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Question 3161Question →

In subtropical ocean regions characterized by persistent dry air and intense sunlight, surface water converts into atmospheric vapor much faster than rainfall can replenish it, leaving dissolved mineral ions behind in the water column. Which hydrologic process is primarily responsible for this localized increase in ocean surface salinity?

Transpiration

Evaporation

Precipitation

Condensation

Show answer & explanation

Answer: Evaporation

Answer

Evaporation is the primary process responsible for the increased surface ocean salinity.

Evaporation is the phase change in which liquid surface water absorbs heat energy and transforms into gaseous water vapor. Because dissolved mineral salts do not evaporate at environmental temperatures, the continuous removal of freshwater vapor concentrates the remaining salts, thereby increasing surface salinity in arid subtropical belts.

Step-by-Step Solution

Analyze the physical phase transition described in the scenario.

Liquid ocean water absorbs solar energy and transitions into atmospheric water vapor (gas).

Identifying the starting state (liquid) and ending state (gas) defines the specific phase change mechanism.

Determine the impact of removing pure water molecules on the remaining solution.

Dissolved mineral ions (such as sodium and chloride) cannot vaporize at ambient temperatures and remain in the liquid layer.

When the solvent (

H_2O

) decreases while the solute remains constant, the concentration (salinity) increases.

Match the identified phase change and oceanographic mechanism to the correct scientific term.

The direct transition of liquid water to gaseous water vapor from an open body of water is evaporation.

Evaporation removes freshwater molecules into the atmosphere, directly driving up salinity in high-temperature, low-rainfall zones.

Key Concept

Phase changes in the hydrologic cycle directly modulate ocean surface salinity by removing freshwater through evaporation.

Estimated Time:1m 0s

Question 3162Question →

Waves transmit energy through space and matter and are described by specific physical characteristics. How should each wave property on the left be paired with its correct definition on the right?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Amplitude pairs with maximum displacement from rest position; Frequency pairs with number of cycles per unit time; Wavelength pairs with distance between successive crests or troughs; Period pairs with time required for one full wave cycle.

Each term is accurately matched to its standard physical definition: amplitude describes height from rest position, frequency measures cycles per second, wavelength measures physical distance between peaks, and period measures the duration of one cycle.

Step-by-Step Solution

Identify spatial wave dimensions

Amplitude corresponds to displacement height from equilibrium, while wavelength is the linear distance between identical points on consecutive waves.

Separating vertical displacement from horizontal spatial extent clarifies the two geometric dimensions of a wave.

Identify temporal wave characteristics

Frequency measures cycle count per second (rate), while period measures total time per cycle (duration).

Frequency (

f

) and period (

T

) are reciprocal properties related by

f = \frac{1}{T}

Key Concept

Fundamental wave parameters (amplitude, frequency, wavelength, and period) define the spatial and temporal behavior of waves.

Estimated Time:45s

Question 3163Question →

Matter exhibits distinct physical properties that dictate how substances behave under mechanical stress, thermal changes, and fluid dynamics. Match each observed physical phenomenon on the left with the specific property of matter it demonstrates on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The phenomenon of motor oil pouring slower when cold matches viscosity; the ceramic tile shattering upon impact matches brittleness; the lead sinking while pine of equal volume floats matches relative density; and the aluminum handle heating rapidly matches thermal conductivity.

Each physical observation correlates directly with an intrinsic property of matter: fluid resistance to pouring reflects viscosity; fracturing without plastic deformation demonstrates brittleness; sink/float behavior of equal volumes demonstrates relative density; and rate of heat transfer through a solid medium defines thermal conductivity.

Step-by-Step Solution

Analyze fluid flow behavior across temperatures

Motor oil resisting flow when cold is a direct manifestation of high fluid friction and resistance to movement, which defines viscosity.

Viscosity is the property of a fluid that determines its rate of flow and internal resistance.

Evaluate the mechanical failure response of the dropped ceramic tile

The ceramic tile shatters upon impact without bending or deforming plastically, which is the defining characteristic of brittleness.

