Chapter Test: Momentum And Its Conservation

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  • 1/34 Questions

    A truck driving along a highway road has a large quantity of momentum. If it moves at the same speed but has twice as much mass, its momentum is ________________.

    • Zero
    • Quadrupled
    • Doubled
    • Unchanged
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Chapter Test: Momentum And Its Conservation - Quiz
About This Quiz

This Chapter Test on Momentum and Its Conservation assesses understanding of momentum, impulse, and their conservation. It includes true\/false questions on vector quantities, momentum conservation, and impulse related scenarios, crucial for learners aiming to master physics fundamentals.

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  • 2. 

    It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply.

    • There is no air in space

    • There is no friction in space

    • There is no gravity in outer space

    • ... nonsense! Rockets do accelerate in outer space.

    Correct Answer
    A. ... nonsense! Rockets do accelerate in outer space.
    Explanation
    Rockets can accelerate in outer space because there is no air resistance or friction to oppose their motion. Additionally, there is still gravity in outer space, although it is weaker compared to Earth's gravity. Therefore, the statement "Rockets do accelerate in outer space" is correct.

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  • 3. 

    A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is ____.

    • Zero

    • Four times as large

    • Twice as large

    • none of these

    Correct Answer
    A. Twice as large
    Explanation
    When an object has more mass, its momentum increases. Momentum is directly proportional to mass, so if the mass of the cart is doubled while its speed remains the same, its momentum will also double. Therefore, the correct answer is "twice as large".

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  • 4. 

     A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is encountered by the ball for a time of ____ seconds.

    • 1.8

    • 2.5

    • 3.6

    • None of these

    Correct Answer
    A. 3.6
    Explanation
    The impulse experienced by an object is equal to the change in momentum of the object. The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the initial momentum of the ball is 3 kg * 9 m/s = 27 kg*m/s, and the final momentum is 3 kg * 3 m/s = 9 kg*m/s. The change in momentum is therefore 27 kg*m/s - 9 kg*m/s = 18 kg*m/s. The impulse is also equal to the force applied to the object multiplied by the time it is applied. In this case, the force is 5 N. Therefore, the time can be calculated by dividing the impulse by the force: 18 kg*m/s / 5 N = 3.6 s.

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  • 5. 

    Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater force?

    • the moth

    • Your car

    • Both the same

    • Both the same

    Correct Answer
    A. Both the same
    Explanation
    When a moth crashes into the windshield of a car, both the moth and the car experience the same force. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the force exerted by the car on the moth is equal in magnitude but opposite in direction to the force exerted by the moth on the car. Therefore, both the moth and the car undergo the same force.

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  • 6. 

    Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will reach the ground at the same time but object A will have a greater ___. Choose all that apply.

    • Speed

    • Acceleration

    • Momentum

    • None of the above quantities will be greater

    Correct Answer
    A. Momentum
    Explanation
    The objects will reach the ground at the same time because their size and shape are the same. However, object A is twice as massive as object B, meaning it has more mass. Momentum is defined as the product of an object's mass and velocity, so object A will have a greater momentum due to its greater mass. Speed and acceleration are not affected by mass, so they will be the same for both objects. Therefore, the correct answer is momentum.

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  • 7. 

     Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater change is momentum?

    • The moth

    • Your car

    • Both the same

    • None of these

    Correct Answer
    A. Both the same
    Explanation
    Both the moth and the car undergo the same change in momentum. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the moth crashes into the windshield, it exerts a force on the car, causing it to experience a change in momentum. At the same time, the car also exerts an equal and opposite force on the moth, causing it to experience a change in momentum. Therefore, both the moth and the car undergo the same change in momentum.

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  • 8. 

    Which of the following statements are true about momentum?  
    1. A less massive object can never have more momentum than a more massive object.
    2. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum.
    3. An object with a changing speed will have a changing momentum.

    • A

    • B

    • C

    • None of the above.

    Correct Answer
    A. C
    Explanation
    An object with a changing speed will have a changing momentum. Momentum is defined as mass times velocity, so if an object's speed is changing, its velocity is changing, and therefore its momentum is also changing. This is because velocity is a vector quantity that includes both speed and direction. As the speed changes, the magnitude of the velocity vector changes, resulting in a change in momentum. Therefore, statement c is true.

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  • 9. 

