西尔斯大学物理双语版题目

Exercise:
1. A particle moving along x axis starts from x 0 with initial velocity
v 0. Its acceleration can be expressed in a =-kv 2 where k is a known
constant. Find its velocity function v =v (x ) with the coordinate x as
variable.
2. A particle moves in xy plane with the motion function as
j t i t t r )3sin 5()3cos 5()(+=(all in SI). Find (a) its velocity )(t v and (b)
acceleration )(t a in the unit-vector notation. (c) Show that v r
⊥.
3. A bullet of mass m is shot into a sand hill along a horizontal
path, assume that the drag of the sand is kv f -=, find the velocity
function v(t) if 0)0(v v = and the gravitation of the bullet can be
ignored.
4. what work is done by a conservative force j i x f 32+= that
moves a particle in xy plane from the initial position j i r i 32+= to the final position j i r f 34--=. All quantities are in SI.
5. The angular position of a point on the rim of a rotating wheel is
given by 320.30.4t t t +-=θ, where θ is in radians and t is in
seconds. Find (a) its angular velocities at t=0s and t =4.0s? (b)
Calculate its angular acceleration at t =2.0s. (c) Is its angular
acceleration constant?
6. A uniform thin rod of mass M and length L can rotate freely
about a horizontal axis passing through its top end o (23
1ML I =). A
bullet of mass m penetrates the rod passing its center of mass
when the rod is in vertical stationary. If the path of the bullet is
horizontal with an initial speed v o before penetration and 2
0v after penetration . Show that (a) the angular velocity of the rod just after the penetration is ML
mv 430=ω. (b) Find the maximum angular max θ the rod will swing upward after penetration.
7. A 1.0g bullet is fired into a block (M=0.50kg) that is mounted
on the end of a rod (L=0.60m). The rotational inertia of the rod
alone about A is 206.0m kg ⋅. The block-rod-bullet system then
rotates about a fixed axis at point A. Assume the block is small
enough to treat as a particle on the end of the rod. Question: (a)
What is the rotational inertia of the block-rod-bullet system about
A? (b) If the angular speed of the system about A just after the
bullet ’s impact is 4.5rad/s , What is the speed of the bullet just
before the impact?
8. A clock moves along the x axis at a speed of 0.800c and reads
zero as it passes the origin. (a) Calculate the Lorentz factor γ
between the rest frame S and the frame S* in which the clock is
rest. (b) what time does the clock read as it passes x =180m ?
9. What must be the momentum of a particle with mass m so
that its total energy is 3 times rest energy?
10. Ideal gas within a closed chamber undergoes the cycle shown
the Fig. Calculate Q net the net energy added to the gas as heat
during one complete cycle.
11. One mole of a monatomic ideal gas undergoes the cycle
shown in the Fig. temperature at state A is 300K.
(a). calculate the temperature of state B and C.
(b). what is the change in internal energy of the gas between state
A and state B? (int E )
(c). the work done by the gas of the whole cycle .
(d). the net heat added to the gas during one complete cycle.
12. The motion of the electrons in metals is similar to the motion
of molecules in the ideal gases. Its distribution function of speed
is not Maxwell ’s curve but given by.
⎩
⎨⎧=0)(2Av v p
the possible maximum speed v F is called Fermi speed. (a)
plot the distribution curve qualitatively. (b) Express the coefficient
A in terms of v F . (c) Find its average speed v avg .
13. Two containers are at the same temperature. The first
contains gas with pressure 1p , molecular mass 1m , and rms
speed 1rms v . The second contains gas with pressure 12p , molecular
mass 2m , and average speed 122rm s avg v v =. Find the mass ratio
21m m .
14. In a quasi-static process of the ideal gas, dW =PdV and
d E int =nC v dT . From th
e 1st law o
f thermodynamics show that the
change of entropy i f v i f
T T nC V V nR S ln ln +=∆ .Where n is the number
of moles, C v is the molar specific heat of the gas at constant
volume, R is the ideal gas constant, (V i , T i ) and (V f , T f ) . are the
initial and final volumes and temperatures respectively.
15. It is found experimentally that the electric field in a certain
region of Earth ’s atmosphere is directed vertically down. At an
altitude of 300m the field is 60.0 N /C ; at an altitude of 200m , the
field is 100N /C . Find the net charge contained in a cube 100m on
edge, with horizontal faces at altitudes of 200m and 300m .
Neglect the curvature of Earth.
16. An isolated sphere conductor of radius R with charge Q . (a)
Find the energy U stored in the electric field in the vacuum outside
the conductor. (b) If the space is filled with a uniform dielectrics of
known r ε what is U * stored in the field outside the conductor
then?
17. Charge is distributed uniformly throughout the volume of an
infinitely long cylinder of radius R. (a) show that, at a distance r
from the cylinder axis (r<R), r E 0
2ερ=, where ρis the volume charge density. (b) write the expression for E when r>R .
18. A non-uniform but spherically symmetric distribution of
charge has a volume density given as follow:
⎩⎨⎧-=0)
/1()(0R r r ρρ
where 0ρ is a positive constant, r is the distance to the symmetric center O and R is the
radius of the charge distribution. Within the charge distribution (r <
R ), show that (a) the charge contained in the co-center sphere of
radius r is )34(31)(430r R
r r q -=πρ, (b) Find the magnitude of electric
field E (r ) within the charge (r < R ). (c) Find the maximum field E max =E (r *) and the value of r *.
19. In some region of space, the electric potential is the following
function of x,y and z: xy x V 22+=, where the potential is measured
in volts and the distance in meter . Find the electric field at the
point x=2m, y=2m . (express your answer in vector form)
20. The Fig. shows a cross section of an isolated spherical metal
shell of inner radius R 1 and outer radius R 2. A point charge q is located at a distance 2
1R from the center of the shell. If the shell is electrically neutral, (a) what are the induced charges (Q in , Q out )
on both surfaces of the shell? (b) Find the electric potential V(0) at
the center O assume V (∞)=0.
21. Two large metal plates of equal area
are parallel and closed
to each other with charges Q A , Q B respectively. Ignore the fringing
effects, find (a) the surface charge density on each side of both
plates, (b) the electric field at
p 1, p 2 . (c) the electric potential
A and B)
22．In a certain region of space, the electric potential is ()2
=-+where A,B,C are positive constant. The ,,,
V x y z Axy Bx Cy
electric field is ; at which point is the electric field equal to zero .
23. A 9.60-μC point charge is at the center of a cube with sides of length 0.500m. The electric flux through one of the six faces of the cube is ; the answer would be if the sides were of length 0.250m.。