Brittle materials fail abruptly under mechanical shock rather than undergoing plastic deformation like ductile or malleable solids.

Compare the sinking and floating behavior of equal-volume blocks in water

Objects sink if their mass per unit volume exceeds that of the displaced fluid (

1.0\text{ g/cm}^3

) and float if it is lower, demonstrating relative density.

Buoyant force depends on the mass of fluid displaced versus the gravitational force acting on the object's mass.

Identify the property responsible for heat distribution along the metal cookware

Heat moving from the base of the aluminum pan to the end of the handle is thermal conduction, governed by thermal conductivity.

Metals have high thermal conductivity due to lattice vibrations and delocalized conduction electrons.

Key Concept

Physical properties of matter describe intrinsic characteristics—such as thermal conductivity, viscosity, brittleness, and density—that can be observed and measured without altering the chemical identity of the substance.

Estimated Time:1m 0s

Question 3164Question →

Although temperatures in Earth's inner core exceed 5,000 °C, which is well above the surface melting point of iron, the inner core remains solid. Which of the following factors is primarily responsible for keeping the inner core in a solid state?

A high concentration of lightweight silicate minerals that resist melting at elevated temperatures

Immense pressure from overlying layers that dramatically elevates the melting point of the iron-nickel alloy

Rapid thermal convection that transfers heat continuously into the cooler lithosphere

Continuous frictional locking along deep transform plate boundaries that stabilizes the core

Show answer & explanation

Answer: Immense pressure from overlying layers that dramatically elevates the melting point of the iron-nickel alloy

Answer

Immense pressure from overlying layers that dramatically elevates the melting point of the iron-nickel alloy

The physical state of matter depends on both temperature and pressure. While the temperature in the inner core is high enough to melt iron under surface conditions, the immense weight of all overlying layers generates millions of atmospheres of pressure. This extreme confining pressure forces the iron and nickel atoms into a tightly packed crystalline lattice, raising the melting temperature above the actual core temperature.

Step-by-Step Solution

Identify the primary chemical composition and thermal state of the inner core

The inner core is composed predominantly of an iron-nickel alloy at temperatures exceeding 5,000 °C.

Understanding composition establishes the baseline physical properties under standard conditions.

Analyze the physical relationship between confining pressure and the melting point of solids

Increasing pressure forces atoms closer together, which raises the temperature required for a substance to transition from solid to liquid.

Phase state depends on both temperature and pressure simultaneously.

Apply this relationship to Earth's center to determine why the inner core is solid while the outer core is liquid

At the center of Earth, pressure exceeds 3.3 million atmospheres, raising the melting point of iron-nickel above the core's actual temperature.

This explains the solid state of the inner core despite extreme heat.

Key Concept

Effect of extreme confining pressure on the melting point and physical state of Earth's internal layers

Estimated Time:45s

Question 3165Question →

Match each fundamental atomic structure term with its correct scientific definition.

Click a left item, then click its matching right item

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Answer

Atomic number matches the number of protons defining element identity; Mass number matches the sum of protons and neutrons; Valence electrons match the outermost shell electrons involved in bonding; Isotopes match atoms of the same element with differing neutron counts.

Each scientific term corresponds directly to its foundational definition in atomic structure: atomic number represents protons; mass number represents protons plus neutrons; valence electrons are the outermost bonding electrons; isotopes are atoms of the same element varying in neutron number.

Step-by-Step Solution

Define atomic number (

Z

)

Identified as the count of protons in the nucleus, defining elemental identity.

By definition, the number of protons is unique to each element and equals its atomic number.

Define mass number (

A

)

Identified as the sum of protons and neutrons.

Electrons have negligible mass, so the mass number accounts for the heavy nuclear particles.

Define valence electrons

Identified as outermost electrons governing bonding.

Only electrons in the outermost energy level participate in chemical reactions and bond formation.

Define isotopes

Identified as atoms of the same element with different neutron numbers.

Since proton number defines the element, isotopes share chemical properties but have different physical masses due to unequal neutrons.

Key Concept

Core definitions of subatomic particles, nuclear notation, and electron configurations in atomic theory.