    Which of the following statements are true about momentum? A. Momentum is a vector quantity. B. The standard unit on momentum is the Joule. C. An object with mass will have momentum. D. An object which is moving at a constant speed has momentum.

    • B & D

    • A & D

    • A & C

    • None of the above

    Correct Answer
    A. A & D
    Explanation
    Momentum is a vector quantity because it has both magnitude and direction. The standard unit for momentum is kilogram-meter per second (kg·m/s), not Joule. An object with mass will have momentum because momentum is defined as the product of an object's mass and its velocity. An object which is moving at a constant speed has momentum because velocity is a component of momentum. Therefore, the correct statements are A & D.

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  • 10. 

    A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s.

    • 3

    • 4

    • 48

    • None of these.

    Correct Answer
    A. 3
    Explanation
    The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the momentum is given as 12 kg•m/s and the mass is given as 4 kg. To find the speed, we divide the momentum by the mass. Therefore, the speed of the object is 12 kg•m/s divided by 4 kg, which equals 3 m/s.

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  • 11. 

    A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a relatively ______. List all that apply.

    • Small velocity change

    • large velocity change

    • Small momentum change

    • Small acceleration

    Correct Answer
    A. large velocity change
    Explanation
    When a relatively large force acts for a relatively long amount of time on a relatively small mass, it will result in a large velocity change. This is because the force will accelerate the mass, causing it to change its velocity significantly. The larger the force and the longer it acts, the greater the velocity change will be. Therefore, a large velocity change is the expected outcome in this scenario.

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  • 12. 

    Which of the following statements are true about collisions?
    1. Two colliding objects will exert equal forces upon each other even if their mass is significantly different.
    2. During a collision, an object always encounters an impulse and a change in momentum.
    3. During a collision, the impulse which an object experiences is equal to its velocity change.
    4. The velocity change of two respective objects involved in a collision will always be equal.

    • A & B

    • B & C

    • C & D

    • All of the above.

    Correct Answer
    A. A & B
    Explanation
    During a collision, two objects will exert equal forces upon each other even if their mass is significantly different. This is because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force exerted by one object on the other will be equal in magnitude but opposite in direction. Additionally, during a collision, an object will always encounter an impulse and a change in momentum. This is because a collision involves a transfer of energy and momentum between the objects involved, resulting in a change in their velocities.

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  • 13. 

    Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it with her bare hand. During the collision between her hand and the block, the ___.

    • Time of impact on both the block and the expert's hand is the same

    • Force on both the block and the expert's hand have the same magnitude

    • Impulse on both the block and the expert's hand have the same magnitude

    • All of the above.

    Correct Answer
    A. All of the above.
    Explanation
    During the collision between the karate expert's hand and the cement block, the time of impact on both the block and the expert's hand is the same. This means that the duration of the collision is equal for both the block and the hand. Additionally, the force on both the block and the expert's hand have the same magnitude. This implies that the impact of the blow is equally distributed between the block and the hand. Finally, the impulse on both the block and the expert's hand have the same magnitude. Impulse is the change in momentum, and since momentum is conserved in the collision, the impulse experienced by both the block and the hand is the same. Therefore, all of the above statements are true.

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  • 14. 

    Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater acceleration?

    • the moth

    • your car

    • Both the same

    • None of these

    Correct Answer
    A. the moth
    Explanation
    The moth undergoes the greater acceleration. This is because the force exerted on the moth by the windshield is much greater than the force exerted on the car by the moth. As a result, the moth experiences a larger change in velocity in a shorter amount of time, leading to a greater acceleration.

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  • 15. 

    Which of the following objects have momentum? Include all that apply. a. An electron is orbiting the nucleus of an atom. b. A UPS truck is stopped in front of the school building. c. A Yugo (a compact car) is moving with a constant speed. d. A small flea walking with constant speed across Fido's back. e. The high school building rests in the middle of town.

    • A,C & D

    • A,B & C

    • B,C & D

    • None of the above.

    Correct Answer
    A. A,C & D
    Explanation
    Objects that have momentum are those that are in motion. In this question, options a, c, and d describe objects that are in motion. An electron orbiting the nucleus of an atom is constantly moving, so it has momentum. A Yugo moving with a constant speed also has momentum. Similarly, a small flea walking with constant speed across Fido's back is also in motion and has momentum. Therefore, options a, c, and d are the correct answers.

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  • 16. 

    Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater impulse?

