大学物理双语练习题

Chapter 1 Particle Kinematics

I) Choose one correct answer among following choices

1. An object is moving along the x-axis with position as a function of time given by

x=x(t). Point O is at x=0. The object is definitely moving toward O when

2. An object starts from rest at x=0 when t=0. The object moves in the x direction with

positive velocity after t=0. The instantaneous velocity and average velocity are related by

A. v v

B. v v

C. v v

dx x can be larger than, smaller than, or equal to

3. An object is moving in the x direction with velocity

A. Negative.

B. Zero.

C. Positive.

D. Not determined from the information given. 4. An object is moving on the xy-plane with position as a function of time given by r = 2 2

a t i +

b t j (a and b are constant). Which is correct?

A. The object is moving along a straight line with constant speed.

B. The object is moving along a straight line with variable speed.

C. The object is moving along a curved path with constant speed.

D. The object is moving along a curved path with variable speed.

5. An object is thrown into the air with an initial velocity v 0 (4.9i 9.8 j)m/s.

Ignore the

air resistance (空气阻力 ). At the highest point the magnitude of the velocity

is ( )

(A) 0 (B) 4.9m/s (C) 9.8m/s (D) (4.9)2 (9.8) 2 m/s

6. Two bodies are falling with negligible air resistance, side by side, above a horizontal

plane. If one of the bodies is given an additional horizontal acceleration during its descent, it A. dx 0 dt B. dx 0 dt C. d(x 2) dt D. d(x 2) dt

D.

v x (t), and x is nonzero x dt

constant. With v x 0 when t=0, then for t>0 the quantity v x dv x v x

dt is

A.strikes the plane at the same time as the other body.

B.strikes the plane earlier than the other body.

C.has the vertical component of its velocity altered.

D.has the vertical component of its acceleration altered.

7. A toy racing car moves with constant speed around the circle shown below. When it is at point A its coordinates are x=0, y=3m and its velocity is 6m/s i . When it is at

point B its velocity and acceleration are:

22

A.-6m/s j and 12m/s i , respectively.

B. 6m/s j and -12m/s i , respectively.

22

C. 6m/s j and 12m/s i , respectively.

D. 6m/s j and 2m/s i , respectively.

8. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0m/s in a vertical circle. Its acceleration at the bottom of the circle is:

2 2 2 2

A. 9.8m/s , up

B. 9.8m/s , down

C. 8.0m/s , up

D. 32m/s , up

9. A boat is able to move through still water at 20m/s. It makes a round trip to a town

3.0 km upstream. If the river flows at 5m/s, the time required for this round trip is:

B.150 s

C. 200 s

D. 320 s

A. 120 s

II)Fill in the empty space with correct answer

1. A particle goes from x=-2m, y=3m, z=1m to x=3m, y=-1m, z=4m. Its displacement is : .

2.The x-component of the position vector of a particle is shown in the graph in Figure

as a function of time.

(a)The velocity component v x at the instant 3.0 s is .

(b)When is the velocity component zero ? The time is .

(c)Is the particle always moving in the same direction along the x-

axis? .

2

3.The angle turned through by a wheel is given byθ ＝at+bt , where a and b are constants. Its angular velocityω ＝, and its angular accelerationβ ＝

4.When a radio wave impinges on the antenna of your car, electrons in the antenna

move back and forth along the antenna with a velocity

component v x as shown schematically in Figure . Roughly sketch

the same graph and indicate the time instants when

(a)The velocity component v x is zero;

(b)The acceleration componenta x is zero;

(c)The acceleration has its maximum magnitude.

5. A car is traveling around a banked, circular curve of radius 150 m on a test track. At the instant when t=0s, the car is moving north, and its speed is 30.0 m/s but decreasing uniformly, so that after 5.0 s its angular speed will be 3/4 that it was when t=0s. The angular speed of the car when t=0s is , the angular speed 5.0 s later

is , the magnitude of the centripetal acceleration of the car when t=0s is , the magnitude of

the centripetal acceleration of the car when t=5.00s is , the magnitude of the angular acceleration is , the magnitude of

the tangential acceleration is .

6. A projectile is launched at speed v 0 at an angle θ (with

the horizontal) from the bottom of a hill of c onstant slope as

shown in Figure. The range of the projectile up the slope is .

III) Calculate Following Problems:

1. An object with mass m initially at rest is acted by a force F k 1i k 2tj , where k 1

and k 2 are constants. Calculate the velocity of the object as a function of time.

2. You are operating a radio-controlled model car on a vacant tennis court. Your position is the origin of coordinates, and the surface of the court lies in the xy-plane. The car, which we represent as a point, has x- and y-cooridnates that vary with time

2 2

3 3 according to x=2.0m-(0.25m/s )t , y=(1.0m/s)t+(0.025m/s )t . a. Find the car's instantaneous velocity at t=2.0s.

b. Find the instantaneous acceleration at t=4.0s.

2

3. An object moves in the xy-plane. Its acceleration has components a x =2.50t and a y =9.00-

1.40t. At t=0 it is at the origin and has velocity v 0 1.00i 7.00 j .

Calculate the velocity and position vectors as functions of time.

2

4. An automobile whose speed is increasing at a rate of 0.600 m/s travels along a circular

road of radius 20.0 m. When the instantaneous speed of the automobile is 4.00 m/s, find (a) the tangential acceleration component, (b) the radial acceleration component, and (c) the

magnitude and direction of the total acceleration.