Estimated Time:45s

Question 3166Question →

A technician is preparing a heavy-duty cable that will be cut into three separate sections. The total length of the cable before any cuts is $15 \frac{4}{5}$ yards. The first section measures $4 \frac{1}{3}$ yards long, and the second section measures exactly $6$ feet long. Assuming no material is lost during cutting, how many yards long must the third section be?

9 \frac{7}{15}

5 \frac{7}{15}

9 \frac{3}{8}

6 \frac{1}{3}

Show answer & explanation

Answer: $9 \frac{7}{15}$

Answer

The third section must be

9 \frac{7}{15}

yards long.

The correct answer is found by first converting the 6 feet into 2 yards. Adding this to the first section gives a total used length of

6 \frac{1}{3}

yards. By finding a common denominator of 15, the total length (

15 \frac{12}{15}

) minus the used length (

6 \frac{5}{15}

) correctly equals

9 \frac{7}{15}

yards.

Step-by-Step Solution

Convert the length of the second section from feet to yards so all units match.

6 \text{ feet} = 2 \text{ yards}

Measurements must be in the same unit (yards) before they can be added or subtracted.

Add the lengths of the first and second sections to find the total length used so far.

4 \frac{1}{3} + 2 = 6 \frac{1}{3} \text{ yards}

This establishes the combined length that needs to be subtracted from the whole.

Find a common denominator for the total cable length and the used cable length.

The common denominator for

5

and

3

15

. Thus,

15 \frac{4}{5} = 15 \frac{12}{15}

and

6 \frac{1}{3} = 6 \frac{5}{15}

Fractions must have common denominators before they can be subtracted.

Subtract the used length from the total length to find the length of the third section.

15 \frac{12}{15} - 6 \frac{5}{15} = 9 \frac{7}{15} \text{ yards}

Subtracting the sum of the known parts from the total length yields the remaining unknown part.

Key Concept

Adding and subtracting mixed numbers with unlike denominators after converting units.

Question 3167Question →

A robotic exploration rover has a mass of $120\text{ kg}$ on Earth. The rover is transported to Mars, where the acceleration due to gravity is approximately $3.7\text{ m/s}^2$ . If the rover accelerates horizontally across a flat, level surface at $2.0\text{ m/s}^2$ , what is the magnitude of the horizontal net force acting on the rover?

24\text{ N}

240\text{ N}

444\text{ N}

684\text{ N}

Show answer & explanation

Answer: $240\text{ N}$

Answer

The magnitude of the horizontal net force acting on the rover is

240\text{ N}

According to Newton's Second Law of Motion (

F = ma

), the net force acting on an object is equal to its mass multiplied by its acceleration. An object's mass is invariant across different gravitational fields. Therefore, accelerating a

120\text{ kg}

rover horizontally at

2.0\text{ m/s}^2

requires a horizontal net force of

120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}

Step-by-Step Solution

Identify the relevant physical law and given values.

Mass

m = 120\text{ kg}

, horizontal acceleration

a = 2.0\text{ m/s}^2

, and Newton's Second Law

F_{\text{net}} = ma

Mass is an intrinsic scalar property that remains constant regardless of location or local gravity.

Calculate the horizontal net force required to accelerate the mass.

F_{\text{net}} = 120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}

Horizontal acceleration is governed strictly by the horizontal net force and mass, independent of vertical gravitational forces on a level surface.

Key Concept

Newton's Second Law of Motion and Independence of Mass from Gravity

Estimated Time:1m 0s

Question 3168Question →

Urine is continuously produced by the human body to filter metabolic waste and maintain fluid balance. Place the following anatomical structures in the correct order through which urine travels, from its initial formation in the kidneys to its final excretion from the body.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Nephrons (filtration units of the kidney) → Ureters (bilateral muscular tubes) → Urinary bladder (expandable muscular reservoir) → Urethra (terminal excretion canal)

The biological pathway of excretion starts in the kidneys, where microscopic nephrons produce urine. Urine collects in the renal pelvis and flows through the bilateral ureters to the urinary bladder for temporary containment, before finally being discharged out of the body through the urethra.