    • the moth

    • your car

    • Both the same

    • None of these

    Correct Answer
    A. Both the same
    Explanation
    Both the moth and the car undergo the same impulse. Impulse is the change in momentum, which is equal to the force applied multiplied by the time it acts for. When the moth crashes into the windshield, it exerts a force on the car, causing it to experience a change in momentum. At the same time, the car exerts an equal and opposite force on the moth, causing it to also experience a change in momentum. Since the forces and times are equal and opposite, the impulses experienced by both the moth and the car are the same.

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  • 17. 

    Which of the following statements are true about momentum? A. An object can be traveling eastward and slowing down; its momentum is westward. B. Momentum is a conserved quantity; the momentum of an object is never changed. C. The momentum of an object varies directly with the speed of the object. D. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.  

    • C & D

    • A & B

    • B & C

    • None of the above

    Correct Answer
    A. C & D
    Explanation
    C. The momentum of an object varies directly with the speed of the object. This statement is true because momentum is defined as the product of an object's mass and velocity, and velocity is directly related to speed.

    D. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum. This statement is also true because momentum is directly proportional to mass. Therefore, if two objects have the same speed but different masses, the one with greater mass will have greater momentum.

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  • 18. 

    Which of the following statements are true about collisions?
    1. While individual objects may change their velocity during a collision, the overall or total velocity of the colliding objects is conserved.
    2. In a collision, the two colliding objects could have different acceleration values.
    3. In a collision between two objects of identical mass, the acceleration values could be different.
    4. Total momentum is always conserved between any two objects involved in a collision.

    • A

    • B

    • C

    • D

    Correct Answer
    A. B
    Explanation
    In a collision, the two colliding objects could have different acceleration values. This means that the objects can experience different rates of change in velocity during the collision, resulting in different acceleration values.

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  • 19. 

     In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be reduced in size principally because ___.

    • The resulting impact velocity is lessened

    • The momentum change is decreased

    • The time of impact is increased

    • None of these

    Correct Answer
    A. The time of impact is increased
    Explanation
    When a baseball player moves their hand backward in the direction of the ball's motion, it increases the time of impact. By increasing the time of impact, the force of impact on the player's hand is reduced. This is because a longer duration of impact allows for a slower change in momentum, decreasing the force experienced by the hand. Therefore, the correct answer is that the time of impact is increased.

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  • 20. 

    Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the same as the speed of the recoiling gun ____.

    • Because momentum is conserved

    • Because velocity is conserved

    • Only if the mass of the bullet equals the mass of the gun

    • None of these

    Correct Answer
    A. Only if the mass of the bullet equals the mass of the gun
    Explanation
    The correct answer is "only if the mass of the bullet equals the mass of the gun". This is because according to the law of conservation of momentum, the total momentum before and after an event must be the same. When the bullet is fired, it exerts a force on the gun causing it to recoil. The momentum of the bullet and the gun must be equal and opposite in order to conserve momentum. Therefore, if the mass of the bullet equals the mass of the gun, the speed of the bullet leaving the muzzle will be the same as the speed of the recoiling gun.

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  • 21. 

    The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller than the bullet's forward speed because the ___.

    • Force against the rifle is relatively small

    • Speed is mainly concentrated in the bullet

    • Rifle has lots of mass

    • None of these

    Correct Answer
    A. Rifle has lots of mass
    Explanation
    The correct answer is that the rifle has lots of mass. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the bullet is fired forward with a high speed, it exerts a force on the rifle in the opposite direction, causing the rifle to recoil backwards. The speed of the rifle's recoil is smaller because the rifle has a larger mass compared to the bullet. This means that the rifle requires more force to accelerate, resulting in a slower recoil speed.

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  • 22. 

    A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the momentum change of the ball to be ____ kg•m/s.

    • -2.5

    • -10

    • -18

    • None of these

    Correct Answer
    A. -18
    Explanation
    When a force is applied to an object, it causes a change in its momentum. The impulse experienced by the object is equal to the change in momentum. In this case, the initial momentum of the ball is calculated by multiplying its mass (3 kg) by its initial velocity (+9 m/s), resulting in a momentum of 27 kg·m/s. The final momentum is calculated by multiplying the mass (3 kg) by the final velocity (+3 m/s), resulting in a momentum of 9 kg·m/s. The change in momentum is then determined by subtracting the final momentum from the initial momentum, resulting in a change of -18 kg·m/s. Therefore, the correct answer is -18.

