Question 1

Momentum is conserved in any system that is

Accepted Answer

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. 
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 2

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?

Accepted Answer

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. 
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 3

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

Accepted Answer

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. 
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 4

When momentum is conserved

Accepted Answer

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. 
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 5

Momentum changes for each of these scenarios except for

Accepted Answer

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. 
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 6

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

Accepted Answer

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). 
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 7

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

Accepted Answer

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. 
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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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 
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 11

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

Accepted Answer

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. 
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 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)  10 kN/s. 
B)  12 kN/s. 
C)  60 kN/s. 
D)  70 kN/s. 
E)  84 kN/s. 
A)  10 kN/s. 
B)  12 kN/s. 
C)  60 kN/s. 
D)  70 kN/s. 
E)  84 kN/s.

Question 14

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

Accepted Answer

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. 
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 15

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

Accepted Answer

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. 
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 16

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?

Accepted Answer

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. 
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 17

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

Accepted Answer

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. 
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 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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. 
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.

Exam 10: Systems of Particles

Momentum is conserved in any system that is

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?

When momentum is conserved

Momentum changes for each of these scenarios except for

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

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

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

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 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

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 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

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 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

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

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

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

Space, Time, and Mass

Motion Along a Straight Line

Vectors

Motion in Two and Three Dimensions

Newtons Laws of Motion

Further Applications of Newtons Laws

Work and Energy

Conservation of Energy

Gravitation

Collisions

Rotation of a Rigid Body

Dynamics of a Rigid Body

Statics and Elasticity

Oscillations

Waves

Sound

Fluid Mechanics

The Ideal Gas

Heat

Thermodynamics

Electric Force and the Electric Charge

The Electric Field

Gauss Law

Electrostatic Potential and Energy

Capacitors and Dielectrics

Currents and Ohms Law

Direct Current Circuits

Magnetic Force and Field

Charges and Currents in Magnetic Fields

Electromagnetic Induction

Alternating Current Circuits

Electromagnetic Waves

Reflection, Refraction, and Optics

Interference and Diffraction

The Theory of Special Relativity

Quanta of Light

Spectral Lines, Bohrs Theory, and Quantum Mechanics

Quantum Structure of Atoms, Molecules, and Solids

Nuclei

Elementary Particles and Cosmology

Filters

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