Step-by-Step Solution

Identify the site of urine formation

Nephrons in the renal cortex and medulla produce urine through filtration, reabsorption, and secretion.

Urine must be generated in the functional units of the kidney before it can enter the transport conduits.

Determine the conduit connecting the kidneys to the central storage organ

The ureters carry urine away from each kidney.

Muscular peristaltic contractions in the ureters transport the newly formed urine from the renal pelvis down toward the pelvic cavity.

Identify the storage organ

The urinary bladder collects and stores urine.

Urine accumulates in the bladder until stretch receptors trigger the urge to urinate.

Identify the final pathway for fluid release

The urethra conducts urine out of the body.

The urethra is the single terminal canal leading from the bladder neck to the external urethral orifice.

Key Concept

Anatomical pathway and flow of urine through the human excretory system

Estimated Time:1m 0s

Question 3169Question →

Match each electromagnetic device or physical phenomenon on the left with its corresponding fundamental mechanism and energy interaction on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Electromagnetic induction matches the generation of an electromotive force via varying magnetic flux; magnetic torque in a motor matches the Lorentz force acting on current-carrying conductors; Joule heating matches the conversion of electrical energy into thermal dissipation through lattice collisions; and capacitor storage matches the retention of potential energy in an electric field across an insulating dielectric.

Each electromagnetic concept correctly corresponds to its underlying physical law: electromagnetic induction generates voltage from changing magnetic flux, motor action generates mechanical torque from magnetic forces on current, resistive heating results from microscopic electron collisions yielding thermal dissipation, and capacitors store potential energy in the electric field between separated charges.

Step-by-Step Solution

Analyze the operational principle of generators versus motors.

Generators convert mechanical work to electricity via changing magnetic flux (induction), whereas motors convert electrical current in a magnetic field to mechanical torque (Lorentz force).

Differentiating between motor action (electrical-to-mechanical) and generator action (mechanical-to-electrical) prevents confusing input and output energy forms.

Analyze energy dissipation in resistive components.

Resistive conduction dissipates energy thermally as moving charge carriers collide with conductor ions.

Ohmic resistance transforms electric potential energy irreversibly into internal thermal energy.

Analyze static field storage in reactive capacitive components.

Capacitors hold charge statically across a dielectric boundary, storing energy within an electric field rather than dissipating it or relying on continuous charge flow.

Capacitive storage is electrostatic and reversible, contrasting with resistive thermal dissipation and magnetic induction.

Key Concept

Fundamental principles of electromagnetism, circuit components, and electromechanical energy conversions

Estimated Time:1m 30s

Question 3170Question →

Oceanic coastlines and marine waters experience diverse dynamic water movements driven by gravitational interactions, atmospheric winds, and nearshore topography. Which of the following correctly matches each marine phenomenon with its defining physical mechanism?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Spring Tide matches maximum tidal range from linear Sun-Moon alignment; Neap Tide matches minimal tidal range from perpendicular Sun-Moon alignment; Coastal Upwelling matches wind-driven offshore surface displacement drawing cold, nutrient-rich deep water upward; Rip Current matches narrow, rapid seaward flow through the surf zone.

Spring tides correspond to maximum tidal amplitudes created by linear gravitational alignment of the Sun, Moon, and Earth. Neap tides correspond to moderate, minimal tidal ranges when the gravitational pulls of the Moon and Sun form a right angle. Coastal upwelling is the vertical ascent of cold, nutrient-dense water triggered by wind-driven surface divergence. Rip currents are narrow, fast-moving jets of water channeling back out to sea through the surf zone.

Step-by-Step Solution

Analyze tidal mechanisms driven by lunar and solar celestial alignment.

Linear alignment (syzygy) creates constructive gravitational reinforcement leading to maximum tidal ranges (Spring Tide), while orthogonal alignment (quadrature) creates destructive interference leading to minimal tidal ranges (Neap Tide).

Tidal amplitudes are governed directly by the relative positions of the Moon and Sun relative to Earth.

Distinguish between vertical offshore water displacement and localized nearshore surface currents.