2

5. Heather in her Corvette accelerates at the rate of (3.00i -2.00 j ) m/s , while Jill in

2

her Jaguar accelerates at (1.00i +3.00 j ) m/s . They both start from rest at the origin

of an xy coordinate system. After 5.00 s, (a) what is Heather ' s speed with respect to Jill, (b)

how far apart are they, and (c) what is Heather ' s acceler atoti oJnill ?re

lative

Chapter 2 Newton 's laws of motion

I) Choose one correct answer among following choices

1. In the SI, the base units (基本单位 ) for length, mass, time are ( )

(A) meters, grams, seconds. (B) kilometers, kilograms, seconds.

(C) centimeters, kilograms, seconds. (D) meters, kilograms, seconds.

2. Which one of the following has the same d imension (量纲) as time ( )

3. Which of the following quantities are independent (无关 ) of the choice of inertial

x (A) (D) vx

(B) (C)

frame(惯性系 )?

(A)v (B) P (C)F (D) W

4.Suppose the net force F on an object is a nonzero constant. Which of the following could also be constant?

A. Position.

B. Speed.

C. Velocity.

D. Acceleration.

5.An object moves with a constant acceleration a. Which of the following expression is also constant? ( )

(A) dv

dt

(B)

dv

dt

(C)

d(v2)

dt dt

6. An object moving at constant velocity in an inertial frame must:

A. have a net force on it.

B. eventually stop due to gravity.

C. not have any force of gravity on it.

D. have zero net force on it.

7. A heavy ball is suspended as shown. A quick jerk on the lower string will break that string but a slow pull on the lower string will break the upper string. The first result occurs because:

A. the force is too small to move the ball

B. action and reaction is operating

C. the ball has inertia

D. air friction holds the ball back

8. A constant force of 8.0 N is exerted for 4.0 s on a

16-kg object initially at rest. The change in speed of this object will be:

A. 0.5m/s

B. 2m/s

C. 4m/s

D. 8m/s

9. A wedge rests on a frictionless horizontal table top. An

object with mass m is tied to the frictionless incline of the

wedge as shown in figure. The string is parallel to the

incline. If the wedge accelerates to the left, when the object

leaves the incline, the magnitude of its acceleration is

A. gsinθ

B. gcosθ

C. gtanθ

D. gcotθ

10. A crane operator lowers a 16,000-N steel ball with a downward acceleration of 2

3m/s . The tension force of the cable is:

A. 4900N

B. 11, 000N

C. 16, 000N

D. 21, 000N 11. A 1-N

pendulum bob is held at an angle θ from the vertical by a 2-N

horizontal force F as shown. The tension in the string supporting

the pendulum bob (in newtons) is:

A. cos θ

B. 2/ cos θ

C. 5

D. 1

2

12. A car moves horizontally with a constant acceleration of 3m/s . A ball is suspended by a string from the ceiling of the car. The ball does not swing, being at rest with respect to the car. What angle does the string make with the vertical?

A. 17?

B. 35?

C. 52?

D. 73?

13. A 32-N force, parallel to the incline, is required to push a certain crate at constant velocity up a frictionless incline that is 30? above the horizontal. The mass of the crate is:

A. 3.3kg

B. 3.8kg

C. 5.7kg

D. 6.5kg II) Fill in the empty space with correct answer

1. A

2.5 kg system has an acceleration a (4i )m s2 . There are two forces acting on the system, and One of the forces is F1 (3i 6j)N . The other force is .

2. Two masses, m1 and m2, hang over an ideal pulley and the system is free to move. The magnitude of the acceleration a of the system of two masses is The

magnitude of the tension in the cord is .

3. You are swinging a mass m at speed v around on a

string in circle of radius r whose plane is 1.00 m above

the ground as shown in Figure. The string makes an

angle θ with the vertical direction.

(a) Apply Newton' s econd law to the horizontal and

vertical direction to calculate theangle θ is .

(b) If the angle θ = 47.4 a°nd the radius of the circle is

1.50 m, the speed of the mass is .

(c) If the mass is 1.50 kg, the magnitude of the tension

in the string is

(d) The string breaks unexpectedly when the mass is moving

exactly eastward. The location the mass will hit the ground is .

III) Calculate Following Problems:

1. A wedge with mass M rests on a frictionless horizontal table

top. A block with mass m is placed on the wedge, and a horizontal force F is

applied to the wedge. What must be the magnitude of F if the block is to

remain at a constant height above the table top?

2. The mass of blocks A and B in Figure are 20.0kg and 10.0kg, respectively.

The blocks are initially at rest on the floor and are connected by a massless

string passing over a massless and frictionless pulley. An upward force F is

applied to the pulley. Find the accelerations a1 of block A and a2 of block B

when F is

(a) 124N ; (b) 294N ; (c) 424N.

3. An object is drop from rest. Find the function of speed with respect to time

and the terminal speed. Assuming that the drag force

2

is given by D = bv .

4. A small bead can slide without friction on a circular hoop that is in

a vertical plane and has a radius of 0.100m. The hoop rotates at a

constant rate of 4.00rev/s about a vertical diameter.

(a) Find the angleβ at which the bead is in vertical equilibrium.

(b) Is it possible for the bead to “ride” at the same elevation as the

center of the hoop?

(c) What will happen if the hoop rotates at 1.00rev/s.

Chapter 3 Linear momentum, Conservation of momentum

I)Choose one correct answer among following choices

1.An object is moving in a circle at constant speedv . The magnitude of the rate of change of momentum of the object

23

A.is zero.

