Chapter Test: Momentum And Its Conservation

When an object has momentum, it means it has mass and is moving. Momentum is calculated by multiplying an object's mass by its velocity. In this question, the truck is moving at the same speed but has twice as much mass. Since momentum is directly proportional to mass, if the mass doubles, the momentum will also double. Therefore, the correct answer is "doubled".

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.

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".

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.