Offshore wind-driven displacement causes deep, nutrient-laden cold water to rise (Coastal Upwelling), whereas focused backflow of trapped surf water creates a strong seaward current (Rip Current).

Upwelling involves vertical circulation across depth layers, while rip currents are horizontal coastal circulation features.

Correlate each named phenomenon with its exact mechanism description.

All four pairs are uniquely matched based on their specific physical drivers and hydrodynamic behaviors.

Ensures complete scientific accuracy without confusing cyclical tidal forces with coastal current patterns.

Key Concept

Oceanic Circulation and Tidal Dynamics

Estimated Time:1m 15s

Question 3171Question →

In an open ocean food chain, microscopic phytoplankton are consumed by zooplankton, which are then eaten by juvenile herring. Which trophic role do the juvenile herring fulfill in this marine ecosystem?

Primary producer

Primary consumer

Secondary consumer

Tertiary consumer

Show answer & explanation

Answer: Secondary consumer

Answer

Secondary consumer

In this ecological chain, phytoplankton serve as autotrophic primary producers and zooplankton function as herbivorous primary consumers. Because juvenile herring prey directly upon the primary consumers, their ecological classification is secondary consumer.

Step-by-Step Solution

Identify the primary producer and primary consumer in the described chain.

Phytoplankton capture sunlight as primary producers, and zooplankton graze on them as primary consumers.

Classifying the initial trophic tiers establishes the baseline structure of the energy flow.

Determine the trophic level of the juvenile herring based on their diet.

Since juvenile herring consume the herbivorous zooplankton (primary consumers), they occupy the secondary consumer level.

Organisms that feed directly on primary consumers are categorized as secondary consumers.

Key Concept

Trophic levels and energy flow in marine ecosystems

Estimated Time:45s

Question 3172Question →

A sensor hovering above a lake simultaneously emits a sound wave and a beam of monochromatic light downward into the water. As both waves transition from the air into the water, which of the following accurately describes the changes in their respective wave properties?

The sound wave's speed and wavelength increase, while the light wave's speed and wavelength decrease; the frequency of both waves remains constant.

Both waves experience a decrease in speed and a corresponding decrease in wavelength, while the frequency of both waves remains constant.

The sound wave's speed decreases and its frequency increases, while the light wave's speed increases and its frequency decreases.

The sound wave's speed and frequency increase, while the light wave's speed and frequency decrease; the wavelength of both waves remains constant.

Show answer & explanation

Answer: The sound wave's speed and wavelength increase, while the light wave's speed and wavelength decrease; the frequency of both waves remains constant.

Answer

The sound wave's speed and wavelength increase, while the light wave's speed and wavelength decrease; the frequency of both waves remains constant.

When any wave crosses a boundary between two media, its frequency remains constant because the number of cycles per second is locked to the original source. Sound is a mechanical wave and travels faster in water than in air because water is denser and more rigid. According to the wave equation (

v = f \lambda

), if speed (

v

) increases and frequency (

f

) is constant, wavelength (

\lambda

) must increase. Conversely, light is an electromagnetic wave that interacts with the atoms in the water, causing its propagation speed to decrease compared to its speed in air. Therefore, with a lower speed and constant frequency, the light wave's wavelength must decrease.

Step-by-Step Solution

Analyze the change in frequency for both waves.

The frequency of both the sound wave and the light wave remains constant.

Frequency is determined exclusively by the wave source and does not change when transitioning between different media.

Determine how the speed of each wave changes when moving from air to water.

The sound wave speeds up, while the light wave slows down.

Sound is a mechanical wave that requires a medium and travels faster in denser, less compressible materials (water > air). Light is an electromagnetic wave that is impeded by matter, so its speed decreases in media with higher optical density (water < air).

Apply the wave equation (

v = f \lambda

) to determine wavelength changes.

The sound wave's wavelength increases, and the light wave's wavelength decreases.

Because frequency (

f

) is constant, wavelength (

\lambda

) must change directly proportionally to wave speed (

v

). Higher speed means longer wavelength; lower speed means shorter wavelength.