B. is proportional to v.

C. is proportional to v .

D. is proportional to v .

2.If the net force acting on a body is constant, what can we conclude about its momentum?

A. The magnitude and/or the direction of P may change.

B.The magnitude of P r remains fixed, but its direction may change.

C.The direction of P remains fixed, but its magnitude may change.

D.P remains fixed in both magnitude and direction.

3.If I is the impulse of a particular force, what is dI /dt ?

A. The momentum

B. The change in momentum

C.The force

D. The change in the force

4. A variable force acts on an object from t i 0 to t f . The impulse of the force is zero. One can conclude that

A. r 0 and P 0.

B. r 0 but possibly P 0.

C. possibly r 0 but P 0.

D. possibly r 0 and possibly P 0.

5. A system of N particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?

A. It must be zero.

B. It could be non-zero, but it must be constant.

C. It could be non-zero, and it might not be constant.

D.The answer depends on the nature of the internal forces in the

system.

6.The x and y coordinates of the center of mass of the three-

particle system shown below are:

A. 0, 0

B. 1.3m, 1.7m

C. 1.4m, 1.9m

D. 1.9m, 2.5m

7.Block A, with a mass of 4 kg, is moving with a speed of 2.0m/s

while block B, with a mass of 8 kg, is moving in the opposite

direction with a speed of 3m/s. The center of mass of

the two block-system is moving with a velocity of:

A. 1.3m/s in the same direction as A.

B.1.3m/s in the same direction as B.

C.2.7m/s in the same direction as A.

D.1.0m/s in the same direction as B.

8. A large wedge with mass of 10kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block 's velocity is 3.0m/s and the horizontal component is 6.0m/s. At that instant the velocity of the wedge is:

A. 3.0m/s to the left

B. 3.0m/s to the right

C. 6.0m/s to the right

D. 6.0m/s to the left

9. A 1.0-kg ball moving at 2.0m/s perpendicular to a wall rebounds from the wall at

1.5m/s. The change in the momentum of the ball is:

A. zero

B. 0.5N s· away from wall

C. 0.5N s· toward wall

D. 3.5N s· away from wall

II)Fill in the empty space with correct answer

1.Two objects, A and B, collide(碰撞). A has a mass of m A 2kg , and B has a mass of m B

4kg. The velocities before the collision are v A (2i 3j)m/s and v B (4i 2j)m/s. After the collision, v A (3i 2 j ) m/s. The final velocity of B

v B m/s.

2. A stream of water impinges on(撞击) a stationary “dished”

turbine blade, as shown in Fig.8. The speed of the water is v, both

before and after it strikes the curved surface of the blade, and the

mass of water striking the blade per unit time is constant at the

value dm/dt . The force exerted by the water on the

blade is ______________ .

o

3. A 320g ball with a speed v of 6.22m/s strikes a wall at angle θ of 30.0o and then rebounds with the same speed and angle. It is in contact with the wall for 10.4 ms.

(a)The impulse was experienced by the wall is .

(b)The average force exerted by the ball on the wall is .

4.The muzzle speed of a bullet can be determined using a device called

a ballistic pendulum, shown in Figure. A bullet of mass m moving at

speed v encounters a large mass M hanging vertically as a pendulum at

rest. The mass M absorbs the bullet. The hanging mass (now consisting of

M + m) then swings to some height h above the initial position of the

pendulum as shown. The initial speed v′ of the pendulum (with the

embedded bullet) after impact is . The muzzle

speedv of the bullet is .

III)Calculate Following Problems:

1. A block of mass m 1=1.60kg initially moving to the right with a speed of 4.00 m/s on a frictionless horizontal track collides with a spring attached to a second block of mass

m2=2.10kg initially moving to the left with a speed of 2.50 m/s, as shown in Figure. The spring constant is 600 N/m.

(a) At the instant block 1 is moving to the right with a speed of 3.00 m/s, as in Figure, determine the velocity of block 2.

(b) Determine the distance the spring is compressed at that instant.

Chapter 4 Work and Energy

I) Choose one correct answer among following choices

1. The work done by gravity during the descent of a projectile:

A. is positive

B. is negative

C. is zero

D. depends for its sign on the direction of the y axis

2. A particle has a constant kinetic energyE k . Which of the following quantities must also

be constant? ( )

(A) r (B) v (C) v (D) P

3. A 0.2kg block slides (滑行) across a frictionless floor with a speed of 10m /s. The

net work done on the block is ( )

(A) -20J (B) -10J (C) 0J (D) 20J

4. A 0.50kg object moves in a horizontal circular track with a radius of 2.5m. An external

force of 3.0N, always tangent to the track, causes the object to speed up as it goes

around. The work done by the external force as the mass makes one revolution is:

A. 24 J

B. 47 J

C. 59 J

D. 94 J

2. A

3.00-kg steel ball strikes a wall with a speed of 10.0

m/s at an angle of 60.0 with t °he surface. It bounces off

with the same speed and angle. If the ball is in contact with

the wall for 0.200 s, what is the average force exerted on

the ball by the wall?

3. A small ball with mass m is released from rest at the top of a container which inside wall is semicircle-shaped

and frictionless. The container with mass M and radius horizontal surface, as shown. When the ball slides to point B at the bottom of the

container, find the normal force exerted by the container on the ball.

