Deck 10: Systems of Particles

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.

Answer 1

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].

Answer 2

[kilogram][meter].

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.

Answer 3

F = $\frac { d } { d t }$ p.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

Question 21

Consider a rocket that attains a given final speed. Any of the following independent modifications in the design of its components will result in a higher final speed except for

A) the use of a fuel with a higher exhaust speed.
B) the use of more mass of fuel.
C) the reduction in mass of nonfuel components.
D) All of the above are true.
E) None of the above is true.

Question 22

A rocket ejects fuel at a constant exhaust speed. If the final mass of the rocket is equal to the mass of the initial fuel on board, the ratio of the final speed of the rocket to the exhaust speed is

A) zero.
B) less than 1/2 but larger than 0.
C) exactly 1/2.
D) larger than 1/2 but less than 1.
E) larger than 1.

Question 23

A flowerpot falls from a balcony. Which statement is true during the fall?

A) The impulse received by the pot is constant during the fall.
B) The impulse received by the pot is zero.
C) The momentum of the pot is conserved.
D) The momentum of the pot-Earth system is conserved.
E) The momentum of the pot-Earth system is not conserved.

Question 24

A constant 10.0-N force acts for 5.0 s on a toy truck is at rest. To determine the toy truck's final momentum, one needs to also know

A) the mass of the toy truck.
B) the direction of the applied force.
C) the direction of the applied force and the mass of the toy truck.
D) the direction of the applied force and the mass and the shape of the toy truck.
E) nothing else.

Question 25

Two skaters at rest, one of 100 kg and the second of 50 kg, push off against one another. Which will gain the largest magnitude of momentum?

A) The 100-kg skater
B) The 50-kg skater
C) Both skaters will gain momentum of the same magnitude.
D) Neither of the skaters will gain any momentum.
E) The momentum of each skater is conserved.

Question 26

Two skaters at rest, one of 100 kg and the second of 50 kg, push off against one another. The total momentum of the system after they push off is

A) positive.
B) zero.
C) negative.
D) increasing as the skaters move away from each other.
E) decreasing as the skaters move away from each other.

Question 27

A sailboat enthusiast has mounted a battery-operated fan on his boat to provide an air current for the sail. If the fan is pushing the air toward the right, straight on the sail,

A) the boat moves in the same direction as the air pushed by the fan.
B) the boat does not move.
C) the boat moves in the direction opposite to the air pushed by the fan.
D) more information is needed to work out the answer.

Question 28

If the following masses are to be stopped by the same constant force, which of the following can be accomplished in the shortest time interval?

A) Stopping a 5.0-kg mass moving at 90 m/s
B) Stopping a 10-kg mass moving at 30 m/s
C) Stopping a 10-kg mass moving at 65 m/s
D) Stopping a 20-kg mass moving at 25 m/s
E) Stopping a 20-kg mass moving at 30 m/s

Question 29

Which of the following situation requires the least average force?

A) Accelerating a 1.0-kg mass from 0 m/s to 10 m/s in 6.0 s
B) Accelerating a 2.0-kg mass from 10 m/s to 20 m/s in 6.0 s
C) Accelerating a 3.0-kg mass from 10 m/s to 30 m/s in 1.0 s
D) Accelerating a 4.0-kg mass from 0 m/s to 20 m/s in 1.0 s
E) Accelerating a 5.0-kg mass from 20 m/s to 30 m/s in 1.0 s

Question 30

A railroad car of mass 12,000 kg is moving horizontally at 10 m/s. Suddenly it starts to rain, and water accumulates in the railroad car. Which of the following is true?

A) The railroad car slows down because the linear momentum of the rain + car system is conserved.
B) The railroad car continues to move at 10 m/s because the rain is falling vertically while the car is moving in a horizontal plane.
C) The railroad car continues to move at 10 m/s because the linear momentum of the rain + car system is conserved.
D) The railroad car continues to move at 10 m/s because the total energy of the rain + car system is conserved.
E) The railroad car speeds up because the potential energy of the rain is converted into kinetic energy for the car.

Question 31

An object's center of mass is located

A) always inside the object.
B) always outside the object.
C) always at the geometrical center.
D) always at the center of symmetry.
E) inside or outside the object, depending on how the mass is distributed.

Question 32

The piece in the figure here was cut from a metallic plate of uniform thickness. The point that corresponds to its center of mass is

A) A
B) B
C) C
D) D
E) E

Question 33

To determine the position of the center of mass of a piece of clay, the object was suspended by a string in two different positions, as shown in the figure here. Its center of mass is therefore placed near point

A) A
B) B
C) C
D) D
E) E

Question 34

A circular hole of radius R was cut from metallic disk of uniform thickness and radius 2R. The center of mass of the disk with the hole is placed

A) R/2 away from the center of the original metallic disk (no hole).
B) R/4 to the right of the center of the original metallic disk (no hole)
C) R/4 to the left of the center of the original metallic disk (no hole).
D) R/3 to the right of the center of the original metallic disk (no hole).
E) R/3 to the left of the center of the original metallic disk (no hole).