Key Concept

Wave Propagation Across Boundaries

Question 3173Question →

When solid baking soda (sodium bicarbonate, $NaHCO_3$ ) is added to vinegar (acetic acid, $CH_3COOH$ ), vigorous bubbling occurs as carbon dioxide gas ( $CO_2$ ), water ( $H_2O$ ), and sodium acetate ( $CH_3COONa$ ) are produced. Why is this process classified as a chemical change rather than a physical change?

The solid dissolves and undergoes a reversible state change from solid to gas.

New chemical substances with distinct molecular structures and properties are formed.

Thermal conduction causes the liquid vinegar to boil rapidly into carbon dioxide vapor.

The total mass of the resulting products increases because new atoms are created.

Show answer & explanation

Answer: New chemical substances with distinct molecular structures and properties are formed.

Answer

New chemical substances with distinct molecular structures and properties are formed.

A chemical change is characterized by the rearrangement of atoms and the formation of one or more entirely new substances with distinct physical and chemical properties, as seen with the production of carbon dioxide, water, and sodium acetate.

Step-by-Step Solution

Analyze the starting reactants and resulting products in the scenario.

Reactants (

NaHCO_3

and

CH_3COOH

) produce entirely new compounds (

CO_2

H_2O

, and

CH_3COONa

Identifying the formation of new chemical identities is fundamental to determining the type of change.

Distinguish between physical and chemical processes.

Physical changes alter only the form or state of matter without changing chemical formulas, whereas chemical changes involve the rearrangement of atoms into new chemical compounds.

The defining characteristic of a chemical change is the synthesis or decomposition of chemical bonds resulting in new substances.

Key Concept

Chemical change involves breaking and forming chemical bonds to produce new substances with different properties.

Estimated Time:1m 0s

Question 3174Question →

An aerospace technician measures a solid titanium equipment casing on Earth and records its mass as $18\text{ kg}$ . If this casing is transported to the surface of the Moon, where gravitational acceleration is roughly one-sixth of Earth's gravity, which statement accurately describes the mass and weight of the casing on the Moon?

Both the mass and the weight decrease to one-sixth of their original values on Earth.

The weight remains constant, while the mass decreases to one-sixth of its original value on Earth.

The mass remains

18\text{ kg}

, while the weight decreases to one-sixth of its value on Earth.

The mass increases due to the lunar vacuum, while the weight decreases to zero.

Show answer & explanation

Answer: The mass remains $18\text{ kg}$ , while the weight decreases to one-sixth of its value on Earth.

Answer

The mass remains

18\text{ kg}

, while the weight decreases to one-sixth of its value on Earth.

Mass is an intrinsic property of matter that quantifies the amount of substance in an object, meaning it remains constant regardless of location or environment. In contrast, weight is the gravitational force acting on that mass (

W = mg

). Because the Moon's gravitational acceleration is one-sixth that of Earth, the casing's weight decreases to one-sixth of its Earth value while its mass remains unchanged at

18\text{ kg}

Step-by-Step Solution

Define mass and determine its value on the Moon.

The mass remains exactly

18\text{ kg}

Mass is an intrinsic property of matter representing the total amount of material in an object, which does not depend on gravitational pull.

Define weight and calculate its change under lunar gravity.

The weight decreases to one-sixth of its Earth measurement.

Weight is the force exerted on an object's mass by gravity (

W = mg

). Because lunar gravity is one-sixth of Earth's gravity, the downward gravitational force is reduced by a factor of six.

Synthesize the properties to identify the correct physical outcome.

Mass is invariant (

18\text{ kg}

), whereas weight is proportionally reduced by the weaker gravitational field.

Comparing the unchanging scalar property of mass with the field-dependent force of weight resolves the scenario.

Key Concept

Distinction between mass (intrinsic amount of matter) and weight (gravitational force on mass)

Estimated Time:45s

Question 3175Question →

Which property of a sound wave directly determines how loud it sounds to a listener?

Frequency

Amplitude

Wavelength

Wave speed

Show answer & explanation

Answer: Amplitude

Answer

Amplitude

The loudness or volume of a sound is directly governed by its amplitude. A sound wave with a larger amplitude carries more mechanical energy and produces greater pressure fluctuations, which human ears perceive as a louder sound.

