Momentum and Impulse

Question 1

Question 1: 1. With respect to a spring oscillator in simple harmonic motion in the horizontal direction, the fo...

1. With respect to a spring oscillator in simple harmonic motion in the horizontal direction, the following statement is correct

A. A. The acceleration must be the same when the oscillator is at its maximum displacement
B. B. The speed of the oscillator must be the same each time it passes through the equilibrium position
C. C. The oscillator has the same displacement on two consecutive passes through the same position
D. D. The oscillator has the same kinetic energy and momentum when it passes through the same position twice in a row

Answer

Answer: C

Solution: A. When the oscillator is at the maximum displacement, the restoring force points to the equilibrium position, and the acceleration at the maximum displacement on both sides is reversed, so A is wrong; B. When the oscillator passes through the equilibrium position, the velocity has two possible directions, so B is wrong; C. The displacement is a directed line segment pointing from the equilibrium position to the position of the vibrator, so the vibrator passes through the same position twice in a row with the same displacement, so C is correct; D. When the oscillator passes through the same position twice in a row (except at the maximum displacement), the velocity is the same, so the kinetic energy is the same; the direction of the velocity is different, so the momentum is different, so D is wrong.

Question 2

Question 2: 2. The following statements about the four diagrams are correct. ![](/images/questions/phys-momentum...

2. The following statements about the four diagrams are correct. ![](/images/questions/phys-momentum/image-001.jpg) ![](/images/questions/phys-momentum/image-002.jpg) B ![](/images/questions/phys-momentum/image-003.jpg) C ![](/images/questions/phys-momentum/image-004.jpg) D

A. A. Conservation of mechanical energy at the moment of the explosion of the shell in Figure A
B. B. Figure B, A, B with a compressed light spring connected to a smooth horizontal surface, after the release of A, B and the spring composed of the system momentum conservation
C. C. In Figure C, the bullet pierces the wooden ball, the system consisting of the bullet and the wooden ball does not conserve momentum in the horizontal direction.
D. D. Figure D in the car is located on a smooth horizontal surface, the person will be thrown horizontally to the left after the ball, the car, the person and the ball composed of a system of conservation of momentum

Answer

Answer: B

Solution: A. Figure A in the moment of the explosion of the shell, there is chemical energy into mechanical energy, so mechanical energy is not conserved, so A error; B. Figure B, A, B with a compressed spring connected to a smooth horizontal surface, after the release of A, B and spring system to meet the conservation of momentum, so B is correct; C. Figure C in the process of the bullet through the wooden ball, the bullet and the wooden ball system can be considered to be subjected to the sum of the external forces is zero, the system to meet the conservation of momentum in the horizontal direction, so C is wrong; D. Figure D in the car is located on a smooth horizontal surface, people will throw the ball horizontally to the left, the car, people and the ball composed of the system to meet the horizontal direction of momentum conservation, but the direction of the system does not meet the conservation of momentum, so D error.

Question 3

Question 3: 3. The following four sets of physical quantities are all scalars

3. The following four sets of physical quantities are all scalars

A. A. Momentum change, magnetic flux
B. B. Magnetic induction, electric field strength
C. C. Induced current, potential difference
D. D. Electric power, impulse

Answer

Answer: C

Solution: Scalar is only the size, no direction of the physical quantity, vector is both the size and direction of the physical quantity, options in the amount of momentum, magnetic induction, electric field strength, impulse belongs to the vector, induced current, potential difference belongs to the scalar. Therefore, choose C.

Question 4

Question 4: 4. As shown in the figure for a sports running shoes publicity map, the picture shows: "the shoes so...

4. As shown in the figure for a sports running shoes publicity map, the picture shows: "the shoes sole EVA material, can effectively absorb the impact of walking or sports, to protect the feet from injury". For the shoes, the following statements are correct. ![](/images/questions/phys-momentum/image-005.jpg)

A. A. Reducing the time of impact between the feet and the soles of the shoes, thus reducing the combined impulse on the feet
B. B. Prolonging the time of impact between the feet and the soles of the shoes, thus reducing the combined impulse on the feet
C. C. Prolongs the time of impact between the feet and the sole, thus reducing the average impact of the sole on the feet
D. D. Reduces the time of impact between the foot and the sole, thus reducing the average impact of the sole on the feet

Answer

Answer: C

Solution: AB . From the Momentum Theorem $I = m v - m v _ { 0 }$, it is clear that the impulse of the combined force on the feet remains the same whether you shorten or lengthen the time of impact between the feet and the soles of the shoes. Therefore, AB is wrong; CD. From $I = \bar { F } \Delta t$, we can know that lengthening the impact time between the feet and the soles reduces the average impact force of the soles on the feet. Therefore, C is correct and D is wrong.

Question 5

Question 5: 5. The motion of the high-speed train at the starting stage can be regarded as a uniformly accelerat...

5. The motion of the high-speed train at the starting stage can be regarded as a uniformly accelerated linear motion with zero initial velocity. Timing from the start of the train, with its position at the time of departure as the initial position, in the start-up phase, the momentum of the train size ()

A. A. is proportional to the time it takes
B. B. is proportional to the quadratic of the time it has taken
C. C. is proportional to the magnitude of its displacement
D. D. is proportional to its kinetic energy

Answer

Answer: A

Solution: FORMULA_3]], then the magnitude of momentum is $P = m v = m \sqrt { 2 a x }$, so C is wrong; according to $P = m v , E _ { k } = \frac { 1 } { 2 } m v ^ { 2 }$, then: $P = \sqrt { 2 m E _ { k } }$, so D is wrong; Therefore, choose A.

Question 6

Question 6: 6. The following statement is correct about the conditions for conservation of momentum ()

6. The following statement is correct about the conditions for conservation of momentum ()

A. A. Momentum cannot be conserved as long as there is friction in the system
B. B. The momentum of the system is conserved as long as the external force on the system is 0.
C. C. The acceleration of the system is 0 and momentum is not necessarily conserved.
D. D. As long as the combined external force on the system is not 0, the system cannot have conservation of momentum in any direction

Answer

Answer: B

Solution: AB. The condition for the conservation of momentum is that the system is subjected to zero external force, and the system has nothing to do with friction, so A is wrong, B is correct; C. When the acceleration of the system is zero, according to Newton's second law can be obtained by the system by the external force is zero, so this time the system momentum conservation, so C error; D. When the system external force is not zero, in a certain direction of the external force may be zero, then in the direction of the system momentum is conserved, so D error.

