Question 1

The momentum of a single particle is defined as
A) p = m( $\frac { d } { d t }$ v).
B) p = m( $\frac { d } { d t }$ a).
C) $\boldsymbol { p } = m \left( \int \boldsymbol { v } d t \right)$
D) p = mv.
E) p = ma.

Accepted Answer

Momentum of a single particle is defined as the product of its mass (m) and its velocity (v), hence p = mv.

Question 2

All of the following dimensions are momentum dimensions except for
A) [kilogram][meter].
B) [kilogram][meter]/[second].
C) [kilogram][watt]/[newton].
D) [newton][second].
E) [joule][second]/[meter].

Accepted Answer

Momentum is defined as the product of mass and velocity. The correct dimensions for momentum are mass times velocity ([kilogram][meter]/[second]), force times time ([newton][second]), or energy times time over distance ([joule][second]/[meter]). Option A, [kilogram][meter], represents mass times distance, not momentum.

Question 3

Newton's Second Law F = ma. expressed in terms of momentum, reads
A) F = p.
B) $\frac { d } { d t }$ F = p.
C) F = $\frac { d } { d t }$ p.
D) F = m( $\frac { d } { d t }$ p).
E) F = p/m.

Accepted Answer

Newton's Second Law in terms of momentum (p = mv) is expressed as F = dp/dt, where dp/dt is the rate of change of momentum with respect to time.

Question 4

Momentum changes for each of these scenarios except for
A) a falling rock from an instant after initial drop from a high tower until an instant before impact.
B) a movie stunt performer flying on a parabolic path before the performer stops on the ground.
C) a rocket sled on a horizontal track from an instant after the drag parachute opens until an instant before the sled comes to rest.
D) a block sliding at constant speed (with friction) down an inclined plane.
E) a neutron in a nuclear reactor that changes the direction but not the magnitude of its velocity when it scatters off another neutron.

Accepted Answer

In scenario D, a block sliding at constant speed down an inclined plane implies that there is no acceleration (since speed is constant), and thus no change in momentum. In all other scenarios, there is either a change in speed or direction, indicating a change in momentum.

Question 5

A 0.20-kg ball, traveling east at 20 m/s, strikes a wall and rebounds at 18 m/s. The change in the ball's momentum is
A) 7.6 N.s, west.
B) 0.4 N.s, west.
C) 2.0 N.s.
D) 0.4 N.s, east.
E) 7.6 N.s, east.

Accepted Answer

The change in momentum is calculated using the formula Δp = m(vf - vi), where m is the mass, vf is the final velocity, and vi is the initial velocity. Here, Δp = 0.20 kg * (-18 m/s - 20 m/s) = -7.6 kg*m/s, indicating a change of 7.6 N.s to the west, since the negative sign indicates a direction opposite to the initial direction (east).

Question 6

A car of mass 1200 kg is driving due south at 40 m/s. After driving around a sharp curve, the car is moving west at 30 m/s. The change in the magnitude of the car's momentum is
A) 10 kN/s.
B) 12 kN/s.
C) 60 kN/s.
D) 70 kN/s.
E) 84 kN/s.

Accepted Answer

The answer of A car of mass 1200 kg is...

Question 7

When momentum is conserved
A) the magnitude of the momentum does not change with time.
B) the direction of the momentum does not change with time.
C) the magnitude and the direction of the momentum do not change with time.
D) none of the above is true.

Accepted Answer

Momentum is a vector quantity, which means it has both magnitude and direction. When momentum is conserved, both the magnitude and the direction of the momentum remain constant over time.

Question 8

The momentum of a system of particles is conserved if
A) there are an even number of particles in the system to allow an integer number of action-reaction pairs.
B) the net force on each particle making up the system is zero.
C) the momentum of each particle making up the system is conserved.
D) no external forces are acting on the system.
E) no internal forces are acting on the system.

Accepted Answer

Momentum conservation in a system occurs when no external forces act on it. Internal forces, regardless of their presence, do not affect the total momentum of the system due to Newton's third law (action-reaction pairs cancel out internally).

Question 9

The hero in a movie punches a villain, who upon the impact flies through a window and destroys a few other objects nearby. Why is this scene a fantasy?
A) It violates the conservation of mass and energy.
B) It violates the conservation of mass and momentum.
C) It violates the conservation of momentum.
D) It violates the conservation of energy.
E) It violates the conservation of momentum and energy.

Accepted Answer

The scene is a fantasy because it likely violates the conservation of momentum and energy. In real life, the forces and reactions involved in such a scenario would not allow for the exaggerated effects seen in movies without violating these fundamental physical laws. Conservation of momentum ensures that the total momentum before and after a collision remains constant in an isolated system, and conservation of energy dictates that energy cannot be created or destroyed, only transformed. The exaggerated effects seen in movies often do not account for these principles accurately.