Step-by-Step Solution

Identify what physical characteristic of a sound wave corresponds to sound volume or intensity.

Loudness is determined by the energy carried by the wave, which is directly proportional to the square of its amplitude.

Greater amplitude means particles in the medium vibrate with greater displacement, creating larger pressure variations detected as louder sound.

Distinguish amplitude from frequency and wavelength.

Frequency and wavelength determine the pitch of the sound, whereas amplitude dictates loudness.

Separating wave energy characteristics (amplitude) from wave oscillation rates (frequency) identifies amplitude as the correct property.

Key Concept

Relationship between sound wave amplitude and perceived loudness

Estimated Time:30s

Question 3176Question →

A neutral atom of silicon contains $14$ protons and $16$ neutrons in its nucleus. What is the mass number of this silicon atom?

2

14

30

16

Show answer & explanation

Answer: $30$

Answer

The mass number of the silicon atom is

30

The mass number (

A

) of an atom equals the total number of protons and neutrons located in its nucleus. For this silicon atom, adding

14

protons and

16

neutrons gives a mass number of

30

Step-by-Step Solution

Identify the given subatomic particles in the nucleus

Protons =

14

, Neutrons =

16

The mass number depends entirely on the nucleons (protons and neutrons) residing in the nucleus.

Apply the mass number formula:

\text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons}

\text{Mass Number} = 14 + 16 = 30

Adding protons and neutrons gives the total nucleon count, which defines the mass number.

Key Concept

Calculation of atomic mass number from protons and neutrons

Estimated Time:45s

Question 3177Question →

A direct-current circuit is powered by a $12\text{ V}$ battery connected in series with a $3\,\Omega$ resistor, followed by two $6\,\Omega$ resistors connected in parallel with each other. If one of the $6\,\Omega$ parallel resistors burns out and creates an open circuit, what is the total electrical power consumed by the remaining active circuit?

24\text{ W}

8\text{ W}

16\text{ W}

48\text{ W}

Show answer & explanation

Answer: $16\text{ W}$

Answer

16\text{ W}

When one of the parallel

6\,\Omega

resistors opens, the parallel network is reduced to the single remaining

6\,\Omega

resistor. This resistor is in series with the

3\,\Omega

resistor, giving a total equivalent resistance of

R = 3\,\Omega + 6\,\Omega = 9\,\Omega

. Applying the power formula

P = \frac{V^2}{R}

with a

12\text{ V}

battery gives

P = \frac{144}{9} = 16\text{ W}

Step-by-Step Solution

Determine the new circuit configuration after component failure

A single

3\,\Omega

resistor in series with the remaining

6\,\Omega

resistor

When one parallel branch burns out into an open circuit, no current flows through that branch, leaving the remaining parallel resistor in direct series with the first resistor.

Calculate the total equivalent resistance (

R_{\text{total}}

)

R_{\text{total}} = 3\,\Omega + 6\,\Omega = 9\,\Omega

Resistances in series add directly together.

Calculate total electrical power using the formula

P = \frac{V^2}{R}

P = \frac{(12\text{ V})^2}{9\,\Omega} = \frac{144}{9} = 16\text{ W}

Electrical power is directly proportional to the square of the source voltage and inversely proportional to the total equivalent resistance.

Key Concept

Series-Parallel Circuit Analysis and Electrical Power Calculation

Estimated Time:1m 30s

Question 3178Question →

Arrange the following media in order of the speed at which sound waves travel through them, from slowest to fastest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Air at sea level, followed by Liquid water, and finally Solid steel bar.

Sound is a mechanical longitudinal wave that relies on molecular collisions to transfer kinetic energy. In gases such as air, molecules are far apart, resulting in the slowest speed. In liquids such as water, molecules are closer together, increasing speed. In rigid solids such as steel, strong atomic bonds and high elasticity allow vibrations to transmit most rapidly.

Step-by-Step Solution

Identify the physical state of matter for each listed medium.

