Deck 1: Conservation Laws Constrain Interactions

Question 1

According to the definition of "science" given in this chapter, astrology is not a science. What does it lack?

A) A community of scholars devoted to its study
B) Agreement that models must be logically consistent
C) Use of reproducible experiments to test models
D) A grand theory embracing the discipline

Answer 1

Use of reproducible experiments to test models

Question 2

According to the definition of "science" given in this chapter, which of the following do you think are sciences? Choose the letter of the first discipline on the list that you think is not a science. (The answer is open to debate!)

A) Geology
B) Psychology
C) Economics
D) Anthropology
E) Political Science
F) Philosophy
G)All are sciences

Answer 2

Economics

Question 3

Which of the following expressions gives the correct units for the volt in terms of base SI units?

A) $1 \mathrm{~V}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \mathrm{C}^{-1} \mathrm{~s}$
B) $1 \mathrm{~V}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \mathrm{~A}^{-1} \mathrm{~s}^{-3}$
C) $1 \mathrm{~V}=1 \mathrm{~kg} \cdot \mathrm{m} \cdot \mathrm{A}^{-1} \mathrm{~s}^{-1}$
D) $1 \mathrm{~V}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \mathrm{~s}^{-2} \mathrm{C}^{-2}$
E) $1 \mathrm{~V}=1 \mathrm{~J} / \mathrm{C}$
F) Some other expression (specify).

Answer 3

$1 \mathrm{~V}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \mathrm{~A}^{-1} \mathrm{~s}^{-3}$

Question 4

Assume that $D$ and $R$ have units of meters, $T$ has units of seconds, $m$ and $M$ have units of kilograms, $V$ has units of meters per second, and $g$ has units of $\mathrm{m} / \mathrm{s}^{2}$ . Which of the following equations has selfconsistent units?

A) $\mathrm{D}=m \mathrm{R}^{2}$
B) $m=M\left[1+R^{2}\right]$
C) $\mathrm{D}=[1-\mathrm{m} / \mathrm{M}] g \mathrm{~T}^{2}$
D) $g=m v^{2} / \mathrm{R}$
E) $\mathrm{D}=v^{2} / \mathrm{R} T$
F) None of these can be correct.

Question 5

One can raise a quantity $q$ to a power a when a has units

Question 6

The following formulas are supposed to describe the speed $V$ of a sphere sinking in a thick fluid. $C$ is a unitless constant, $\rho$ is the fluid's density in $\mathrm{kg} / \mathrm{m}^{3}, A$ is the sphere's cross-sectional area, $m$ is its mass, and $g$ is the gravitational field strength in $\mathrm{N} / \mathrm{kg}$ . Which could be right?

A) $v=C A \rho g$
B) $v=C m g / \rho A$
C) $v=(C m g / \rho A)^{2}$
D) $v=(C m g / P A)^{1 / 2}$
E) None of these can be correct.

Question 7

The speed $V$ of sound waves in a gas like air might plausibly depend on the gas's pressure $P$ (which has units of $\mathrm{N} / \mathrm{m}^{2}$ ), the gas's density $\rho$ (which has units of $\mathrm{kg} / \mathrm{m}^{3}$ ) and its temperature $T$ (which has units of $\mathrm{K}$ ), and some unitless constant $C$ . Assuming that no other quantities are relevant, which of the following formulas might possibly correctly give the speed of sound in a gas?

A) $v=\mathrm{CP} \rho \mathrm{T}$
B) $v=\mathrm{CTP} / \rho$
C) $V=\mathrm{CP} / \rho$
D) $v=C \sqrt{P / \rho}$
E) $V=C \sqrt{\rho / P}$
F) $v=\mathrm{C}(\mathrm{P} / \rho)^{2}$
G) None of these can be correct.

Question 8

The two stars in a binary star system revolve around each other with a certain period $T$ . Which of the quantities listed below is not likely to be a part of the formula for this revolution period?

A) $m_{1}, m_{2}$ (the masses of the stars in the system)
B) $r$ (the distance between the binary stars)
C) $\hbar$ (Planck's constant, which is generally associated with phenomena involving quantum mechanics)
D) $G$ (the universal gravitational constant)

Question 9

A baseball player slides into third base. Why, according to the modern model of mechanics, does the player eventually come to rest?