R rests on a frictionless

5. A man pushes an 80-N crate a distance of 5.0m upward along a frictionless slope that makes an angle of 30? with the horizontal. His force is parallel to the slope. If the 2

speed of the crate decreases at a rate of 1.5m,/ sthen the work done by the man is: A. -200 J B. 61 J C. 140 J D. 200 J

6.When a certain rubber band is stretched a distance x, it exerts a restoring force of 2 magnitude F = ax+bx , where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:

2 3 2 2 3

A. aL2 + bLx3

B. aL + 2bL2

C. a + 2bL

D. aL2/2 +bL3/3

7.An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it the spring is extended 6.0cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10cm. While the spring is being extended by the force, the work done by the spring is: A. -3.6J B. -3.3J C. 3.6 J D. 3.3J

8.Two objects with masses of m1 and m2 have the same kinetic energy and are both moving to the right. The same constant force F is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is:

A. 1:4

B. 4:1

C. 1:2

D. 1:1

9.At time t = 0 a 2-kg particle has a velocity of (4m/s) i - (3m/s) j . At t = 3s its velocity is (2m/s) i + (3m/s) j . During this time the work done on it was:

A. 4 J

B. -4J

C. -12 J

D. -40 J

10. A 2-kg block starts from rest on a rough inclined plane that makes an angle of 6o0 with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0m down the plane, the mechanical energy of the Earth-block system changes by: A. 0 B. -9.8J C.

9.8J D. - 4.9 J

II)Fill in the empty space with correct answer

1. A chain(链条) is held on a frictionless table with one-fourth of

its length hanging over the edge, as shown in figure. If the chain

has a lengthL and a massm , the work required to pull the hanging

part back on the table is J.

2. A 0.1kg block is dropped from a height of 2m onto a spring of

force constant k = 2N/m, as shown. The maximum distance the

spring will be compressed is ____________ m . (g=10m/2s)

3. A single constant force F 3i 5j N acts on a

4.00-kg particle.

(a) If the particle moves from the origin to the point having the vector position r 2i 3j m, the work down by this force is .

(b) If its speed at the origin is 4.00 m/s, the speed of the particle at r is .

(c)The change in the potential energy of the system is

III)Calculate Following Problems:

1. A 3.00-kg mass starts from rest and slides a distance d down a

frictionless 30.0 incline°. While sliding, it comes into contact with

an unstressed spring of negligible mass, as shown. The mass slides

an additional 0.200 m as it is brought momentarily to rest by

compression of the spring (k=400

N/m). Find the initial separation d between the mass and the

spring.

2.Two masses are connected by a light string passing over a light frictionless pulley as shown. The 5.00-kg mass is released from rest.

(a)Determine the speed of the 3.00-kg mass just as the 5.00-kg mass hits the ground.

(b)Find the maximum height to which the 3.00-kg mass rises.

Chapter 5 Angular momentum and Rigid body

I)Choose one correct answer among following choices

1. A particle moves with position given by r 3ti 4j , where r is measured in meters when t is measured in seconds. For each of the following, consider only t > 0. The magnitude of the angular momentum of this particle about the origin is A. increasing in time. B. constant in time. C. decreasing in time. D. undefined

2. A solid object is rotating freely without experiencing any external torques. In this case

A. Both the angular momentum and angular velocity have constant direction.

B.The direction of angular momentum is constant but the direction of the angular velocity might not be constant.

C.The direction of angular velocity is constant but the direction of the angular momentum might not be constant.

D.Neither the angular momentum nor the angular velocity necessarily has a constant direction.

3. A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. The magnitude of its angular momentum about the center of the circle is:

2 2 2 2 2

A. 6.0kg m·2/s

B. 12 kg m·2/s

C. 48 kg/m2· s

D. 72 kg m·2/s2

4. A 6.0-kg particle moves to the right at 4.0m/s as shown. The

magnitude of its angular momentum about the point O is:

22

A. zero

B. 288 kg·m /s

C. 144 kg·m /s

D.

24kg·m2/s

5.Two objects are moving in the x, y plane as shown. The

magnitude of their total angular momentum (about

the origin O) is:

A. zero

B. 6kg m·2/s

C. 12kg m·2/s

D. 30kg m·2/s

6. A 2.0-kg block starts from rest on the positive x axis 3.0m from the origin and

2

thereafter has a constant acceleration given by a 4i 3j(m/s2). At the end of 2s its

angular momentum about the origin is:

2 2 2

A. 0

B. (-36 kg ·2/sm) k

C. (+48 kg m·2/s) k

D. (-96 kg ·2/sm)k

7.As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of

12rad/s. The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75m from the origin. The z component of the angular momentum around the origin is:

2 2 2 2

A. 6.0kg m·2/s

B. 9.0kg m·2/s

C. 11kg m·2/s

D. 14kg m·2/s

II)Fill in the empty space with correct answer

1. A particle located at the position vector r (2i j) m is acted by a force

F (i 3j)N. The torque about the origin should be _______________ N m.

2.The velocity of a m=2kg body moving in the xy plane is given by v (i 2j) m/s.

Its position vector is r (2i j)m. Its angular momentum L about the origin should

be _____________ kg m2s.

3.Two particles each of mass m and speed v, travel in

opposite directions along parallel lines separated by a distance

d. The total angular momentum of the system about any origin

is .

4. A particle is located at r = (0.5m) i + (-0.3m) j + (0.8m) k . A constant force of

magnitude 2N acts on the particle. When the force acts in the positive x direction, the components of the torque about the origin is , and when the force acts in the negative x direction, the components of the torque about the origin is .