Question 7

Question 7: 7. If two objects have the same momentum, they must have ( )

7. If two objects have the same momentum, they must have ( )

A. A. Same speed
B. B. equal mass
C. C. same direction of motion
D. D. Same kinetic energy

Answer

Answer: C

Solution: AB. The magnitude of the momentum is $$ p = m v $$ The momentum may be the same even if the mass and velocity are different, so it is not possible to determine that the mass or velocity are the same from the same momentum, so AB is incorrect ; C. Momentum is a vector, momentum is the same, its size and direction have to be the same, and the direction of momentum and the direction of the velocity is the same, so with the same momentum, the direction of motion must be the same, so C is correct; D. By $$ E _ { \mathrm { k } } = \frac { p ^ { 2 } } { 2 m } $$ It can be seen that kinetic energy is not necessarily the same when momentum is the same, so D is wrong.

Question 8

Question 8: 8. In the sport of "bungee jumping", one end of a long elastic cord is fixed and the other end is ti...

8. In the sport of "bungee jumping", one end of a long elastic cord is fixed and the other end is tied to a person who jumps from a height of several tens of meters. The process of bungee jumping is simplified to the movement of the person in a straight direction. From the elastic cord is just straight, to the first drop to the lowest point of the process, if the air resistance is not counted, the following statements are correct

A. A. The person's speed is greatest when the elastic cord is exactly straightened out
B. B. The impulse of the elastic cord on the person is always upward and the momentum of the person is always decreasing
C. C. The tension of the elastic cord on the person always does negative work and the person's kinetic energy always decreases
D. D. The tension on the elastic cord is equal to the force of gravity on the person when the person's speed is maximum

Answer

Answer: D

Solution: A. The elastic rope is exactly straight, the rope on the person's tension is zero, due to gravity is greater than the rope on the person's tension, so the person is still accelerating, this time the speed is not the maximum value, A error; BCD. elastic rope on the person's tension is always up, so the elastic rope on the person's impulse is always up, the elastic rope on the person's tension is always negative work, at first on the person's tension is less than gravity, the person to do the acceleration of the movement, when the person's tension is equal to the force of gravity, the speed of the person reaches a maximum, when the person's tension is greater than the force of gravity the person to do deceleration of the movement, the person to do the acceleration first do the deceleration, so the person's momentum first increase after Decrease, the kinetic energy increases and then decreases, BC is wrong, D is correct.

Question 9

Question 9: 9. In the device shown in the figure, wood block B and the horizontal plane between the contact surf...

9. In the device shown in the figure, wood block B and the horizontal plane between the contact surface is smooth, the bullet A along the horizontal direction into the wood block to stay in the wood block, the spring will be compressed to the shortest. For a system consisting of a wooden block, a spring, and a bullet, the process from the beginning of the bullet shot into the spring compressed to the shortest ![](/images/questions/phys-momentum/image-006.jpg)

A. A. Conservation of momentum, conservation of mechanical energy
B. B. No conservation of momentum, no conservation of mechanical energy
C. C. Momentum is conserved, mechanical energy is not.
D. D. Momentum is not conserved, mechanical energy is conserved.

Answer

Answer: B

Solution: The entire movement process, due to the wall on the spring has a force, the system is subject to the combined external force is not zero, so momentum is not conserved, the bullet shot into the wooden block of the process of friction heat, the system mechanical energy is not conserved.

Question 10

Question 10: 10. The mass of 150 g of Lianjiang red orange from the ground from a height of 5 m from the static f...

10. The mass of 150 g of Lianjiang red orange from the ground from a height of 5 m from the static fall, regardless of air resistance, take the size of the acceleration of gravity ${ } ^ { g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } }$, then in the process of descending, gravity on the size of the impulse of the red orange is ()

A. A. $1.5 \mathrm {~N} \cdot \mathrm {~s}$
B. B. $2 \mathrm {~N} \cdot \mathrm {~s}$
C. C. $2.5 \mathrm {~N} \cdot \mathrm {~s}$
D. D. $3 N \cdot s$

Answer

Answer: A

Solution: A red orange in free-fall motion has $h = \frac { 1 } { 2 } g t ^ { 2 }$ During the fall, the magnitude of the impulse of gravity on the red orange $I = m g t$ Solve for $I = 1.5 \mathrm {~N} \cdot \mathrm {~s}$

Question 11

Question 11: 11. A toy car with a mass of 0.2 kg changes its speed from $3 \mathrm {~m} / \mathrm { s }$ to the l...

11. A toy car with a mass of 0.2 kg changes its speed from $3 \mathrm {~m} / \mathrm { s }$ to the left to $5 \mathrm {~m} / \mathrm { s }$ to the right, with the positive direction to the left, the change in kinetic energy and momentum of the car are ( )

A. A. $1.6 \mathrm {~J} , 0.4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$
B. B. $3.4 \mathrm {~J} , 0.4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$
C. C. $1.6 \mathrm {~J} , - 1.6 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$
D. D. ${ } ^ { 3.4 \mathrm {~J} } , - 1.6 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$

Answer

Answer: C

Question 12

Question 12: 12. As shown in the figure, the mass of $m$ of the object, in the horizontal force $F$ role, with a ...

12. As shown in the figure, the mass of $m$ of the object, in the horizontal force $F$ role, with a speed of $v$ along the horizontal plane of uniform velocity, when the object is moving to the point of A withdrawal of the external force $F$, the object continues to slide forward from point A in the process of passing through point B, then the object from point A to $B$ point in the process, the following statements are correct ( ). When the object moves to point A, the external force $F$ is withdrawn, and the object passes through point B as it continues to slide forward from point A. The following statements are correct during the process of moving the object from point A to point $B$ ( ) ![](/images/questions/phys-momentum/image-007.jpg)

A. A. The larger $V$ is, the greater the impulse of friction on the object; the more work is done by friction
B. B. The larger $v$ is, the greater is the impulse of the friction force on the object; the work done by the friction force is independent of the size of $v$.
C. C. The larger $V$ is, the smaller the impulse of the friction force on the object; the less work is done by the friction force
D. D. The larger $v$ is, the smaller the impulse of friction on the object is; the work done by friction is independent of the size of $v$

Answer

Answer: D

Solution: From the meaning of the question can be seen, the object moves to point A at uniform speed, indicating that the object is subject to friction is equal to the pull, so the size of the pull is unchanged; from A to B movement of the displacement is equal, so the friction force to do work has nothing to do with the size of the speed; if the greater the speed, the shorter the time from A to B, the $I = F t$ can be known that the smaller the impulse, so the D is correct, the ABC is wrong.

