surface of Earth is R
E
= 6.37 ×10
6
m, the mass of Earth is M
E
×10 24
kg, and g
’ = 9.00 m/s² at the top of the tower.
= 5.98 h = _________m e) (5%)When the charged ball was raised from the surface of Earth to the top of the tower, the gravitational potential energy of the earth-plus-ball system:
INCREASED DECREASED REMAINED THE SAME
7

Name _______________________________________________________________________
1.
2. v f x f

 v
0 x
0
 a
 t f
 v
0
( t f
 t
0

 t
0
)
 1
2 a ( t f
 t
0
)
2
23.
24.
U
U g


  m

F cons g ( y


 d x y
0
)
3.
4.
5.
6.
7. x f
 x
0
 1
2
( v
0
 v f
)( t f x f
 x
0
 f
( f
 t
0
)
 v
 f
T
2


F

 v

0
2 
F net
2
 v r
2 a

 x m f
 a
 x
0

2
1
 t
0
)
( f
 t
0
)
2
25.
26.
27.
28.
29.
30.
U
 s
K


1
2
 k (
U x

 x
0
)
2
W non
 cons s
  r v tangential
  r a tangential
  
0

  r

 t
 t
0

8.
9.
10.
11.
12.
13.
14.
15. a


P

J d d centripeta l a
 p radial
 m

 v



P t

F


 v
2
  r
 a centripeta l
 2

F net


F net
  p i dt

F ext
 d
 p
 d
 t
 p
M
  m i r
16.
17.
18.
19.
20. x cm

1
 a

P

 b


M
 a
M
 v
W
W

  
 m i x b cos(

)

F


F
 d
 d x i
 a x y cm b x


1
M a y b y

 m i y i a z b z
21.
22.
K
K f
 1 m

2
K i v 2

 1
2 m ( v x
2
W net
 v y
2
)
31.
32.
33.
34.
35a.
35b.
36.
37.
38.
39.
40.
41.
42.
43.
I
 


0
  
0
 m
 
0
( t
 i
1
2
(

0 r i
2
 t
0
)

K
W rot


 r


1

I

2

F
 d
 2




L l


L



I
 r

I

 l

 p i
 d

L d t
1
2

( t
 
)( t
 t
0
)


 a
 a
2





 b b

0


2
0

 a

(
 t
2



  t
0

)


0
1
2
 b sin(

)

 a y b z
 a z b y
 iˆ

(

 a z b x
 a x b z
 jˆ

 a x b y
 t a
 y
 t
0
)
2 t
0
)
2 b x
 kˆ
44x.
44y.
44z.
45a. m
1 v
1 , x , before m
1 v
1 , y , before m
1 v
1 , z , before v
1 , f
 m m
1
1


 m
2 v
2 , x , before
 m
2 v
2 , y , before
 m
2 v
2 , z , before m
2 m
2 v
1 , i
 m
1


 m
1 v
1 , x , after m
1 v
1 , y , after m
1 v
1 , z , after
 m
2 v
2 , x , after
 m
2 v
2 , y , after
 m
2 v
2 , z , after
2 m
2
 m
2 v
2 , i
45b. v
2 , f
 m
1
2 m
1
 m
2 v
1 , i
 m
2 m
1
 m
1
 m
2 v
2 , i
8

46a.
46b.
47a.
47b.
48a.
48b.
49.
|

F |

G m
1 r
2 m
2

F

G m
1 m
2 r
2
|

F |

4

1

0 rˆ
| q
1 r
2
|| q
2

F

4

1

0 q
1 r
2 q
2 (
 rˆ )
|
|

E i
|

1
4
 
0
| q i r i
2
|

E

F
 
 q

E
4
1
 
0 q i r i
2
(
 rˆ i
)
50.
51.
52.
53x.
53y.
53z.
54.
55.
V
  1
4
 
U
V
E x


 q



V

E



V x
 d x
0
E y
 

V
 y

F
E z

 q

 v

V


 z
B r
 m v q B q i r i
Universal Gravitation Constant G

6 .
673

10

11
N m
2 kg

2 
6 .
67

10

11
Electrostatic Force Constant
Magnetic Constant
Speed of Light in Vacuum
Charge of a Proton
Electron-Volt Conversion Constant
Mass of a Proton
Mass of an Electron
1
4
 
0

8 .
987551788

10

9 N m 2 C

2 
9 .
0

10

9

0

4
 
10

7 H m

1 
1 .
26

10

6 c

2 .
99792458

10

8 m s

1 
3 .
0

10

8 e

1 .
602176462

10

19
C

1 .
6

10

19
1 e V

1 .
602176462

10

19
J

1 .
6

10

19 m p

1 .
67262158

10

27 kg

1 .
67

10

27 m e

9 .
10938188

10

31 kg

9 .
1

10

31
9