Air is a gas, water is a liquid, and steel is a solid.

Sound is a mechanical wave that requires a physical medium to propagate via particle collisions.

Apply the general rule for sound propagation speed across states of matter.

Sound travels slowest in gases, faster in liquids, and fastest in solids.

Closer particle spacing and higher elastic properties in condensed matter allow vibrational energy to transfer more rapidly.

Sequence the media from slowest transmission speed to fastest transmission speed.

Air at sea level (

343\text{ m/s}

) < Liquid water (

1{}480\text{ m/s}

) < Solid steel bar (

5{}000\text{ m/s}

Matches the requested ordering criterion from lowest to highest wave speed.

Key Concept

Sound Wave Propagation Speed in Different States of Matter

Estimated Time:45s

Question 3179Question →

A landscaper lays down $\frac{1}{2}$ of a ton of gravel in the front yard and $\frac{3}{8}$ of a ton of gravel in the backyard. What is the total amount of gravel used?

\frac{7}{8}

ton

\frac{2}{5}

ton

\frac{1}{8}

ton

\frac{1}{2}

ton

Show answer & explanation

Answer: $\frac{7}{8}$ ton

Answer

\frac{7}{8}

ton

The correct answer is found by identifying that finding the total amount requires addition. Converting the

\frac{1}{2}

ton to an equivalent fraction of

\frac{4}{8}

allows it to be added directly to the

\frac{3}{8}

of a ton, resulting in a total of

\frac{7}{8}

ton.

Step-by-Step Solution

Identify the operation needed.

The problem asks for the 'total amount', which means adding

\frac{1}{2}

and

\frac{3}{8}

To find the combined weight of gravel used in both yards, the two quantities must be added together.

Find a common denominator for the fractions.

The least common multiple of 2 and 8 is 8.

Fractions must have the same denominator before they can be added.

Convert

\frac{1}{2}

to an equivalent fraction with a denominator of 8.

Multiply both the numerator and denominator by 4:

\frac{1 \times 4}{2 \times 4} = \frac{4}{8}

This creates an equivalent fraction that can be directly added to

\frac{3}{8}

Add the numerators and keep the common denominator.

\frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8}

Once denominators are the same, only the parts (numerators) are added.

Key Concept

Adding fractions with unlike denominators requires converting them to equivalent fractions with a common denominator first.

Question 3180Question →

Tectonic plate motion is driven by a combination of gravitational forces and heat transfer within Earth's mantle. Match each plate-driving mechanism on the left with its correct physical description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Slab pull pairs with the gravitational sinking of cold, dense subducting lithosphere into the asthenosphere; Ridge push pairs with the gravitational sliding of elevated, buoyant lithosphere away from mid-ocean spreading centers; Basal drag pairs with the frictional traction transferred to the underside of tectonic plates by circulating mantle convection currents.

The correct matches accurately align the physical mechanisms driving plate tectonics with their proper definitions: slab pull is the gravitational descent of dense oceanic slabs at subduction zones, ridge push is the gravitational sliding away from elevated mid-ocean ridges, and basal drag is the frictional traction applied to the base of plates by asthenospheric convection.

Step-by-Step Solution

Analyze the mechanics of slab pull

Identify that cold oceanic crust becomes denser than underlying mantle rock as it ages, causing it to sink gravitationally at subduction trenches and pull the rest of the plate behind it.

Slab pull is primarily a negative buoyancy/density-driven gravitational phenomenon occurring at convergent boundaries.

Analyze the mechanics of ridge push

Identify that newly formed lithosphere at divergent ridges is thermally elevated and buoyant, creating a gravitational slope that pushes the plate outward as it cools and thickens.

Ridge push is a topography-driven gravitational force operating at divergent boundaries.

Analyze the mechanics of basal drag

Identify that convective flow within the asthenosphere exerts shear traction directly on the base of the overlying lithosphere.

Basal drag represents the direct frictional coupling between mantle convection and lithospheric motion.

Key Concept

Mechanisms of Plate Tectonic Motion (Slab Pull, Ridge Push, and Basal Drag)

Estimated Time:1m 0s

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