Question 13

Question 13: 13. As shown in the figure, A and B are moving in opposite directions on a horizontal road. It is kn...

13. As shown in the figure, A and B are moving in opposite directions on a horizontal road. It is known that the mass of A is 40 kg and the velocity is $v _ { 1 } = 5 \mathrm {~m} / \mathrm { s }$; the mass of B is 80 kg and the velocity is $v _ { 2 } = 2.5 \mathrm {~m} / \mathrm { s }$. The following statement is correct ( ) ![](/images/questions/phys-momentum/image-008.jpg)

A. A. The momentum of A is greater than that of B.
B. B. A and B have the same momentum
C. C. A's momentum magnitude is $200 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } ^ { 2 }$
D. D. B's momentum magnitude is $200 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$

Answer

Answer: D

Solution: According to the formula $$ p = m v $$ It can be seen that the momentum of A is $200 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, then the unit of C is wrong; the momentum of B is $200 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, and the momentums of A and B are equal, but the directions of the momentums are different, so the momentums of A and B are different. Then D is correct and ABC is wrong.

Question 14

Question 14: 14. With respect to the momentum of an object, one of the following statements is correct

14. With respect to the momentum of an object, one of the following statements is correct

A. A. The direction of momentum of a moving object at any given moment must be the direction of velocity at that moment
B. B. An object's momentum must be constant if its acceleration is constant
C. C. The greater the momentum of an object, the greater its speed must be
D. D. The more momentum an object has, the more mass it must have

Answer

Answer: A

Solution: A. Momentum has instantaneous, any moment the direction of the object's momentum, that is, the direction of the velocity of the moment, A positive A is correct; B. Acceleration is constant, the rate of change of the object's speed is constant, the object's speed changes uniformly, so its momentum also changes uniformly, B error; C. The size of the object's momentum by the object's mass and speed of the size of the joint decision, not only by the object's speed, so the object's momentum is large, its speed is not necessarily large, C error; D. The greater the momentum of the object, its mass is not necessarily greater, D error.

Question 15

Question 15: 15. A water pulling car has two water storage tanks, just before the beginning of the water tank has...

15. A water pulling car has two water storage tanks, just before the beginning of the water tank has water, behind the water tank without water, if the water from the front of the tank pumped to the back of the tank, assuming that the water pulling car parked on a smooth horizontal surface, then after pumping, pulling the water car with the original position compared with the

A. A. The water puller moved forward some distance
B. B. The water hauler backed up a bit
C. C. The water truck is still in its original position.
D. D. Couldn't locate the water truck.

Answer

Answer: A

Solution: The system consisting of the water and the water-pulling cart (including the tank) conserves momentum as the water is pumped from the front tank to the back tank, and as the water undergoes a displacement backward, the cart undergoes a displacement forward.

Question 16

Question 16: 16. One of the landmarks in Tianjin, China "Tianjin Eye" is the world's only bridge overlooking the ...

16. One of the landmarks in Tianjin, China "Tianjin Eye" is the world's only bridge overlooking the Ferris wheel. Ferris wheel suspension transparent cockpit, passengers with the cockpit in the firm straight surface to do track radius $R$, angular velocity of $\omega$ uniform circular motion, known as the local gravitational acceleration of $g$, the mass of $m$ passengers from the highest point to the lowest point of the process of movement, the impulse of gravity size of $m$, the mass of $m$. 3]] of the passenger from the highest point to the lowest point of the movement process, the impulse of gravity size is ![](/images/questions/phys-momentum/image-009.jpg)

A. A. 0
B. B. $2 m \omega R$
C. C. $2 m g R$
D. D. $\frac { \pi m g } { \omega }$

Answer

Answer: D

Solution: The time elapsed during the passenger's movement from the highest point to the lowest point is $t = \frac { \pi } { \omega }$ , then the impulse of gravity : $I = m g t = \frac { \pi m g } { \omega } ;$ A. 0 , which is inconsistent with the conclusion, option A is wrong; B. $2 m \omega R$ , which is inconsistent with the conclusion, option B is wrong; C. ${ } ^ { 2 m g R }$ is inconsistent with the conclusion, and option D is wrong; D. $\frac { \pi m g } { \omega }$, is consistent with the conclusion, option D is correct;

Question 17

Question 17: 17. As shown in the figure, there is a car stationary on a smooth horizontal surface, standing on th...

17. As shown in the figure, there is a car stationary on a smooth horizontal surface, standing on the car will be the right tube of the ball one by one into the left basket (the ball is still in the car). With the person, the car and the ball as a system, the following judgment is correct ( ) ![](/images/questions/phys-momentum/image-010.jpg)

A. A. Since the combined external force on the system is zero, the cart will not move
B. B. When the ball is all the way into the frame on the left, the car still has speed to the right
C. C. Since the momentum of the system is conserved in the horizontal direction, the cart moves to the right
D. D. If a person bends his knees and jumps up to throw the ball, then the system has conservation of momentum in the firm straight direction

Answer

Answer: C

Solution: AC. In the process of throwing the ball, the person and the car (including basketball) system by the combined external force is not zero, but the horizontal direction of the combined external force is zero, the system of momentum conservation in the horizontal direction, the basketball by the horizontal to the left of the momentum, then the person and the car system to obtain the right of the horizontal momentum, so the car still has the speed of the right, the car to the right, so the C is correct, A is wrong; B. Before the ball is thrown, the momentum of the system consisting of the man and the car (including the basketball) is zero, when the ball is put into the left frame, the speed of the ball is zero, according to the law of conservation of momentum, the momentum of the car is also zero, and the car will stop, so B is wrong; D. If a person jumps up and throws the ball with knees bent, the combined external force on the system in the direction of firmness is not zero, then the momentum of the system in the direction of firmness is not conserved, so D is wrong.

Question 18

Question 18: 18. The ball is one of the basic techniques of soccer. If a soccer ball with a mass of 400 g is lift...