A) All moving objects naturally come to rest eventually.
B) Friction overpowers the force of the player's motion.
C) The force of the player's motion eventually wears out.
D) A friction interaction changes the player's motion.
E) Other (specify).

Question 10

A car moves backward $10 \mathrm{~m}$ in $2 \mathrm{~s}$ at a steady rate. The car's speed is therefore $-5 \mathrm{~m} / \mathrm{s}$

Question 11

An object is moving at a constant velocity. This means that an interaction must be delivering momentum to the object at a constant nonzero rate.

Question 12

A bicyclist rounding a curve at a constant speed is receiving a nonzero net flow of momentum.

Question 13

A deep space probe moving forward in space needs to make a course correction and so fires a thruster on the side of the probe $90^{\circ}$ away from its direction of motion, as shown below. This thruster, while on, exerts a constant force on the probe perpendicular to its original direction of motion. While the thruster is operating, which trajectory best describes the probe's motion? (Hint: Note that the thrust force delivers an upward impulse to the probe during every successive time interval. Consider what happens to the ball in figure C2.4 as it receives analogous continual downward impulses.)

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

Question 14

A deep space probe moving forward in space needs to make a course correction and so fires a thruster on the side of the probe $90^{\circ}$ away from its direction of motion, as shown below. After the thruster is turned off, which trajectory best describes the probe's subsequent motion?
Possible final trajectories (thruster off):

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

Question 15

A cup sitting on a table constantly receives upward momentum from the table

Question 16

A human being's weight could be $150 \mathrm{~kg}$

Question 17

Suppose I throw a ball toward the floor. It hits the floor and rebounds upward. What type of interaction causes the ball to rebound?

A) Gravitational
B) Electrostatic
C) Magnetic
D) Compression
E) Friction
F) Tension
G) Something else (explain)

Question 18

An empty floating boat interacts gravitationally with the earth. A different interaction with something else keeps the boat from responding to the gravitational interaction by sinking.

-What type of interaction is involved?

A) A tension interaction
B) An electrostatic interaction
C) A friction interaction
D) A compression interaction
E) Other (specify)

Question 19

An empty floating boat interacts gravitationally with the earth. A different interaction with something else keeps the boat from responding to the gravitational interaction by sinking.

-What is the other object that interacts with the boat?

A) The water
B) The atmosphere
C) The earth
D) The lake floor
E) Other (specify)

Question 20

Suppose a $1.0-\mathrm{kg}$ object traveling rightward at $1.0 \mathrm{~m} / \mathrm{s}$ hits a $3.0 \mathrm{~kg}$ object at rest. Afterward, we observe the lighter object to move leftward with a speed of $0.75 \mathrm{~m} / \mathrm{s}$ . What impulse did the collision interaction give the smaller object at the expense of the larger?

A) None; the larger object was at rest and so had no momentum to give the smaller object.
B) None; the smaller object gave an impulse to larger, not the other way around.
C) $0.75 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ leftward.
D) $1.0 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ leftward.
E) $1.75 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ leftward.

Question 21

Suppose a moving cart (cart $A$ ) hits an identical cart (cart $B$ ) at rest. Cart $B$ remains at rest after the collision, and cart $A$ rebounds with a speed equal to its original speed. Cart $B$ must have participated in some other interaction during the collision process,

Question 22

Suppose two identical objects traveling toward each other with the same speed collide. According to the momentum-transfer principle, if we observe one of the objects to be at rest after the collision, the other object:

A) Must be at rest also.
B) Must rebound backward with its original speed.
C) Must rebound backward with twice its original speed.
D) Must continue forward with twice its original speed.
E) The process as described violates the principle.

Question 23

The $x, y$ , and $z$ directions of a reference frame point up, west, and north, respectively. Such a coordinate system is right-handed.

Question 24

The $x$ and $y$ axes of a reference frame point forward and to your right, respectively. The frame is righthanded if the $z$ axis points up

Question 25

We can describe a vector's magnitude and direction without a reference frame

Question 26

The components of a displacement vector $\Delta \vec{r}$ between two position vectors $\overrightarrow{r_{1}}$ and $\overrightarrow{r_{2}}$ depend on one's choice of reference frame origin.