5. A uniform beam of length l is in a vertical position with its lower end on a rough surface that prevents this end from slipping. The beam topples. At the instant before impact with the floor, the angular speed of the beam about its fixed end is .

6. A disk of mass m and radius R is free to turn about a fixed, horizontal axle. The

disk has an ideal string wrapped around its periphery from which another mass m (equal to the mass of the disk) is suspended, as indicated in Figure. The

magnitude of the acceleration of the falling mass is , the magnitude of the

angular acceleration of the disk is .

III)Calculate Following Problems:

2

1.The pulley has radius 0.160m and moment of inertia 0.480kg·m . The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.

2. A block with mass m slides down a surface inclined 30 to the horizontal. The coefficient of kinetic friction is μ. A string attached to the block is wrapped around a wheel on a fixed axis. The wheel has massm and radius R with respect to the axis of rotation. The string pulls without slipping.

a) What is the acceleration of the block down the plane? b)

What is the tension in the string?

3. A wooden block of mass M resting on a frictionless horizontal surface is attached

to a rigid rod of length l and of negligible mass. The rod is pivoted

at the other end. A bullet of mass m traveling parallel to the

horizontal surface and normal to the rod with speedv hits the block

and becomes embedded in it. What is the angular momentum of

the bullet–block system?

Chapter 9 Mechanic oscillation

I)Choose one correct answer among following choices

1. A particle on a spring executes simple harmonic motion. If the mass of the particle and the amplitude are both doubled then the period of oscillation will change by a factor of

A. 4.

B. 8.

C. 2.

D. 2

2. A particle is in simple harmonic motion with amplitude A. At time t=0 it is at x=-A/2 and is moving in the negative direction, then the initial phase is:

A. 2π3/ rad

B. 4π3/ rad

C. π rad

D. 3 π /2 rad

3. A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. Of the following times, at which time is it furthest from the equilibrium point?

A. 0.5T

B. 0.7T

C. T

D. 1.4T

4. A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:

A. T

B. 2T

C. T/2

D. 4T

5.The displacement of an object oscillating on a spring is given by x(t) = A cos( ω t + φ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phasec onstant φ is:

A. 0

B. π /2 rad

C. π rad

D. 3 π/2 rad

6.An object is undergoing simple harmonic motion with period T, amplitude A and

1

initial phase . Its graph of x versus t is:

7.An object of mass m, oscillating on the end of a spring with spring constant k, has amplitude A. Its maximum speed is:

A. A k /m

B. A2k/m

C. A m/ k

D. Am/k

II)Fill in the empty space with correct answer

1. The total energy of a s imple harmonic oscillato(r谐振子) with amplitude A and force constant k is _________________ .

2. Find the initial phases(初相) of the simple harmonic motion as shown in figure.

12

III)Calculate Following Problems:

1. An object oscillates with simple harmonic motion along the x axis. Its displacement from the origin varies with time according to the equation: x (4.00m)cos( t 4 ). where t is in seconds and the angles in the parentheses are in radians.

(a) Determine the amplitude, frequency, and period of the motion.

(b) Calculate the velocity and acceleration of the object at any time t.

(c)Determine the maximum speed and maximum acceleration of the object.

2. A 50.0-g mass connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with amplitude of 4.00 cm.

Find (a) the total energy of the system and (b) the speed of the mass when the displacement is 1.00cm.

Find (c) the kinetic energy and (d) the potential energy when the displacement is 3.00cm.

Chapter 10 Waves

I) Choose one correct answer among following choices

1. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:

A. f = 1/T

B. f = v + T

C. f = vT

D. f = v/T

2. Water waves in the sea are observed to have a wavelength of 300m and a frequency of

0.07 Hz. The speed of these waves is:

A. 0.00021m/s

B. 2.1m/s

C. 21m/s

D. 210m/s

3.The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

A. upward

4. A wave is described by y 0.05cos(6 t 0.06 x), where x and y are in meters and t is in seconds. Which of the following is correct?

2

A. wavelength is 5m

B. wave speed is 10m/s

C. period of the wave is 1/3s

D. wave moves in the positive x direction

5. A wave travels in the negative x direction, which have angular speed ω and wave speed u. At t=T/4 the displacement as a function of time is graphed. The wave equation is:

xx

A. y Acos[ (t ) ]

B. y Acos[ (t ) ] u u 2

C. y Acos[ (t x) ]

D. y Acos[ (t x) ] u 2 u

II)Fill in the empty space with correct answer

1. A transverse wave on a string is described by the wave function y 0.20cos(

2.50 t x) . The amplitude of the wave is

; the wavelength of the

wave is ; the angular frequency of the wave is ; the frequency of the wave is ; the period of the wave is

; the speed of the wave is

;

the displacement of the point x = 3.00 m when

2. A simple harmonic transverse wave is propagating along a string toward the left (or -

x) direction with wave speed 0.08m/s. The figure shows a plot of the displacement as a function

of position at time t=0. The wave equation is .

The motion equation of the point P is .

III)Calculate Following Problems:

1. A sinusoidal wave traveling in the positive x direction has an amplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency of 8.00 Hz. The vertical displacement of the medium at and is also 15.0 cm, as shown.

(a) Find the angular wave number k, period T, angular frequency, and speed of the wave.

(b) Find a general expression for the wave function.

2. A transverse wave is described by the expression y 0.08cos(4 t 2 x), where x and y are in the meters, t is in

the seconds.