18. The ball is one of the basic techniques of soccer. If a soccer ball with a mass of 400 g is lifted up with the foot, and then falls to the horizontal ground with a speed of $4 \mathrm {~m} / \mathrm { s }$, and then bounces back with a speed of $3 \mathrm {~m} / \mathrm { s }$, and takes the positive direction of the ball as the positive direction, in the time the soccer ball contacts the ground, the following judgments are correct ( ) about the amount of change of the momentum of the soccer ball $\triangle p$ and the work done by the combined external force on the soccer ball. [INLINE_FORMULA_2]] and the work done by the combined external force on the soccer ball $W$, the following judgment is correct ( ) ![](/images/questions/phys-momentum/image-011.jpg)

A. A. $\triangle p = 1.4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } \quad W = - 1.4 \mathrm {~J}$
B. B. $\triangle p = - 1.4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } \quad W = 1.4 \mathrm {~J}$
C. C. $\triangle p = 2.8 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } \quad W = - 1.4 \mathrm {~J}$
D. D. $\triangle p = - 2.8 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } \quad W = 1.4 \mathrm {~J}$

Answer

Answer: C

Solution: The change in momentum of a soccer ball during its collision with the ground $$ \Delta p = m v _ { 2 } - m v _ { 1 } = 0.4 \times 3 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } - 0.4 ( - 4 ) \mathrm { kg } \cdot \mathrm {~m} / \mathrm { s } = 2.8 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } $$ The direction is vertically upward; By the kinetic energy theorem, the work done by the combined external force $$ W = \frac { 1 } { 2 } m v _ { 2 } ^ { 2 } - \frac { 1 } { 2 } m v _ { 1 } ^ { 2 } = \frac { 1 } { 2 } \times 0.4 \times 3 ^ { 2 } \mathrm {~J} - \frac { 1 } { 2 } \times 0.4 \times 4 ^ { 2 } \mathrm {~J} = - 1.4 \mathrm {~J} $$

Question 19

Question 19: 19. At a certain point in time, object A has a mass of 3 kg and a velocity of $3 \mathrm {~m} / \mat...

19. At a certain point in time, object A has a mass of 3 kg and a velocity of $3 \mathrm {~m} / \mathrm { s }$ in an eastward direction; object B has a mass of 4 kg and a velocity of 4 $\mathrm { m } / \mathrm { s }$ in a westward direction. The sum of their momentums is ()

A. A. $25 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ , heading east
B. B. $12.5 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ , Direction West
C. C. $7 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ , heading east
D. D. $7 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ , Direction West

Answer

Answer: D

Solution: Taking eastward as the positive direction, the momentum of A $p _ { \mathrm { A } } = m _ { \mathrm { A } } \cdot v _ { \mathrm { A } } = 3 \mathrm {~kg} \times 3 \mathrm {~m} / \mathrm { s } = 9 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ is directed eastward; the momentum of $B$ $p _ { \mathrm { B } } = m _ { \mathrm { B } } \cdot v _ { \mathrm { B } } = 4 \mathrm {~kg} \times ( - 4 ) \mathrm { m } / \mathrm { s } = - 16 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ direction west; the total momentum $p _ { \text {总 } } = p _ { \mathrm { A } } + p _ { \mathrm { B } } = 9 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } + ( - 16 ) \mathrm { kg } \cdot \mathrm { m } / \mathrm { s } = - 7 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, with a negative sign indicating a westward direction, is of size $7 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$.

Question 20

Question 20: A ball of a certain mass is placed on a firm spring and pressed down to position $A$ as shown in fig...

A ball of a certain mass is placed on a firm spring and pressed down to position $A$ as shown in figure A. The ball is then lifted to the highest position $C$ (figure C). After a quick release, the spring springs the ball up and it rises to the highest position $C$ (Figure C), passing through the position $B$ on the way to the point where the spring resumes its position. The spring is restored to its length when it passes through position $B$ on the way (Figure B). The mass of the spring and the air resistance are negligible. The following statements are correct O. $C$ ![](/images/questions/phys-momentum/image-012.jpg)

A. A. The momentum of the ball increases from $A$ to $C$.
B. B. A to $C$, the impulse of the ball's gravity is less than the impulse of the spring's elastic force
C. C. $A$ to $B$, the increase in the momentum of the ball is equal to the impulse of the spring force
D. D. From $A$ to $B$, the impulse of the ball's gravity has been getting larger

Answer

Answer: D

Solution: A. The ball from $A$ to $C$ position of the process, the first acceleration, when the $B$ point of the spring of the elastic force $k \triangle x = m g$, the combined force of zero, acceleration decreases to zero, the speed reaches a maximum, and then the ball continues to rise, the spring force is less than gravity, until after leaving the spring, the ball are decelerating, so the ball from $A$ to $A$ rise to $A$, and the ball is decelerating. After the ball continues to rise, the spring force is less than the force of gravity, until after leaving the spring, the ball are doing deceleration, so the ball from $A$ up to $C$ in the process of the first increase in speed and then reduced, the momentum is also the first increase and then reduced, so A error; B. According to the theorem of momentum, the impulse of gravity of the ball is equal to the impulse of the spring force in the process from $A$ to $C$, so B is wrong; C. According to the theorem of momentum, the impulse of gravity of the ball is equal to the impulse of the spring force in the process from $A$ to $B$. C. $A$ to $B$, according to the momentum theorem, $I _ { \text {弹 } } I _ { \text {重 } } = m v - 0$, it can be seen that the increase in the momentum of the ball is less than the impulse of the spring force, so C is wrong; D. According to the impulse of gravity is equal to $I _ { \text {重 } } = m g t$, it can be known that the impulse of gravity of the ball has been getting bigger during the process from $A$ to $B$, so D is correct.

Question 21

Question 21: 21. Mass equal $A , B$ two small balls in the air at the same height, the $A$ ball thrown horizontal...