Question 10

Momentum is conserved in any system that is
A) closed and isolated from the rest of the universe.
B) directly visible from somewhere in the universe.
C) a well-defined portion of the known universe.
D) a yet-to-be discovered segment of the universe.
E) at rest when compared with the rest of the universe.

Accepted Answer

Momentum is conserved in a system that is closed and isolated from external forces. This means no external forces are acting on the system, allowing the total momentum before and after any event within the system to remain constant.

Question 11

Particles A and B are held together with a compressed (massless) spring between them. When they are released, the spring pushes them apart and they fly off in opposite directions, free of the spring. The mass of A is two times larger than the mass of B, and the energy stored in the spring was 120 J. Assuming that all the stored energy is transferred to the particles, the kinetic energies of particles A and B after the transfer of energy has taken place are
A) 0 J and 120 J respectively.
B) 40 J and 80 J respectively.
C) 60 J and 60 J respectively.
D) 80 J and 40 J respectively.
E) 120 J and 0 J respectively.

Accepted Answer

The kinetic energy of a particle is given by KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity. Since the total energy stored in the spring is 120 J, and all of this energy is transferred to the particles, the total kinetic energy of the particles is also 120 J. Since the mass of A is two times larger than the mass of B, the velocity of A will be half the velocity of B. Therefore, the kinetic energy of A will be 1/4 of the total kinetic energy, or 30 J, and the kinetic energy of B will be 3/4 of the total kinetic energy, or 90 J.

Question 12

A truck collides head-on with a car. The larger change in momentum magnitude is experienced by
A) the truck.
B) the car.
C) Both the truck and the car experience the same change in momentum magnitude.
D) Both the truck and the car experience no change in momentum magnitude.
E) More information is needed to work out the answer.

Accepted Answer

According to the law of conservation of momentum, in the absence of external forces, the total momentum of a system remains constant. In a head-on collision between a truck and a car, both vehicles experience forces of equal magnitude but in opposite directions for the same amount of time, leading to changes in momentum of equal magnitude but in opposite directions. Therefore, both the truck and the car experience the same change in momentum magnitude.

Question 13

Two identical 1.0-kg toy cars move at 3.0 m/s, one due north and the other due west. The total momentum of the system is
A) 0 N.s.
B) 3.0 N.s, NW.
C) 4.2 N.s, NW.
D) 6.0 N.s, NW.
E) 18.0 N.s, NW.

Accepted Answer

The total momentum is found by combining the momenta of the two cars vectorially. Each car has a momentum of $1.0 \, \text{kg} \times 3.0 \, \text{m/s} = 3.0 \, \text{N.s}$. Since they are perpendicular to each other, use the Pythagorean theorem to find the resultant: $\sqrt{(3.0)^2 + (3.0)^2} = \sqrt{18} = 4.2 \, \text{N.s}$, and the direction is northwest (NW) because the momenta are equal and perpendicular.

Question 14

A tennis ball moving south at 2.0 m/s collides with a stationary bowling ball. The tennis ball bounces back to the north, and the bowling ball moves very slowly to the south. The ball that experiences the greater magnitude impulse is
A) the tennis ball.
B) the bowling ball.
C) Both the tennis and bowling balls experience the same magnitude impulse.
D) Both the tennis and bowling balls experience zero impulse.
E) More information is needed to work out the answer.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the magnitude of the impulse experienced by the tennis ball is equal to the magnitude of the impulse experienced by the bowling ball, even though their masses and the resulting accelerations are different.

Question 15

Cars are equipped with air bags to protect vehicle occupants from injuries. The role of the air bag is to
A) increase the average forces required to bring the passenger to rest by increasing the change in momentum experienced by the human body.
B) decrease the average forces required to bring the passenger to rest by increasing the change in momentum experienced by the human body.
C) increase the average forces required to bring the passenger to rest by increasing the time interval over which those forces act.
D) decrease the average forces required to bring the passenger to rest by increasing the time interval over which those forces act.

Accepted Answer

Air bags work by increasing the time interval over which the forces act on the passenger during a crash, which decreases the average force required to bring the passenger to rest, thereby reducing the likelihood of injury.

Question 16

A 100-kg cannon is placed on a frozen pond. It fires a 0.50-kg projectile at 20 m/s at an angle of 60^o with the surface of the pond. Ignoring friction, the recoil speed of the cannon is A) 0.20 m/s. B) 0.12 m/s. C) 0.10 m/s. D) 0.09 m/s. E) 0.05 m/s.

Accepted Answer

The answer of A 100-kg cannon is placed on a...

Question 17

A frictionless puck of mass 1.0 kg travels east at 90 m/s toward an initially motionless puck of mass 2.0 kg. When the pucks are 12 meters apart, the center of mass of the system is located
A) 3.0 m from the motionless puck.
B) 4.0 m from the motionless puck.
C) 6.0 m from the motionless puck.
D) 8.0 m from the motionless puck.
E) 12 m from the motionless puck.

