武汉理工大学考试试题纸（
课程名称
大学物理阿 A 上
专业班级 计算机 gj41
题号
一
二
三
四
五
六
七
题分
30
21
9
10
10
10
10
备注:
A 卷）
八
九
十
总分
学生不得在试题纸上答题(含填空题、选择题等客观题)
一. Select the right answer of the following questions.(each question is 3 cent, and the sum cents is
30 )
1. At a certain time a moving particle’s position vector is r , then the magnitude of its velocity is
dr
A)
dt
dr
B)
dt
dr
C)
dt
2
D)
 dx   dy 
   
 dt   dt 
2
2. The position of a particle is given by r  at 2i  bt 2 j (a, b is constant), the particle moves
A)
B)
C)
D)
with constant velocity.
with constant acceleration.
along a projectile curve.
along a general curve.
3. Two objects interact with each other and with no other objects. Initially object A has a speed
of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their
initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:
A) the potential energy changed from the beginning to the end of the trip.
B) mechanical energy was increased by nonconservative forces.
C) mechanical energy was decreased by nonconservative forces.
D) mechanical energy was increased by conservative forces.
4. The sum of the kinetic and potential energies of a system of objects is conserved:
A) only when no external force acts on the objects.
B) only when the objects move along closed paths.
C) only when the work done by the resultant external force is zero.
D) none of the above.
5.
A man, with his arms at his sides, is spinning on a light frictionless turntable. When he
extends his arms:
A) his angular velocity increases.
B) his rotational inertia decreases.
C) his rotational kinetic energy increases.
D) his angular momentum remains the same.
6.
A source emits sound with a frequency of 1000 Hz. Both it and an observer are moving in the
same direction with the same speed, 100 m/s. If the speed of sound is 340 m/s, the observer
hears sound with a frequency of:
A) 294 Hz.
B) 545 Hz .
C) 1000 Hz .
D) 1830 Hz .
7.
An ideal gas is to taken reversibly from state i, at
temperature T1, to another state, at temperature T2. Of
the five processes shown on the p-V diagram below,
which results in the greatest change in the entropy of
the gas?
A)
B)
C)
D)
8.
A
B
C
E
The diagrams below depict four different charge distributions. The charges are all the same
distance from the origin. Rank the situations according to the magnitude of the electric field
at the origins, least to greatest.
A)
B)
C)
D)
1, 2, 3, 4
4, 3, 2, 1
2, 1, then 3 and 4 tie
1, 2, then 3 and 4 tie
 
9. Consider Gauss's law:  EdA  q  0 Which of the following is true?

A) E must be the electric field due to the enclosed charge

B) If q = 0 then E everywhere on the Gaussian surface is zero
C) If the charge inside consists of an electric dipole, and then the integral is zero

D) If a charge is placed outside the surface, then it cannot affect E on the surface
10. Two parallel-plate capacitors with the same plate separation but different capacitance are
connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT
the same for both capacitors when they are fully charged is:
A) potential difference
B) energy density
C) electric field between the plates
D) charge on the positive plate
二. Fill the blanks with right answer（each question is 3 cent, and the sum cent is 30）
1 A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60°above
the horizontal. The highest point (relative to ground level) that it can reach is
horizontal range of the projectile is
, the
. The potential energy of the projectile at its highest
(g=10m/s2).
point is
2 A block is projected up a frictionless inclined plane with initial speed v0  4.00 m/s . The angle
of incline is 30 . The maximum distance that the block has traveled is _
to get there. When the block gets back to the bottom, its speed is
_, the block needs
.
3 The escape velocity at the surface of Earth is approximately 8 km/s. The escape velocity for a
planet whose radius is 4 times and whose mass is 100 times that of Earth is
4 In the figure, two springs are joined and
connected to a block with mass m. the surface
is frictionless, if springs both have spring
constant
k,
oscillation is f=
the
block’s
.
frequency
of
.
5
A wave traveling along a string is described by y  x, t   0.00327sin  72.1x  2.72t  , in which
the numerical constants are in SI units (0.00327m, 72.1rad/m, and 2.72rad/s). the amplitude of
the wave is
6
, the wavelength is
, the period is
.
The motor in a refrigerator has a power of 200 W. if the freezing compartment is at 270 K and
the outside air is at 300 K, and assuming the efficiency of a Carnot refrigerator, the coefficient
of performance is
, the maximum amount of energy that is extracted as heat from the
freezing compartment in 10.0 min is
7
.
Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy and capacitor
B is uncharged. The capacitors are then connected in parallel. The total stored energy in the
capacitors is now
.
三. A 1.0 kg block at rest on a horizontal frictionless surface is connected to an unstretched spring
(k=200N/m) whose other end is fixed. A 2.0 kg block moving at 4.0m/s collides with the 1.0 kg
block. If the two blocks stick together after the one-dimensional collision, what maximum
compression of the spring occurs when the blocks momentarily stop?（9 cent）
四. The right figure shows a uniform disk, with mass M=2.5kg, and radius R=20cm, mounted on a
fixed horizontal axis. A block with mass m=1.2 kg hangs from a massless cord that is wrapped
around the rim of the disk. Find the acceleration of the falling block, the angular acceleration of
the disk, and the tension in the cord. The cord does not slip; there is no friction at the axle.
（10cent）
五. In the overhead view of the right figure, a long uniform rod of length l and mass m is free to rotate in
horizontal plane about a vertical axis through its center. A spring with force constant k is connected
horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the
wall. What is the period of the small oscillations that result when the rod is rotated slightly released?
（10cent）
六. An ideal diatomic gas, whose molecules are rotating but not oscillating, is taken through the
cycle in right figure. Determine for all three processes, in terms of p1, V1, T1, and R: (a) p2, p3,
and T3 and (b) W, Q, Eint , and S (10 cent)
七. What is the capacitance of the capacitor, of plate area A, shown in this figure?（10 cent）
A/ 2
A/ 2
2d
1
2
d
3
d
武汉理工大学教务处
试题标准答案及评分标准用纸
|
八. | 一
课程名称 大学物理 B
（
A 卷）
Select the right answer of the following problems
装
1
2
3
4
5
6
7
8
9
10
D
B
C
D
D
C
D
B
C
D
|
| 二
Fill the blanks with right answer
5 3
m, 18.75 J ,
2
|
1 3.75m.
|
2
0.4 m, 0.2 s, 4.0 m/s (each one is 1.0 cent)
|
3
40 km/s (3 cent)
钉
4
|
5
3.27 mm, 8.71 cm, 2.31s (each one is 1.0 cent)
|
6
9, 1.08 106 J (each one is 1.5 cent)
|
7
2J (3 cent)
线 三
f 
(each one is 1 cent)
k 2m
(3 cent)
2
Because the two blocks stick together after the one-dimensional collision, and the
momentum is conserved. Thus they have the same speed v
|
m1v 1 m v2 
2 (m 1 m )v2 (3 cent)
|
|
|
0k m / s 8
 m/ s (1cent)
3
After the collision, the mechanical energy of the system is conserved (1cent)
1
1
 m1  m2  v 2  kx 2 (3 cent)
2
2
装
|
2 . 0k g 4k m /s 1 . 0k g
(2.
0 1 .kg0 )
v
 2  1 kg  8 m / s  0.33m
x
四
200 N/m
3
(1cent)
The free-diagrams of the block and the disk are shown in this figure.
|
There are two forces acts on the block, tension T and gravitational force Fg
|
m g T m a(2)
|
The net torque acts on the disk is
|
R T 
I (2)
|
The inertia of the disk is
|
I 
R
0
MR 2
r  2 rdr 
(2)
2
2
|
Because the cord doesn’t slip
|
a  R (1)
钉
Where a is the acceleration, and  is the angular acceleration
|
a
mg
 4 . 8m s/2
M
2