21. Mass equal $A , B$ two small balls in the air at the same height, the $A$ ball thrown horizontally to the right, at the same time will be $B$ ball thrown obliquely upward, the two balls thrown the same size of the initial velocity, the two small balls in the air trajectory as shown in the figure, do not count the air resistance. The trajectories of the two balls in the air are shown in the figure, not counting the air resistance. Then the two balls in the air in the process of movement, the following statement is correct ![](/images/questions/phys-momentum/image-013.jpg)

A. A. The amount of change in velocity may be different for the same amount of time
B. B. At the same moment, the speed of change may be different
C. C. The kinetic energy must be the same when they fall to the same height after being thrown
D. D. The magnitude of the impulse of gravity may be different at the same time

Answer

Answer: C

Solution: A. By $$ \Delta v = g \Delta t $$ It can be seen that in the same time, the amount of speed change must be the same, so A is wrong; B. The acceleration is equal to the acceleration of gravity, so at the same time, the speed change must be the same, so B is wrong; C. thrown down to the same height, according to the theorem of kinetic energy can get $$ m g h = \frac { 1 } { 2 } m v ^ { 2 } - \frac { 1 } { 2 } m v _ { 0 } ^ { 2 } $$ As gravity does the same work, the initial kinetic energy of the two balls thrown out of the same, then the two balls down to the same height when the kinetic energy must be the same, so C is correct; D. According to $$ I = m g t $$ it can be seen that the impulse of gravity must have the same magnitude at the same time, so D is wrong.

Question 22

Question 22: 22. If the combined external force on an object in motion is not zero, then during motion

22. If the combined external force on an object in motion is not zero, then during motion

A. A. The kinetic energy of an object may be constant
B. B. The momentum of an object may be constant
C. C. The acceleration of the object must be constant
D. D. The direction of motion of the object must be constant

Answer

Answer: A

Solution: ACD. object in the process of motion by the combined external force is not zero, if the combined force is always perpendicular to the speed, such as uniform circular motion, at this time the combined force does not do work, by the theorem of kinetic energy that the kinetic energy of the object is unchanged, the acceleration of the object of uniform circular motion is constantly changing, the direction of the object's motion is constantly changing, CD error A correct; B. The force is the reason for changing the speed of the object, the combined force is not zero, the speed of the object must change, the momentum must change, B error. Therefore, choose A.

Question 23

Question 23: 23. As shown in the figure, two objects on a horizontal plane $A , B$ are tied to each other with a ...

23. As shown in the figure, two objects on a horizontal plane $A , B$ are tied to each other with a line, a spring is squeezed tightly, $A , B$ the ratio of the masses of the two objects is $2 : 1$, and the ratio of the kinetic friction factors between them and the horizontal plane is $1 : 2$. ]. Now the wire is burnt and the $A , B$ object is bounced away from rest, then the following is true ![](/images/questions/phys-momentum/image-014.jpg)

A. A. The system $A , B$ and the spring consists of conservation of momentum and conservation of mechanical energy.
B. B. A, B and the spring form a system with conservation of momentum and non-conservation of mechanical energy
C. C. $A , B$ The system with the spring has no conservation of momentum and conservation of mechanical energy.
D. D. $A , B$ A system with a spring does not conserve momentum and does not conserve mechanical energy.

Answer

Answer: B

Solution: After $A , B$ is bounced off, according to $f = \mu m g$, we can see that the frictional forces on the two objects are equal in magnitude and opposite in direction, then the combined force on the system consisting of $A , B$ and the spring is zero, and the system momentum is conserved; since there is friction doing work, the mechanical energy of the system is not The system momentum is conserved; because of the work done by friction, the system mechanical energy is not conserved.

Question 24

Question 24: 24. The mass of $m$ is thrown horizontally, after a period of time the speed of the ball is $v$, if ...

24. The mass of $m$ is thrown horizontally, after a period of time the speed of the ball is $v$, if the impulse of gravity in the process of the size of $I$, the acceleration of gravity is $g$, regardless of the size of air resistance, then the initial velocity of the ball when it is thrown is $g$. ], not counting the magnitude of air resistance, then the size of the initial velocity of the ball when thrown is ( )

A. A. $v - \frac { I } { m }$
B. B. $v - \frac { I } { m g }$
C. C. $\sqrt { v ^ { 2 } - \frac { I ^ { 2 } } { m ^ { 2 } } }$
D. D. $\sqrt { v ^ { 2 } - \frac { I ^ { 2 } } { m ^ { 2 } g ^ { 2 } } }$

Answer

Answer: C

Solution: From the meaning of the question $$ I = m g t $$ Solve $$ t = \frac { I } { m g } $$ After $t$ time, the magnitude of the velocity of the ball in the firm straight direction is $$ v _ { y } = g t = \frac { I } { m } $$ According to the velocity decomposition, the magnitude of the initial velocity is $$ v _ { 0 } = \sqrt { v ^ { 2 } - \frac { I ^ { 2 } } { m ^ { 2 } } } $$ Therefore, C is correct and ABD is wrong.

Question 25

Question 25: 25. As shown in the figure, an object $m$ is placed on an inclined plane $M$, and there is no fricti...

25. As shown in the figure, an object $m$ is placed on an inclined plane $M$, and there is no friction between $M$ and the horizontal plane. FORMULA_4]] and $M$ form a system ( ) ![](/images/questions/phys-momentum/image-015.jpg)

A. A. Conservation of momentum of the system
B. B. Conservation of the momentum component of the system in the firm direction
C. C. Conservation of the momentum component of the system in the horizontal direction
D. D. The momentum component of the system is not conserved in any direction

Answer

Answer: C

Solution: From the question, $m$ has a downward acceleration in the firmament direction as it rushes up from the bottom to the top along the incline, so the system consisting of $m$ and $M$ does not conserve the momentum component of the system in the firmament direction. The momentum components of the systems $M$ are not conserved. The system consisting of $m$ and $M$ is not subjected to external forces in the horizontal direction, so the system consisting of $m$ and $M$ consists of a system that conserves the momentum component in the horizontal direction. Therefore, choose C.

Question 26

Question 26: 26. A gun is fixed horizontally on a cart, the cart is placed on a smooth horizontal surface, the gu...

26. A gun is fixed horizontally on a cart, the cart is placed on a smooth horizontal surface, the gun fires the bullet, the correct statement about the car, the gun and the bullet is

A. A. A system of guns and bullets has conservation of momentum.
B. B. The system of the gun and the car has conservation of momentum.
C. C. The system of the gun, the car, and the bullet has conservation of momentum.
D. D. If friction is ignored, the system of the gun and the car consists of conservation of momentum

Answer

Answer: C

Solution: ABD . When firing a bullet, the system consisting of the gun and the bullet, or the system consisting of the gun and the car, is subjected to a non-zero sum of external forces, so momentum is not conserved, so ABD is wrong; C.When the bullet is fired, the system consisting of the gun, the car and the bullet is subjected to the sum of the external forces is zero, and the momentum of the system is conserved, so C is correct.