Accepted Answer

The center of mass (COM) of a system can be found using the formula: COM = (m1*x1 + m2*x2) / (m1 + m2), where m1 and m2 are the masses and x1 and x2 are their respective positions from a reference point. Here, if we take the position of the 2.0 kg puck as the reference (x2 = 0), and the distance between them as 12 m (x1 = 12 m), we get COM = [(1.0 kg * 12 m) + (2.0 kg * 0 m)] / (1.0 kg + 2.0 kg) = 12 m / 3 kg = 4.0 m from the motionless puck.

Question 18

For two particles of masses m₁ and m₂ and velocities v₁ and v₂, the velocity of the center of mass is A) (v₁+ v₂)/(m₁+ m₂). B) (v₁ . v₂)/(m₁+ m₂). C) (v₁ $\times$ v₂)/(m₁+ m₂). D) (m₂v₁+ m₁v₂)/(m₁+ m₂). E) (m₁v₁+ m₂v₂)/(m₁+ m₂).

Accepted Answer

The velocity of the center of mass is calculated by taking the weighted average of the velocities of the particles, where the weights are their respective masses. This is represented by choice E.

Question 19

A frictionless puck of mass 1.0 kg travels east at 90 m/s toward an initially motionless puck of mass 2.0 kg. When the pucks are 12 meters apart, the speed of the center of mass of the system is
A) 30 m/s.
B) 40 m/s.
C) 60 m/s.
D) 80 m/s.
E) 90 m/s.

Accepted Answer

The total momentum of the system is conserved, so the center of mass will move at a constant velocity. The initial momentum of the system is 90 kg m/s to the east. The final momentum of the system will be the sum of the momenta of the two pucks, which will be 180 kg m/s to the east. The center of mass will therefore move at a velocity of 180 kg m/s / 3 kg = 60 m/s to the east.

Question 20

A rocket achieves a high speed in empty space without the need for any external forces because it
A) circumvents the law of conservation of momentum.
B) retains only a portion of its original mass.
C) turns energy into momentum.
D) Nonsense! No material object can attain a high speed without an external force.

Accepted Answer

Rockets operate on the principle of conservation of momentum. As they expel mass in the form of gas at high speed in one direction, they are propelled in the opposite direction. This process does not require an external force once the rocket is in motion; instead, it relies on the momentum exchange between the rocket and the expelled gas.

Quiz 10: Systems of Particles

The momentum of a single particle is defined as

All of the following dimensions are momentum dimensions except for

Newton's Second Law F = ma. expressed in terms of momentum, reads

Momentum changes for each of these scenarios except for

A 0.20-kg ball, traveling east at 20 m/s, strikes a wall and rebounds at 18 m/s. The change in the ball's momentum is

A car of mass 1200 kg is driving due south at 40 m/s. After driving around a sharp curve, the car is moving west at 30 m/s. The change in the magnitude of the car's momentum is

When momentum is conserved

The momentum of a system of particles is conserved if

The hero in a movie punches a villain, who upon the impact flies through a window and destroys a few other objects nearby. Why is this scene a fantasy?

Momentum is conserved in any system that is

A truck collides head-on with a car. The larger change in momentum magnitude is experienced by

Two identical 1.0-kg toy cars move at 3.0 m/s, one due north and the other due west. The total momentum of the system is

A tennis ball moving south at 2.0 m/s collides with a stationary bowling ball. The tennis ball bounces back to the north, and the bowling ball moves very slowly to the south. The ball that experiences the greater magnitude impulse is

Cars are equipped with air bags to protect vehicle occupants from injuries. The role of the air bag is to

A 100-kg cannon is placed on a frozen pond. It fires a 0.50-kg projectile at 20 m/s at an angle of 60o with the surface of the pond. Ignoring friction, the recoil speed of the cannon is

A frictionless puck of mass 1.0 kg travels east at 90 m/s toward an initially motionless puck of mass 2.0 kg. When the pucks are 12 meters apart, the center of mass of the system is located

For two particles of masses m1 and m2 and velocities v1 and v2, the velocity of the center of mass is

A frictionless puck of mass 1.0 kg travels east at 90 m/s toward an initially motionless puck of mass 2.0 kg. When the pucks are 12 meters apart, the speed of the center of mass of the system is

A rocket achieves a high speed in empty space without the need for any external forces because it

A 100-kg cannon is placed on a frozen pond. It fires a 0.50-kg projectile at 20 m/s at an angle of 60^o with the surface of the pond. Ignoring friction, the recoil speed of the cannon is

For two particles of masses m₁ and m₂ and velocities v₁ and v₂, the velocity of the center of mass is