m


(1)
|

a
 24 rad/s 2
R
(1)
|
T  m g a 6 . 0
线
N
(1)
|
|
|
五
|
F   kx  
|
Thus the torque acts on the rod is
装
l
 kl
 kl
   cos  
sin   

4
2
 2

|
|
|
When the rod rotate a small angle, the spring force is
kl
s i n
2
(2)
2
  I  I
d 2
kl 2



dt 2
4
(2)
where I is the inertia of the rod
m 2l 2
1 2
ml
l x dx 


l 2
12
I
钉
kl 2
3k

the frequency is  
4I
m
|
|
|

According to the Newton’s second law
|
|
(2)
The period is
六
T
2

 2
(2)
m
3k
(1)
(1)
The diatomic molecular are rotating but not oscillating
(0.5)
CV = 5/2R, Cp = 7/2R, and γ = 7/5
(1.5)
(a) Process 1 → 2 is isothermal, then the pressure p2 is p2 
p1V1 p1

V2
3
(0.5)

|
V 
p
Process 3 → 1 is adiabatic p3  p1  1   1.41 ,
3
 V3 
(0.5)
V 
T3  T1  1 
 V3 
|
|
 1

p1
30.4
(0.5)
(b) In process 1 → 2, Eint  0
W  
线
V2
V1
(0.5)
p d V   R1 lTn 3
(0.5)
|
Q  Ei n t  W  R T
l1n 3
(0.5)
|
S 
Q
 Rl n 3
T
(0.5)
|
In process 2 → 3
|
Ei n t  CV  T 2  T 1  0. 8 8 9R T1
装
Q  Ei n t  0 . 8 8 9R T1
|
S 
3
2
W 0
T
d Q T3
dT 5
 CV
 Rl n 3
T
1
T
T 2
T
1
(0.5)
(0.5)
(0.5)
1 . 1 0R
(0.5)
|
In process 3 → 1 Q  0 ,
(0.5)
|
S  0
(0.5)
|
In the cycle, Eint(12)  Eint(23)  Eint(31)  0 ,
(0.5)
|
Which implies in process 3-1 Eint  0.889RT1
(0.5)
|
|
|
W   Ei n t  0. 8 8 9R T1
七
(0.5)
In this question, the capacitor can be seen as two capacitors in parallel
For capacitor 1, the Gauss’s surface is shown in the figure, assume
++++++++++++++
q
|
|
which enclose free charge q. According to Gauss’s law with dielectric


 1 0  E1  dA  q
(2)
S
|
The directions of electric field and the normal of the Gauss’s surface are same
------------------------
|
E

C1 
|
q 2d
 1 0  A 2
q  1 0 A

V1
4d
(1)
(1)

For capacitor C2, electric field E2 in the region with
|
|
(1)
 1 0 A


V1   E1  dS 
|
|
2q1
dielectric constant  2 can be calculated according to Gauss’s law


 2 0  E2  dA  q  E2 
S
2q
A 2 0


 3 0  E3  dA  q  E3 
S
2q
A 3 0
(1)
(1)
| Then the potential difference between the conductor slab is
|
|
|
|
|
|
d
2d
0
d
V2   E3 ds   E2 ds 
C2 
A 0
q

V2
2d
C  C1  C 2 
2qd   2   3 


A 0   2 3 
  2 3 


 2  3 
0 A 
2 2 3 
  1 

4d 
 2   3 

E2

E3
-------------------------------

| with the same method, electric field E 3 is
|
+++++++++++++++++
(1)
(1)
(1)