Question 27

Question 27: 27. A cart with a total mass of $M$ loaded with sand is moving on a smooth horizontal surface at a c...

27. A cart with a total mass of $M$ loaded with sand is moving on a smooth horizontal surface at a constant speed of $V _ { 0 }$. On the way there is a mass of $m$ sand leakage from the car, then the speed of the car after the sand leakage should be

A. A. $v _ { 0 }$
B. B. $\frac { M v _ { 0 } } { M - m }$
C. C. $\frac { m v _ { 0 } } { M - m }$
D. D. $\frac { ( M - m ) v _ { 0 } } { M }$

Answer

Answer: A

Solution: At the moment when the sand leaks from the car, due to inertia the velocity is still $v ^ { 0 }$ and the speed of the car is $v ^ { \prime }$, according to horizontal Conservation of momentum in the horizontal direction $$ M v _ { 0 } = m v _ { 0 } + ( M - m ) v $$ The solution is given by $$ M v _ { 0 } = m v _ { 0 } + ( M - m ) v $$ $$ v ^ { \prime } = v _ { 0 } $$ Therefore, A is correct and BCD is incorrect.

Question 28

Question 28: 28. The following is a correct understanding of collisions.

28. The following is a correct understanding of collisions.

A. A. A collision is a process in which objects in relative motion meet in such a way that their state of motion changes significantly over a long period of time
B. B. In collision phenomena, the internal forces are generally much larger than the external forces, so the total momentum of the system can be considered to be conserved during the collision
C. C. If the mechanical energy is also conserved during the collision, such a collision is called an inelastic collision
D. D. The collision of microscopic particles does not satisfy the condition of conservation of momentum because no direct contact occurs, and the law of conservation of momentum cannot be applied to the solution

Answer

Answer: B

Solution: A. Collision is a very common phenomenon, it is a phenomenon that occurs when objects in relative motion meet, collision in a very short period of time in their state of motion has changed significantly, so A error; B. In the collision phenomenon, because the internal force is much larger than the external force, so you can ignore the role of the external force; that the collision of the total momentum of the system is conserved, so B is correct; C. If the collision process mechanical energy is also conserved, the collision is elastic collision, so C is wrong; D. microscopic particles close to each other, although not a direct collision, in the process of interaction, in line with the definition of conservation of momentum, so its momentum is likely to be conserved, so D error.

Question 29

Question 29: 29. Which of the following statements about momentum are true

29. Which of the following statements about momentum are true

A. A. An object with a large mass must have a large momentum
B. B. An object with a large velocity must have a large momentum
C. C. When two objects have equal momentum, their kinetic energies must be equal.
D. D. Two objects have equal kinetic energy, but not necessarily the same momentum.

Answer

Answer: D

Solution: AB. According to the $$ p = m v $$ According to $$ p = m v $$, it can be seen that objects with large mass do not necessarily have large momentum, but also depend on the speed; objects with large speed do not necessarily have large momentum, but also depend on the mass, so AB is wrong; CD. $$ E _ { \mathrm { k } } = \frac { 1 } { 2 } m v ^ { 2 } , \quad p = m v $$ we can get $$ p = \sqrt { 2 m E _ { \mathrm { k } } } $$ D is correct and C is incorrect because kinetic energy is not necessarily equal when the momentum of the objects is equal, and the momentum of the objects is not necessarily equal when their kinetic energies are equal.

Question 30

Question 30: 30. There is a long boardwalk parked on a smooth, horizontal road with an adult standing at the left...

30. There is a long boardwalk parked on a smooth, horizontal road with an adult standing at the left end and a child standing at the right end. If the adult walks to the right, the child (whose mass is smaller than the adult's) walks to the left. Their speeds are of the same magnitude, then during their walks

A. A. The car may move to the right
B. B. The car must be moving to the left.
C. C. The car may remain stationary.
D. D. indeterminate

Answer

Answer: B

Question 31

Question 31: 31. As shown in the figure, one end of the spring is fixed on a solid wall, a smooth curved groove w...

31. As shown in the figure, one end of the spring is fixed on a solid wall, a smooth curved groove with a mass of $m$ is resting on a smooth horizontal surface, and the bottom is connected smoothly with the horizontal surface, a ball with a mass of $m$ starts to slide down from the groove at a height of $h$, and the mass of ![](/images/questions/phys-momentum/image-016.jpg) is ![](/images/questions/phys-momentum/image-016.jpg). ![](/images/questions/phys-momentum/image-016.jpg)

A. A. The momentum of the ball and the slot is always conserved in subsequent motions
B. B. The interaction force between the ball and the trough always does no work during the decline
C. C. After the ball is bounced by the spring, the mechanical energy of the ball and the slot is not conserved and the ball can return to the slot height $h$ at
D. D. After being bounced by the spring, both the ball and the slot move in a straight line with constant velocity

Answer

Answer: D

Solution: A. When the ball is moving on the groove, the ball is subject to gravity, so the sum of the external forces of the system composed of two objects is not zero, so the momentum is not conserved; when the ball is in contact with the spring, the ball is subject to external forces, so the ball and the groove composed of a system of momentum is not conserved, so the A error; B. decline in the process of the two objects have horizontal displacement, and the force is perpendicular to the surface of the ball, so the direction of the force and the direction of the displacement is not perpendicular to the direction of the two forces are doing work, so B error; CD. small ball in a smooth arc groove groove sliding process, the ball and groove of the system composed of the horizontal direction of momentum conservation, the ball and groove of the mass is equal, the ball and groove separation, the ball and groove of the speed of the magnitude of the ball and groove, the ball was rebounded ball and groove of the speed of the speed of the ball and groove are equal, the ball and groove do rate of constant linear motion, the ball can not be slid to the groove, can not return to the groove high $h$ ] place, so C is wrong and D is correct;

Question 32

Question 32: 32. A ball bolted to a thin string moves in a circular motion in the firmament, from point $A$ to po...