Question 35

A fire fighter sprays water horizontally at 10.0 m/s directly at the wall of a house on fire. If 25 kg of water are delivered in 2.5 seconds, the magnitude of the average force on the wall due to water, assuming that after the impact the water falls straight down the wall, is

A) 6.25 N.
B) 62.5 N.
C) 100 N.
D) 625 N.
E) 15.6 kN.

Question 36

An arrow of mass 0.50 kg is shot at an angle of 30^o with the horizontal. The bow exerts a force of 100 N on the arrow for 0.40 s. The maximum height reached by the arrow assuming no air resistance is

A) 8.16 m.
B) 3.19 km.
C) 81.6 m.
D) 245 m.
E) 327 m.

Question 37

A system is made of four objects. The masses and the positions of their centers of mass in a rectangular frame are as follows: Particle 1 of mass 2.0 kg is placed at r₁ = 3.0i - 2.0j m; particle 2 of mass 3.0 kg is placed at r₂ = -1.0i + 1.0j m; particle 3 of mass 2.0 kg is placed at r₃ = 3.0j m; and particle 4 of mass 4.0 kg is placed at r₄ = -1.0i m. The x component of the center of mass of the system is

A) -1.0 m.
B) -0.090 m.
C) 13 m.
D) 0.090 m.
E) 1.0 m.

Question 38

A system is made of four objects. The masses and the positions of their centers of mass in a rectangular frame are as follows: Particle 1 of mass 2.0 kg is placed at r₁ = 3.0i - 2.0j m; particle 2 of mass 3.0 kg is placed at r₂ = -1.0i + 1.0j m; particle 3 of mass 2.0 kg is placed at r₃ = 3.0j m; and particle 4 of mass 4.0 kg is placed at r₄ = -1.0i m. The y component of the center of mass of the system is

A) -2.0 m.
B) -0.45 m.
C) 0.0 m.
D) 0.45 m.
E) 2.0 m.

Question 39

A pole-vaulter has his center of mass 1.00 m above the ground. He starts running from rest, accelerating at 2.5 m/s², and travels 10.0 m before he begins to use the pole. How high above the ground can the athlete raise his center of mass?

A) 1.6 m.
B) 2.6 m.
C) 3.6 m.
D) None of the above is correct.
E) More information is needed to work out the answer.

Question 40

After stealing a 20-kg bag of oranges, an 80-kg thief finds himself at rest on a frozen lake. He attaches himself to the bag of oranges with a long rope and pushes himself off from the bag by giving himself a rightward velocity. When the rope runs out

A) the thief and the bag of oranges will move to the right because the thief has a larger mass.
B) the thief and the bag of oranges will move to the right because the thief has a larger kinetic energy.
C) the thief and the bag will stop.
D) the thief and the bag of oranges will move to the left because the thief has a larger mass.
E) the thief and the bag of oranges will move to the left because the thief has a larger kinetic energy.

Question 41

Alex and Kaylee are placed at the two ends of a boat on a still lake. Alex, of mass 80 kg, decides to swap seats with Kaylee, of mass 60 kg. As a result, the boat will

A) move in the same direction Kaylee moves.
B) move in the same direction Alex moves.
C) move in the same direction Alex moves, then move in the same direction Kaylee moves; but its net displacement is zero.
D) move in the same direction Kaylee moves, then move in the same direction Alex moves; but its net displacement is zero.
E) not move at all.

Question 42

A 540- kg,10-m-long boat is placed perpendicular to a dock. When a 60-kg boy starts walking from the end to the front of the boat, the front of the boat touches the dock. The boy's distance from the dock when the boy reaches the front of the boat is

A) 0.0 m.
B) 0.50 m.
C) 1.0 m.
D) 4.5 m.
E) 5.5 m.

Question 43

A 540-kg boat, originally at rest, is placed perpendicular to a dock so that the front of the boat touches the dock. A 60-kg boy jumps horizontally at 4.0 m/s from the dock to the front of the boat. The speed of the boat just after the boy jumps in is

A) 0.40 m/s.
B) 0.44 m/s.
C) 1.0 m/s.
D) 4.0 m/s.
E) 4.4 m.

Question 44

A car of mass 10 kg moves eastward at 30 m/s while a second car of mass 30 kg moves at 10 m/s westward. The magnitude of the linear momentum and the kinetic energy of the system are

A) 0 kg.m/s and 3.0 kJ.
B) 600 kg.m/s and 3.0 kJ.
C) 300 kg.m/s and 4.5 kJ.
D) 600 kg.m/s and 6.0 kJ.
E) 0 kg.m/s and 6.0 kJ.

Question 45

A 3.0-N force pointing east is acting on a 2.0-kg mass, while a 4.0-N force pointing south is acting on a 3.0-kg mass. The acceleration of the center of mass of the system is

A) 0.20 m/s², 53^o S of E.
B) 0.60 m/s², E.
C) 0.80 m/s², S.
D) 1.0 m/s², 53^o S of E.
E) 1.4 m/s², 37^o S of E.

Question 46

The velocities of three identical masses are shown in the figure here. The velocity of their center of mass is

A) -1.0i - 1.0j m/s.
B) -0.33i - 0.33j m/s.
C) -1.0i + 6.0j m/s.
D) -0.33i + 2.0j m/s.
E) 0.0 m/s.