(a) Find the phase of origin x=0 and the phase of point x=0.10 at t=2.1s.

(b) Find the phase difference between x=0.80m and x=0.30m.

大学物理活页作业答案(全套)

1.质点运动学单元练习（一）答案 1．B 2．D 3．D 4．B 5．3.0m ；5.0m （提示：首先分析质点的运动规律，在t <2.0s 时质点沿x 轴正方向运动；在t =2.0s 时质点的速率为零；，在t >2.0s 时质点沿x 轴反方向运动；由位移和路程的定义可以求得答案。） 6．135m （提示：质点作变加速运动，可由加速度对时间t 的两次积分求得质点运动方程。） 7．解：（1）)()2(22 SI j t i t r )(21m j i r )(242m j i r )(3212m j i r r r )/(32s m j i t r v （2）)(22SI j t i dt r d v )(2SI j dt v d a )/(422s m j i v )/(222 s m j a 8．解： t A tdt A adt v t o t o sin cos 2 t A tdt A A vdt A x t o t o cos sin

9．解：（1）设太阳光线对地转动的角速度为ω s rad /1027.73600 *62 /5 s m t h dt ds v /1094.1cos 32 （2）当旗杆与投影等长时，4/ t h s t 0.31008.144 10．解： ky y v v t y y v t dv a d d d d d d d -k y v d v / d y C v ky v v y ky 2 22 121, d d 已知y =y o ，v =v o 则2 020 2 121ky v C )(22 22y y k v v o o

大学物理学上下册公式(整合版)

大学物理公式集1 1概念（定义和相关公式） 1．位置矢量：r ，其在直角坐标系中：k z j y i x r ++=；222z y x r ++=角位置：θ 2．速度：dt r d V = 平均速度：t r V ??= 速率：dt ds V = （τ V V =）角速度： dt d θω= 角速度与速度的关系：V=ｒω 3．加速度：dt V d a =或 2 2dt r d a = 平均加速度：t V a ??= 角加速度：dt d ωβ= 在自然坐标系中n a a a n +=ττ其中dt dV a = τ（=ｒβ），r V n a 2 = （=r 2 ω） 4．力：F =ｍa （或F = dt p d ） 力矩：F r M ?=（大小：M=rFcos θ方向：右手螺旋 法则） 5．动量：V m p =，角动量：V m r L ?=（大小：L=rmvsin θ方向：右手螺旋法则） 6．冲量：? = dt F I （=F Δｔ）；功：? ?= r d F A （气体对外做功：A=∫PdV ） 7．动能：mV 2/2 8．势能：A 保= – ΔE p 不同相互作用力势 能形式不同且零点选择不同其形式 不同，在默认势能零点的情况下： 机械能：E=E K +E P 9．热量：CRT M Q μ =其中：摩尔热容 量C 与过程有关，等容热容量C v 与等压热容量C p 之间的关系为：C p = C v +R 10． 压强：ωn tS I S F P 3 2= ?== 11． 分子平均平动能：kT 23=ω；理想气体内能：RT s r t M E )2(2 ++=μ 12． 麦克斯韦速率分布函数：NdV dN V f =)(（意义：在V 附近单位速度间隔内的分子 数所占比率） 13． 平均速率：πμ RT N dN dV V Vf V V 80 )(= = ? ?∞ mg(重力) → mgh -kx （弹性力） → kx 2/2 F= r r Mm G ?2 - (万有引力) →r Mm G - =E p r r Qq ?420πε(静电力) →r Qq 04πε

大学物理双语2012-2013-1月A答案及评分标准

标准答案及评分标准 一．Choice(20分，每题4分) 1. a 2. b 3. c 4. d 5. a 二．Blanks （20分） 6. 0.5 （1分） 3 (1分) 1/2 (1分) π/6（2分） 3π or 9.42 (3pts) 7. 1.26 （3分） 8. 2.26°(3分) 9. 3.56×10-28 (3分) 10. 1.14eV (3分) 三．Questions(10分) 11. (5pts) The relativity principle: The laws of physics must be the same in all inertial reference frames. 一切物理规律在惯性系中相同。(2分) The constancy of the speed of light: The speed of light in vacuum has the same value c in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light. 真空中的光速在任何惯性系中都是c ，与光源或观察者的运动无关。（3分） 12. (5pts) The maximum kinetic energy of photoelectrons is independent of light intensity. (2分) No electrons are emitted if the incident light frequency falls below some cutoff frequency fc , whose value is characteristic of the material being illuminated, regardless of the light intensity.（3分） 四. Problems （50分） 13(10pts) (1) The average transitional kinetic energy 21101.623-?== kT K t J ………………… 3pts (2) the rms speed s m M RT v rms /4803≈= ………………… 3pts (3) the internal energy RT i E 2 = ………………… 1pts For O 2, i = 5, ………………… 1pts the internal energy 60912≈= RT i E J ………………… 2pts 14(10pts) (1) 1→2: Isothermal expansion )/ln( 12V V nRT Q H H = ………………… 2pts 3→4: Isothermal compression )/ln( 34V V nRT Q L L = ………………… 2pts (2) 2→3: Adiabatic expansion 1312 --=γγV T V T L H ………………… 1pts