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  • 23. 

    Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than non-padded ones because they ____. List all that apply.

    • increase the impact time

    • Decrease the impact force

    • Both A and B

    • None of the above

    Correct Answer
    A. Both A and B
    Explanation
    Padded dashboards increase the impact time during collisions, which helps to reduce the force exerted on the occupants. This is because the padding absorbs some of the energy from the impact, spreading it out over a longer period of time. As a result, both the impact time and force are decreased, making padded dashboards safer than non-padded ones.

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  • 24. 

    A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___.

    • less than 1 unit

    • 1 unit

    • More than 1 unit

    • not enough information

    Correct Answer
    A. 1 unit
    Explanation
    When the wad of chewed bubble gum collides with the heavy box and sticks to it, the momentum of the gum is transferred to the box. Since the gum has a momentum of 1 unit, the combined momentum of the gum and the box after the collision will also be 1 unit. Therefore, the correct answer is 1 unit.

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  • 25. 

    A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced by the ball is ____ N•s.

    • -2.5

    • -10

    • -45

    • None of these

    Correct Answer
    A. -45
    Explanation
    The impulse experienced by an object can be calculated using the equation Impulse = Force * Change in Time. In this question, the force applied to the ball is 5 N. The change in velocity is the final velocity (3 m/s) minus the initial velocity (9 m/s), which is -6 m/s. Since impulse is equal to force multiplied by change in time, and change in time is equal to mass multiplied by change in velocity, we can use the equation Impulse = Force * Change in Time = Force * (Mass * Change in Velocity). Plugging in the values, we get Impulse = 5 N * (3 kg * -6 m/s) = -45 N·s. Therefore, the correct answer is -45.

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  • 26. 

    Which of the following statements are true about impulse?
    1. The kg•m/s is equivalent to the units on impulse.
    2. An object which experiences a net impulse will definitely experience a momentum change.
    3. In a collision, the net impulse experienced by an object is equal to its momentum change.
    4. A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N acting for 2.0 seconds.

    • A & B

    • B & C

    • C & D

    • All of the above.

    Correct Answer
    A. All of the above.
    Explanation
    All of the statements are true about impulse. The kg•m/s is indeed equivalent to the units on impulse. An object which experiences a net impulse will definitely experience a momentum change. In a collision, the net impulse experienced by an object is equal to its momentum change. Additionally, a force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N acting for 2.0 seconds. Therefore, all of the above statements are true.

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  • 27. 

    Which of the following statements are true about collisions?
    1. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force.
    2. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change.
    3. A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater collision force.
    4. A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater momentum change.

    • A & B

    • B & C

    • C & D

    • None of the above.

    Correct Answer
    A. None of the above.
    Explanation
    None of the statements are true about collisions. In a collision between a moving object and a stationary object of identical mass, both objects experience the same collision force and momentum change according to the law of conservation of momentum. Similarly, in a collision between a moving object and a stationary object with significantly less mass, both objects still experience the same collision force and momentum change.

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  • 28. 

    Which of the following statements are true about impulse?
    1. Impulse is a force.
    2. Impulse is a vector quantity.
    3. An object which is traveling east would experience a westward directed impulse in a collision.
    4. Objects involved in collisions encounter impulses.

    • B & D

    • A & B

    • C & D

    • None of the above.

    Correct Answer
    A. B & D
    Explanation
    Impulse is a vector quantity because it has both magnitude and direction. It is defined as the change in momentum of an object, which is a vector quantity. Objects involved in collisions encounter impulses because when two objects collide, their momentum changes, and this change in momentum is equal to the impulse experienced by the objects. Therefore, the correct statements about impulse are B & D.

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  • 29. 

     Which of the following statements are true about elastic and inelastic collisions?
    1. Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects.
    2. Most collisions tend to be partially to completely elastic.
    3. Momentum is conserved in an elastic collision but not in an inelastic collision.
    4. The kinetic energy of an object remains constant during an elastic collision.

    • A

    • B

    • C

    • D

    Correct Answer
    A. A
    Explanation
    The statement "Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects" explains that elastic and inelastic collisions exist on a spectrum, with perfectly elastic and perfectly inelastic collisions being the two extremes. The position of a collision on this spectrum depends on the amount of kinetic energy conserved by the objects involved.

