Deck 10: Systems of Particles and Conservation of Momentum

Question 1

The value of the momentum of a system is the same at a later time as at an earlier time if there are no

A)collisions between particles within the system.
B)inelastic collisions between particles within the system.
C)changes of momentum of individual particles within the system.
D)internal forces acting between particles within the system.
E)external forces acting on particles of the system.

Answer 1

external forces acting on particles of the system.

Question 2

The linear density of a rod, in g/m, is given by . The rod extends from the origin to x = 0.400 m. What is the location of the center of mass of the rod?

A)x = 0.213 m
B)x = 0.315 m
C)x = 0.384 m
D)x = 0.184 m
E)x = 0.208 m

Answer 2

x = 0.213 m

Question 3

At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant?

A)16 m/s
B)45 m/s
C)23 m/s
D)20 m/s
E)36 m/s

Answer 3

16 m/s

Question 4

Two bodies with masses m1 and m² are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the center of mass of this system of two bodies is

A)less than v1.
B)equal to v1.
C)equal to the average of v1 and v2.
D)greater than v1 and less than v2.
E)greater than v2.

Question 5

A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s²) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3 000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed?

A)56 kN
B)48 kN
C)52 kN
D)44 kN
E)36 kN

Question 6

At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system?

A)3.8 m/s
B)3.4 m/s
C)5.0 m/s
D)4.4 m/s
E)4.6 m/s

Question 7

A pitcher claims he can throw a baseball with as much momentum as a 3.00-g bullet moving with a speed of 1500 m/s. A baseball has a mass of 0.145 kg. What must be its speed if the pitcher's claim is valid?

Question 8

A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system

A)no matter what height h' it reaches.
B)only if h' < h.
C)only if h' = h.
D)only if h' > h.
E)only if h' ≥ h.

Question 9

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m-high ladders. The center of mass of the Earth (mE = 5.90 1024 kg) is then displaced

A)0 m.
B)1.84 × 10−23 m.
C)1.84 × 10−14 m.
D)1.80 × 10−13 m.
E)2 m.

Question 10

The law of conservation of momentum applies to a collision between two bodies since

A)they exert equal and opposite forces on each other.
B)they exert forces on each other respectively proportional to their masses.
C)they exert forces on each other respectively proportional to their velocities.
D)they exert forces on each other respectively inversely proportional to their masses.
E)their accelerations are proportional to their masses.

Question 11

At an instant when a particle of mass 50 g has an acceleration of 80 m/s² in the positive x direction, a 75-g particle has an acceleration of 40 m/s² in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?

A)60 m/s²
B)56 m/s²
C)40 m/s²
D)50 m/s²
E)46 m/s²

Question 12

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (−2, −2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin?

A)(−3, −1) m
B)(+1, +3) m
C)(+3, −1) m
D)(−1, −3) m
E)(−0.5, −2) m

Question 13

Two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls?

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

Question 14

Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (−2, −6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin?

A)(−1, −3) m
B)(−1, 2) m
C)(−1, 12) m
D)(−1, 7) m
E)(−1, 3) m

Question 15

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than , one quarter circle, the center of mass of the two cars

A)remains at the initial point.
B)travels along a diameter of the circle at speed v' < v.
C)travels along a diameter of the circle at speed v' = v.
D)travels along a diameter of the circle at speed v' > v.
E)remains at the center of the circle.

Question 16

A uniform thin wire has a length and is bent into a semicircular arc of radius R. If the wire starts at (x, y) = (R, 0) and curves counterclockwise to (x, y) = (−R, 0), what is the y coordinate of its center of mass?

Question 17

A car of mass m1 traveling at velocity v passes a car of mass m² parked at the side of the road. The momentum of the system of two cars is

A)0.
B)m1v.
C)(m1 − m²)v.
D)
E)(m1 + m²)v.

Question 18

A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the magnitude of the momentum the Earth acquires to the magnitude of the momentum the ball acquires is

A)0.
B) .
C) .
D)1
E) .

Question 19

A rocket with an initial mass of 1000 kg adjusts its thrust by varying the rate at which mass is ejected. The ejection speed relative to the rocket is 40 km/s. If the acceleration of the rocket is to have a magnitude of 20 m/s² at an instant when its mass is 80% of the original mass, at what rate is mass being ejected at that instant? Ignore any external forces on the rocket.

A)0.40 kg/s
B)0.50 kg/s
C)0.60 kg/s
D)0.70 kg/s
E)0.80 kg/s

Question 20

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?

A)42 kN
B)39 kN
C)45 kN
D)48 kN
E)35 kN

Question 21

The value of the momentum of a system is the same at a later time as at an earlier time if there are no

A)collisions between particles within the system.
B)inelastic collisions between particles within the system.
C)changes of momentum of individual particles within the system.
D)internal forces acting between particles within the system.
E)external forces acting on particles of the system.

Question 22

At an instant when a particle of mass 50 g has an acceleration of 80 m/s² in the positive x direction, a 75-g particle has an acceleration of 40 m/s² in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?

A)60 m/s²
B)56 m/s²
C)40 m/s²
D)50 m/s²
E)46 m/s²

Question 23

A car of mass m1 traveling at velocity v passes a car of mass m² parked at the side of the road. The momentum of the system of two cars is

A)0.
B)m1v.
C)(m1 − m²)v.
D)
E)(m1 + m²)v.

Question 24

At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant?

A)16 m/s
B)45 m/s
C)23 m/s
D)20 m/s
E)36 m/s

Question 25

A 6.0-kg object moving 2.0 m/s in the positive x direction has a one-dimensional elastic collision with a 4.0-kg object moving 3.0 m/s in the opposite direction. What is the total kinetic energy of the two-mass system after the collision?

A)30 J
B)62 J
C)20 J
D)44 J
E)24 J