(完整版)大学物理上册复习提纲

《大学物理》上册复习纲要 第一章 质点运动学 一、基本要求： 1、 熟悉掌握描述质点运动的四个物理量——位置矢量、位移、速度和加速度。会处理两类问题：（1）已知运动方程求速度和加速度；（2）已知加速度和初始条件求速度和运动方程。 2、 掌握圆周运动的角速度、角加速度、切向加速度和法向加速度。 二、内容提要： 1、 位置矢量： z y x ++= 位置矢量大小： 2 22z y x ++= 2、 运动方程：位置随时间变化的函数关系 t z t y t x t )()()()(++= 3、 位移?： z y x ?+?+?=? 无限小位移：k dz j dy i dx r d ++= 4、 速度： dt dz dt dy dt dx ++= 5、 加速度：瞬时加速度： k dt z d j dt y d i dt x d k dt dv j dt dv i dt dv a z y x 222222++=++= 6、 圆周运动： 角位置θ 角位移θ? 角速度dt d θω= 角加速度22dt d dt d θ ωα== 在自然坐标系中：t n t n e dt dv e r v a a +=+=2 三、 解题思路与方法： 质点运动学的第一类问题：已知运动方程通过求导得质点的速度和加速度，包括它沿各坐标轴的分量；

质点运动学的第二类问题：首先根据已知加速度作为时间和坐标的函数关系和必要的初始条件，通过积分的方法求速度和运动方程，积分时应注意上下限的确定。 第二章 牛顿定律 一、 基本要求： 1、 理解牛顿定律的基本内容； 2、 熟练掌握应用牛顿定律分析问题的思路和解决问题的方法。能以微积分为工具，求解一维变力作用下的简单动力学问题。 二、 内容提要： 1、 牛顿第二定律: a m F = 指合外力 a 合外力产生的加速度 在直角坐标系中： x x ma F = y y ma F = z z ma F = 在曲线运动中应用自然坐标系: r v m ma F n n 2 == dt dv m ma F t t == 三、 力学中常见的几种力 1、 重力: mg 2、 弹性力: 弹簧中的弹性力kx F -= 弹性力与位移成反向 3、 摩擦力：摩擦力指相互作用的物体之间，接触面上有滑动或相对滑动趋势产生的一种阻碍相对滑动的力，其方向总是与相对滑动或相对滑动的趋势的方向相反。 滑动摩擦力大小: N f F F μ= 静摩擦力的最大值为：N m f F F 00μ= 0μ静摩擦系数大于滑动摩擦系数μ 第三章 动量守恒定律和能量守恒定律 一、 基本要求： 1、 理解动量、冲量概念，掌握动量定理和动量守恒定律，并能熟练应用。 2、 掌握功的概念，能计算变力作功，理解保守力作功的特点及势能的概念。 3、 掌握动能定理、功能原理和机械能守恒定律并能熟练应用。 4、 了解完全弹性碰撞和完全非弹性碰撞的特点。 二、 内容提要 （一） 冲量

大学物理习题及答案

x L h 书中例题：1.2, 1.6（p.7;p.17）（重点） 直杆AB 两端可以分别在两固定且相互垂直的直导线槽上滑动，已知杆的倾角φ＝ωt 随时间变化，其中ω为常量。 求：杆中M 点的运动学方程。 解：运动学方程为： x=a cos(ωt) y=b sin(ωt) 消去时间t 得到轨迹方程： x 2/a 2 + y 2/b 2 = 1 椭圆 运动学方程对时间t 求导数得速度： v x ＝dx/dt ＝-a ωsin(ωt) v y ＝dy/dt ＝b ωcos(ωt) 速度对时间t 求导数得加速度： a x ＝d v x /dt ＝－a ω2cos(ωt) a y ＝d v y /dt ＝－b ω2sin(ωt) 加速度的大小： a 2＝a x 2＋a y 2 习题指导P9. 1.4（重点） 在湖中有一小船，岸边有人用绳子跨过一高处的滑轮拉船靠岸，当绳子以v 通过滑轮时， 求：船速比v 大还是比v 小？ 若v 不变，船是否作匀速运动？ 如果不是匀速运动,其加速度是多少？ 解： l ＝（h2＋x2）1/2 221/2 122()d l x d x v d t h x d t ==+ 221/2()d x h x v d t x += 当x>>h 时，dx/dt ＝v ，船速＝绳速 当x →0时，dx/dt →∞ 加速度： x y M A B a b φ x h

220d x d t =2221/22221/2221/2221/2221/22221/2()1()11()()1112()2()d x d h x v dt dt x d h x v dt x d dx d h x dx h x v v dx x dt x dx dt dx x dx h x v v x dt x h x dt ?? +=??????=?+???? +??=?++ ???=-?+++ 将221/2()d x h x v d t x +=代入得： 2221/2221/2 221/2 22221/21()112()()2()d x h x x h x h xv v v v d t x x x h x x ++=-?+++3222232222)(x v h x v v x x h dt x d -=++-= 分析： 当x ∞, 变力问题的处理方法（重点） 力随时间变化：F ＝f （t ） 在直角坐标系下，以x 方向为例，由牛顿第二定律： ()x dv m f t dt = 且：t ＝t 0 时，v x ＝v 0 ；x ＝x 0 则： 1 ()x dv f t dt m = 直接积分得： 1 ()()x x v dv f t dt m v t c ===+?? 其中c 由初条件确定。 由速度求积分可得到运动学方程：