Question 27

Consider the displacement vectors shown below.


- Which vector (if any) is equal to $\vec{A}$

Question 28

Consider the displacement vectors shown below.


-Which is not equal to $\vec{A}$ but has the same magnitude?

Question 29

Consider the displacement vectors shown below.


- Which is equal to $-\vec{C}$ ?

Question 30

Consider the displacement vectors shown below.


-Which is equal to $2 \vec{B}$ ?

Question 31

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

- $\vec{F}_{\text {tot }}=\vec{F}_{1}+\vec{F}_{2}$ implies that $\left|\vec{F}_{2}\right|=\left|\vec{F}_{\text {tot }}\right|-\left|\vec{F}_{1}\right|$ .

Question 32

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

- $\vec{F}_{A} \equiv[\Delta \vec{p}]_{A} / \Delta t$ implies that $\Delta t=[\Delta \vec{p}]_{A} / \vec{F}_{A}$ .

Question 33

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

-If an object moves at a rate of $5 \mathrm{~m} / \mathrm{s}$ in the $-x$ direction, then $\vec{v}_{x}=-5 \mathrm{~m} / \mathrm{s}$ .

Question 34

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

- If an object moves at a rate of $5 \mathrm{~m} / \mathrm{s}$ in the $-y$ direction, then $\vec{v}=+5 \mathrm{~m} / \mathrm{s}$ .

Question 35

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

- If $\vec{v}=5 \mathrm{~m} / \mathrm{s}$ and $m=2.0 \mathrm{~kg}$ , then $\vec{p}=10 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ .

Question 36

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

-The forces on the object cancel, so $\vec{F}_{\text {tot }}=0$ .

Question 37

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.

- The speed at the end of the interval is $v=v_{0}+1$ .

Question 38

An object has an initial position $\overrightarrow{r_{1}}$ , but is found a short time later at position $\overrightarrow{r_{2}}$ , where
$$\overrightarrow{r_{1}}=\left[\begin{array}{r}1)5 \mathrm{~m} \\2)0 \mathrm{~m} \\-4)2 \mathrm{~m}\end{array}\right], \overrightarrow{r_{2}}=\left[\begin{array}{r}1)5 \mathrm{~m} \\-3)0 \mathrm{~m} \\-4)2 \mathrm{~m}\end{array}\right]$$
In a frame in standard orientation on the earth's surface, what is the direction of the object's displacement during this time interval?

A) East
B) West
C) North
D) South
E) Down

Question 39

$|\vec{u}-\vec{w}| \geq|\vec{u}|-\mid \vec{w} \|$ for all vectors $\vec{u}$ and $\vec{w}$

Question 40

The only way a vector's magnitude can be zero is if all its components are zero

Question 41

In a situation where an object can move only along the $x$ axis, a book states "the force on the object is $\mathrm{F}=$ $k x$ , where $k$ is a constant, and $x$ is the object's position coordinate." Is $F$ being used here as a shorthand symbol for $|\vec{F}|(A)$ or $F_{x}(C)$ ?
$\bullet$ A
$\bullet$ C

Question 42

In a situation where an object can move only along the $x$ axis, you see this statement in a book: "The object's velocity is $\mathrm{v}=\left(x-x_{0}\right) / t$ , where $x$ is the object's position at time $t$ to the left or right of its position $x_{0}$ at time $t=0$ ." Is $v$ being used here as a shorthand for $|\vec{v}|(\mathrm{A})$ or $v_{x}(\mathrm{C})$ ?
$\bullet$ A
$\bullet$ C

Question 43

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-An electron

Question 44

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-An atom

Question 45

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-A rock

Question 46

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-A swarm of bees

Question 47

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-The earth's atmosphere

Question 48

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-The water in an ocean current

Question 49

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-Sugar molecules dissolved in a cup of water

Question 50

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable.

-The vacuum between galaxies

Question 51

We can consider a set of all chlorine atoms in a block of salt (sodium chloride) to be a "system."