32. A ball bolted to a thin string moves in a circular motion in the firmament, from point $A$ to point $A$ again, the following statements are correct ![](/images/questions/phys-momentum/image-017.jpg)

A. A. The impulse of the combined force is 0
B. B. The impulse of the combined force is not 0
C. C. The impulse of gravity is 0
D. D. The impulse of the tension in the rope is greater than the impulse of gravity

Answer

Answer: A

Solution: AB. According to the momentum theorem, the impulse of the combined force is equal to the change in momentum, and the change in momentum is zero as the ball moves from point $A$ to point $A$ again, so the impulse of the combined force is 0. Option A is correct and B is wrong; C. The impulse of gravity is $m g T$, then it is not zero 0, option C is wrong; D. The impulse of the combined external force is equal to the vector sum of the impulse of the tension and gravity, the impulse of the combined external force is 0, the impulse of the tension in the rope is equal to the impulse of gravity, option D is wrong.

Question 33

Question 33: A light spring, suspended from the ceiling at its upper end and tied at its lower end to a flat plat...

A light spring, suspended from the ceiling at its upper end and tied at its lower end to a flat plate of mass $M$, is in equilibrium. A mass of $m$ uniform ring outside the spring, and the distance from the plate is $h$, as shown in the figure, let the ring free fall, hit the plate, the ring is known to be touched after the plate to the same speed downward motion, the ![](/images/questions/phys-momentum/image-018.jpg)

A. A. If the collision time is very short, then the total momentum of the ring and the plate during the collision is conserved
B. B. If the collision time is very short, then the total mechanical energy of the ring and the plate during the collision is conserved
C. C. The new equilibrium position of the plate after the ring hits the plate is related to the size of the $h$
D. D. During the fall of the plate and the ring together after touching, the total mechanical energy of the ring and the plate is conserved

Answer

Answer: A

Solution: AB. Ring and plate collision process, if the collision time is very short, the internal force is much larger than the external force, the total momentum of the system is conserved, due to the same speed after the touch, for the completely inelastic collision, mechanical energy is not conserved, the reduction of mechanical energy into internal energy, so A is correct, B is wrong; C. After the collision equilibrium, there are $$ k x = ( m + M ) g $$ That is, the new equilibrium position after the collision is independent of the falling height $h$, so C is wrong; D. After the collision of the ring and the plate together in the process of falling, the sum of their kinetic energy and gravitational potential energy is equal to the increase in the spring elastic potential energy, the total mechanical energy of the ring and the plate is not conserved, so D is wrong.

Question 34

Question 34: 34. Basketball is very popular among students. When playing basketball, a student stretched out his ...

34. Basketball is very popular among students. When playing basketball, a student stretched out his hands to catch the incoming basketball, and his hands quickly contracted to his chest with the basketball, as shown in the figure. The effect of his doing so is ![](/images/questions/phys-momentum/image-019.jpg)

A. A. Reducing the impact of basketball opponents
B. B. Decrease the amount of change in momentum of the basketball
C. C. Decrease the amount of change in kinetic energy of the basketball
D. D. Reducing the impulse of a basketball opponent

Answer

Answer: A

Solution: ABD. first outstretched two arms to meet, hand contact with the ball, two arms with the ball led to the chest, which can increase the time of contact between the ball and the hand, according to the theorem of momentum to get $$ - F t = 0 - m v $$ Solution: $$ F = \frac { m v } { t } $$ When time increases, the rate of change of the ball's momentum decreases, the force decreases, and the amount of change in both impulse and momentum remains the same, so A is correct and BD is incorrect. C. The velocity decreases from $v$ to 0, and the change in kinetic energy is constant, so C is wrong.

Question 35

Question 35: 35. The FIVB (International Volleyball Federation) specifies that the standard competition volleybal...

35. The FIVB (International Volleyball Federation) specifies that the standard competition volleyball has a mass of $260 \sim 280 \mathrm {~g}$, and the training volleyball may have a slightly smaller mass. Assuming that a training volleyball has a mass of ${ } ^ { m } = 250 \mathrm {~g}$, the athlete pads a volleyball coming at a speed of $v _ { 0 } = 4 \mathrm {~m} / \mathrm { s }$ and a direction at an angle of $37 ^ { \circ }$ to the horizontal toward a teammate at an equal and opposite speed, and that the ball makes contact with the arm at a time of $t = 0.1 \mathrm {~s}$, and that the time of contact between the ball and the arm is $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$. FORMULA_4]] The magnitude of gravitational acceleration $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ and air resistance is neglected, then () ![](/images/questions/phys-momentum/image-020.jpg)

A. A. The magnitude of the impulse of gravity during the player's pads is $2.5 \mathrm {~N} \cdot \mathrm {~s}$
B. B. The magnitude of the impulse of the combined external force on the volleyball during contact with the player's arm is $2 \mathrm {~N} \cdot \mathrm {~s}$
C. C. The direction of the change in momentum of the ball during the padding process is the same as ${ } ^ { V _ { 0 } }$.
D. D. The average force of the hand on the ball during the cushioning process is 20 N.

Answer

Answer: B

Solution: A. The magnitude of the impulse of gravity during the cushioning process $I _ { \mathrm { G } } = m g t = 0.25 \times 10 \times 0.1 \mathrm {~N} \cdot \mathrm {~s} = 0.25 \mathrm {~N} \cdot \mathrm {~s}$ is $I _ { \mathrm { G } } = m g t = 0.25 \times 10 \times 0.1 \mathrm {~N} \cdot \mathrm {~s} = 0.25 \mathrm {~N} \cdot \mathrm {~s}$, so A is wrong; B. According to the momentum theorem $I = \Delta p$ According to the momentum theorem $I = \Delta p$, the magnitude of the impulse of the volleyball is $I = \left| - m v _ { 0 } - m v _ { 0 } \right|$. Substituting the data, we can get $I = 2 \mathrm {~N} \cdot \mathrm {~s}$, so B is correct; C. The change in momentum of the ball during the cushioning process is $\Delta p = - m v _ { 0 } - m v _ { 0 } = - 2 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, so B is correct. C. The change in momentum of the ball $\Delta p = - m v _ { 0 } - m v _ { 0 } = - 2 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ during the cushioning process is opposite to the initial velocity ${ } ^ { v _ { 0 } }$, so C is wrong; D. If gravity is ignored, according to the law of momentum $F t = I$, we can find that during the cushioning process, the player's hand is moving in the opposite direction. D. If we ignore gravity, according to the law of momentum $F t = I$, we can get the average size of the hand force on the ball during the cushioning process $F = 20 \mathrm {~N}$. But the ball is also subjected to gravity, then the average force on the ball during the cushioning process of the athlete's hand is not equal to 20 N, so D is wrong.