大学物理上下册常用公式

大学物理第一学期公式集 概念（定义和相关公式） 1．位置矢量：r ，其在直角坐标系中：k z j y i x r ；222z y x r 角位置：θ 2．速度：dt r d V 平均速度：t r V 速率：dt ds V （ V V ）角速度：dt d 角速度与速度的关系：V=ｒω 3．加速度：dt V d a 或 2 2dt r d a 平均加速度：t V a 角加速度：dt d 在自然坐标系中n a a a n 其中dt dV a （=ｒβ），r V n a 2 （=r 2 ω） 4．力：F =ｍa （或F =dt p d ） 力矩：F r M （大小：M=rFcos θ方向：右手螺旋法则） 5．动量：V m p ，角动量：V m r L （大小：L=rmvcos θ方向：右手螺旋法则） 6．冲量： dt F I （=F Δｔ）；功： r d F A （气体对外做功：A=∫PdV ） 7．动能：mV 2/2 8．势能：A 保= – ΔE p 不同相互作用力势能形式不同 且零点选择不同其形式不同，在默认势能零点的 情况下： 机械能：E=E K +E P 9．热量：CRT M Q 其中：摩尔热容量C 与过程 有关，等容热容量C v 与等压热容量C p 之间的关系为：C p = C v +R 10． 压强： n tS I S F P 3 2 11． 分子平均平动能：kT 23 ；理想气体内能：RT s r t M E )2(2 12． 麦克斯韦速率分布函数：NdV dN V f )(（意义：在V 附近单位速度间隔内的分子数所占比率） 13． 平均速率： RT N dN dV V Vf V V 80 )( 方均根速率： RT V 22 ；最可几速率： RT p V 3 14． 熵：S=Kln Ω（Ω为热力学几率，即：一种宏观态包含的微观态数） 15． 电场强度：E =F /q 0 （对点电荷：r r q E ?42 ） 16． 电势： a a r d E U （对点电荷r q U 04 ）；电势能：W a =qU a (A= –ΔW) 17． 电容：C=Q/U ；电容器储能：W=CU 2/2；电场能量密度ωe =ε0E 2/2 18． 磁感应强度：大小，B=F max /qv(T)；方向，小磁针指向（S →N ）。 mg(重力) → mgh -kx （弹性力） → kx 2/2 F= r r Mm G ?2 (万有引力) →r Mm G =E p r r Qq ?420 (静电力) →r Qq 04

大学物理双语2012-2013-1月A

一、Choice (4pts*5) 1. Free expansion . A adiabatic container has two parts connected by a valve (阀门). The volume of the two parts is the same ( Fig.1 ). The left part is filled with ideal gas (diatomic molecule 双原子分子) with temperature T . When the valve is opened, the gas will expand freely to fill both parts. After the system reach thermal equilibrium, the temperature of the gas is () (a) T (b) 2/T (c) 3/22/T (d) T 2 2 A red star and a blue star, which has higher surface temperature? (a) The red star (b) The blue star (c) They have the same surface temperature (d) Unable to determine 3. A particle’s location is measured and specified as being exactly at x = 0, with zero uncertainty in the x direction. How does that location affect the uncertainty of its momentun component in the y direction? (a) It does not affect it. (b) It makes it infinite. (c) It makes it zero. 4. Unpolarized light passes through two polarizers whose optical axes are in the same direction. The intensity of the emerging light is I 0. If a third polarizer is placed between the polarizers so that its axis is at an angle θ with the other two, the intensity of the emerging light is (a) zero (b) I 0 (c) I 0 cos 2θ (d) I 0 cos 4θ 5. The following functions may represent the wave motion f (x ,t ) in a one-dimensional elastic medium in terms of position x , time t , and positive constants A , a , and b . Which function represents a traveling wave moving in the negative x-direction? (a) ()()bt ax A t x f +=sin , (b) ()()bt ax A t x f -=sin , (c) ()bt ax A t x f cos cos ,= (d) ()bt ax A t x f sin sin ,= Fig.1

大学物理上册答案详解

大学物理上册答案详解 习题解答 习题一 1—１ |r ?｜与r ? 有无不同？ t d d r 和t d d r 有无不同? t d d v 和t d d v 有无不同?其不同在哪里？试举例说明． 解：(1)r ?是位移的模，?r 是位矢的模的增量，即 r ?12r r -=,12r r r -=?； (２) t d d r 是速度的模，即t d d r ==v t s d d . t r d d 只是速度在径向上的分量。 ∵有r r ?r =（式中r ?叫做单位矢），则 t ?r ?t r t d d d d d d r r r += 式中 t r d d 就是速度径向上的分量， ∴ t r t d d d d 与r 不同如题1—1图所示. 题1—1图 （３）t d d v 表示加速度的模,即t v a d d =，t v d d 是加速度a 在切向上的分 量. ∵有ττ (v =v 表轨道节线方向单位矢），所以 t v t v t v d d d d d d ττ +=

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1.Reference frames. 2.Displacement, velocity, acceleration. 3.Motion in 1 and 2 dimensions. 4.Vector (i, j, k form). 5.Projectile motion 6.Circular motion 7.Relative motion

[] j v i v j t y i t x dt d dt r d v y x r r r r r r +=+== )()(Instantaneous velocity (瞬时速度) : Instantaneous Acceleration: 22d d d d t r t v a r r r ==j a i a a y x r r r +=??? ????====2222 d d d d d d d d t y t v a t x t v a y y x x

[] j v i v j t y i t x dt d dt r d v y x r r r r r r +=+== )()(Instantaneous velocity (瞬时速度) : Instantaneous Acceleration: 22d d d d t r t v a r r r ==j a i a a y x r r r +=??? ????====2222 d d d d d d d d t y t v a t x t v a y y x x

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