Question 52

The electric field inside a conductor must be zero in all possible circumstances.

Question 53

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

- The contact interactions between the earth and a car moving on the earth's surface

Question 54

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

- The gravitational interaction between the earth and the International Space Station

Question 55

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

-The gravitational interaction between two planets

Question 56

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

-The gravitational interaction between a given planet and the sun

Question 57

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

-The magnetic interaction between the sun and the earth (both have magnetic fields)

Question 58

Consider the solar system as a "system" of particles. Which of the below qualify as internal interactions (A) and which as external interactions (E)?

-The gravitational interaction between the sun and the larger galaxy

Question 59

Suppose a planet with mass $M$ has a moon with mass $M$ . Where is the system's center of mass? Refer to the diagram below.

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

Question 60

Two rods with the same density and diameter form a cross, as shown below. Where is the system's center of mass? (Hint: Treat each rod as a uniform object, whose center of mass is its geometric center.)

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

Question 61

In example C4.2, if we had modeled the atoms as solid spheres instead of modeling the nuclei as pointlike particles, we would have gotten the same result for the system's center of mass

Question 62

Consider a three-particle system. The center of mass of this system must lie on the plane that contains all three particles. Be prepared to explain why or why not. (Hint: A clever choice of reference frame makes answering this question easier.)

Question 63

In a reference frame floating in space, which do you think follows the straighter path?

A) The earth
B) The moon
C) The center of mass of the earth/moon system

Question 64

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A NRF attached to Jupiter's center of mass
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 65

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A NRF attached to a satellite orbiting the earth
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 66

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A frame attached to a car moving with a fixed speed on a straight road
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 67

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A reference frame constructed in a sports stadium
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 68

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A reference frame attached to a roller-coaster car
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 69

Consider the types of reference frames listed below.
(NRF = nonrotating frame)



-A reference frame attached to a freely falling elevator
A. A NRF in deep space
B. A NRF that is freely floating
C. A NRF attached to the earth's center of mass
D. A frame attached to the earth's surface (or a similarly slowly rotating object)
E. A frame moving at a constant velocity relative to one of the frame types described above
F. A noninertial frame

Question 70

Which of the following frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon?

-A frame attached to the earth's surface

A) if the frame is appropriate
B) if it would be bad for this purpose.

Question 71

Which of the following frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon?

-A frame attached to the earth's center of mass (CM)

A) if the frame is appropriate
B) if it would be bad for this purpose.

Question 72

Which of the following frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon?

-A frame attached to the earth-moon system's CM

A) if the frame is appropriate
B) if it would be bad for this purpose.

Question 73

Which of the following frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon?

-A frame attached to the sun's CM

A) if the frame is appropriate
B) if it would be bad for this purpose.

Question 74

Which of the following frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon?

-A frame attached to the entire solar system's CM

A) if the frame is appropriate
B) if it would be bad for this purpose.

Question 75

In the situation discussed in problem C4T.10, which would be the easiest reasonably valid frame to use?

Question 76

A reference frame attached to a train is a reasonably good inertial frame if the train is stopped at a station.

Question 77

A reference frame attached to a train It is a good inertial frame if it is moving at a fixed speed in a straight line

Question 78

A reference frame attached to a train It is a good inertial frame if it is moving at a fixed speed around a curve

Question 79

To which of the following two-object systems can we apply conservation of momentum, and why? In each case, answer "A" if we can apply conservation of momentum because the system floats in space, "F" if it's because the system is functionally isolated, " $C$ " if it's because the system undergoes a collision, and " $\mathrm{D}$ " if momentum is not conserved at all because the system is not isolated.

-Two magnetic hockey pucks slide on a flat plane of frictionless ice. They attract each other as they pass, changing each other's trajectories without touching.

Question 80

To which of the following two-object systems can we apply conservation of momentum, and why? In each case, answer "A" if we can apply conservation of momentum because the system floats in space, "F" if it's because the system is functionally isolated, " $C$ " if it's because the system undergoes a collision, and " $\mathrm{D}$ " if momentum is not conserved at all because the system is not isolated.

-An asteroid imbeds itself in a planet.