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  • 30. 

     Which of the following statements are true about elastic and inelastic collisions?
    1. Elastic collisions occur when the collision force is a non-contact force.
    2. Most collisions are not inelastic because the collision forces cause energy of motion to be transformed into sound, light and thermal energy (to name a few).
    3. A ball is dropped from rest and collides with the ground. The higher that the ball rises upon collision with the ground, the more elastic that the collision is.
    4. A moving air track glider collides with a second stationary glider of identical mass. The first glider loses all of its kinetic energy during the collision as the second glider is set in motion with the same original speed as the first glider. Since the first glider lost all of its kinetic energy, this is a perfectly inelastic collision.

    • A, B & C

    • B, C & D

    • A, B & D

    • All of the above.

    Correct Answer
    A. A, B & C
    Explanation
    The given answer is A, B & C.



    Statement A is true because elastic collisions occur when there is no physical contact between the objects involved, and the collision force is exerted over a distance.

    Statement B is true because inelastic collisions usually result in a loss of kinetic energy, which is transformed into other forms of energy such as sound, light, and thermal energy.

    Statement C is true because the height to which a ball rises after colliding with the ground is a measure of how much kinetic energy is conserved during the collision. A higher bounce indicates a more elastic collision.

    Therefore, the correct answer is A, B & C.

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  • 31. 
    Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____. - ProProfs

    Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____.

    • 4 N down

    • 5 N up

    • 10 N up

    • Zero

    Correct Answer
    A. Zero
    Explanation
    The net or unbalanced force acting on box Y is zero because the forces acting on it are balanced. The weight of box Y is 5 N down, but there is an equal and opposite force of 5 N up from the table supporting it. Therefore, the net force on box Y is zero.

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  • 32. 

     In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces.

    • 0.5 m/s

    • 0.33 m/s

    • 1.0 m/s

    • none of these

    Correct Answer
    A. 0.5 m/s
    Explanation
    When the two carts collide, they stick together and form a system with a combined mass. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is equal to its mass multiplied by its velocity.
    Before the collision, the momentum of the first cart is 2 kg*m/s (mass of 1 kg multiplied by velocity of 2 m/s) and the momentum of the second cart is -1 kg*m/s (mass of 1 kg multiplied by velocity of -1 m/s). The negative sign indicates the opposite direction of motion.
    After the collision, the carts stick together and have a combined mass of 2 kg. Let's assume their final velocity is v m/s. The total momentum after the collision is then equal to 2 kg * v m/s.
    Setting the total momentum before the collision equal to the total momentum after the collision, we have:
    2 kg*m/s + (-1 kg*m/s) = 2 kg * v m/s
    1 kg*m/s = 2 kg * v m/s
    v = 0.5 m/s
    Therefore, the correct answer is 0.5 m/s.

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  • 33. 

    Which of the following are true about the relationship between momentum end energy?
    1. Momentum is a form of energy.
    2. If an object has momentum, then it must also have mechanical energy.
    3. If an object does not have momentum, then it definitely does not have mechanical energy either.
    4. Object A has more momentum than object B. Therefore, object A will also have more kinetic energy.
    5. Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy.

    • B & E

    • A & C

    • D & A

    • None of the above.

    Correct Answer
    A. B & E
    Explanation
    Momentum is a property of an object that depends on its mass and velocity, while energy is the ability to do work. Momentum is not a form of energy, so statement A is incorrect. If an object has momentum, it does not necessarily mean that it has mechanical energy, so statement B is incorrect. If an object does not have momentum, it does not mean that it does not have mechanical energy, so statement C is incorrect. Statement D is correct because an object with more momentum will also have more kinetic energy. Statement E is correct because two objects with the same momentum but different masses will have different kinetic energies, with the less massive object having the greater kinetic energy.

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  • 34. 

    Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and momentum. Force and time is related to momentum change in the same manner as force and displacement pertains to ___________.

    • Impulse

    • work

    • Energy change

    • none of these

    Correct Answer
    A. Energy change
    Explanation
    Force and displacement are related to work in the same manner as force and time are related to impulse. Work is defined as the product of force and displacement, while impulse is defined as the product of force and time. Similarly, force and time are related to momentum change, while force and displacement are related to energy change. Therefore, the correct answer is energy change.

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  • Mar 21, 2023
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  • Aug 21, 2011
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