Question 36

Question 36: 36. The following statements are correct ()

36. The following statements are correct ()

A. A. When the action force does positive work, the reaction force must do negative work
B. B. The work of a pair of action and reaction forces must be equal in magnitude and opposite in direction
C. C. The impulses of a pair of action and reaction forces must be equal in magnitude and opposite in direction.
D. D. Sliding friction must do negative work on the object

Answer

Answer: C

Solution: AB. Action and reaction forces are acting on two interacting objects; action and reaction forces can do negative work or positive work at the same time; such as two small children at rest on the ice after pushing each other a little bit, the two people at the same time backward, then the two forces to do positive work; and the two relative motion of the object after the collision, the action and reaction forces are doing negative work, so AB is wrong; C. force and reaction forces equal in size and direction, so their impulse must be equal in size and direction; C is correct; D. Sliding friction can do positive work can also do negative work, but also can not do work, so D error.

Question 37

Question 37: 37. In the smooth horizontal surface of the mass of ${ } ^ { 1 \mathrm {~kg} }$ of the object, by th...

37. In the smooth horizontal surface of the mass of ${ } ^ { 1 \mathrm {~kg} }$ of the object, by the horizontal tension $F$ role, the tension $F$ with the time $t$ change in the image shown in the figure, then the following statements is correct ( ) ![](/images/questions/phys-momentum/image-021.jpg)

A. A. $0 \sim 4 \mathrm {~s}$ The displacement of the object inside is zero
B. B. $0 \sim 4 \mathrm {~s}$ The work done on the object by the internal tension force is 4 J
C. C. The momentum of the object at the end of 4 s is zero
D. D. The change in momentum of the object in $0 \sim 4 \mathrm {~s}$ is $4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$

Answer

Answer: C

Solution: A. By analyzing the figure, we can see that the object in $0 \sim 4 \mathrm {~s}$ first does uniform acceleration and then does uniform deceleration, and the speed at the end of 4 s is zero, and the displacement has been increasing, so A is wrong; B. In $0 \sim 2 \mathrm {~s}$, the tension does positive work, and in $2 \sim 4 \mathrm {~s}$, the tension does negative work, and the algebraic sum of the work done by the tension in the two periods of time is zero, so B is wrong; C. The speed of the object at the end of 4 s is zero, and the momentum is zero, so C is correct; D. In $0 \sim 4 \mathrm {~s}$, the initial momentum of the object is zero, and the final momentum is also zero, so the change of momentum is zero, so D is wrong. D. The change in momentum is zero, so D is wrong.

Question 38

Question 38: 38. As shown in the figure, there are $A , B$ two balls of the same size moving in the same straight...

38. As shown in the figure, there are $A , B$ two balls of the same size moving in the same straight line on a smooth horizontal surface. The two ball mass relationship for $m _ { B } = 2 m _ { A }$, the provisions of the positive direction to the right, $A , B$ two ball momentum are $8 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, the movement process of the two ball collision, collision of $A$ the ball's momentum increment of $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$ the ball's momentum is the $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$. INLINE_FORMULA_5]], then ( ![](/images/questions/phys-momentum/image-022.jpg)

A. A. The right side is the $A$ ball, and after the collision $A , B$ the ratio of the speeds of the two balls is $2 : 3$.
B. B. The right side is the $A$ ball, and after the collision $A , B$ the ratio of the speeds of the two balls is $1 : 6$.
C. C. The left side is the $A$ ball, and after the collision the ratio of the magnitudes of the velocities of the $A , B$ two balls is $2 : 3$
D. D. The left side is the $A$ ball, and after the collision the ratio of the magnitudes of the velocities of the $A , B$ two balls is $1 : 6$

Answer

Answer: C

Solution: To the right is the positive direction, $A , B$ the momentum of both balls is positive, the velocity of both balls is to the right, in order for the two balls to touch, the left ball has a larger velocity; the mass relationship between the two balls is $m _ { B } = 2 m _ { A } , A , B$ the momentum of both balls is $8 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s } , A$ the ball has a smaller mass and a larger velocity; then the left ball is the $A$ ball. After the collision, the momentum of the $A$ ball is $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, then the momentum of the $A$ ball after the collision is 4 $\mathrm { kg } \cdot \mathrm { m } / \mathrm { s }$; according to the conservation of momentum, we can get that after the collision, the momentum of the $B$ ball after the collision is $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$, then the momentum of the ball after the collision is $- 4 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$. The ball momentum is $12 \mathrm {~kg} \cdot \mathrm {~m} / \mathrm { s }$; the mass relationship between the two balls is $m _ { B } = 2 m _ { A }$, and according to the conservation of momentum, it is $m _ { B } = 2 m _ { A }$. $p = m v _ { \text {可得 } } v _ { A } : v _ { B } = 2 : 3$.

Question 39

Question 39: 39. A point in uniformly accelerated straight-line motion increases its velocity by $x$ and its mome...

39. A point in uniformly accelerated straight-line motion increases its velocity by $x$ and its momentum becomes three times that of its predecessor during a displacement of $v$. The acceleration of the point is

A. A. $\frac { v ^ { 2 } } { 2 x }$
B. B. $\frac { v ^ { 2 } } { x }$
C. C. $\frac { 3 v ^ { 2 } } { 4 x }$
D. D. $\frac { 4 v ^ { 2 } } { 3 x }$

Answer

Answer: B

Solution: Momentum becomes 3 times the original, according to the $$ p = m v $$ Then the velocity becomes 3 times, let the initial velocity is $v _ { 0 }$, then the velocity becomes $3 v _ { 0 }$ after passing through the displacement $x$, and from the meaning of the question, we can obtain $$ v = 3 v _ { 0 } - v _ { 0 } = 2 v _ { 0 } $$ According to $$ 2 a x = \left( 3 v _ { 0 } \right) ^ { 2 } - v _ { 0 } ^ { 2 } $$ The solution by association is $$ a = \frac { v ^ { 2 } } { x } $$

Momentum and Impulse

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