Physical Science Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 3

Question 41Question →

A bowling ball rolls down a lane toward the pins. Which form of energy does the rolling ball primarily possess as a result of its motion?

Potential energy

Thermal energy

Kinetic energy

Chemical energy

Show answer & explanation

Answer: Kinetic energy

Answer

Kinetic energy

Kinetic energy is defined as the energy an object possesses by virtue of being in motion. Because the bowling ball is rolling down the lane, its mechanical energy is predominantly kinetic energy.

Step-by-Step Solution

1

Identify the physical state of the object described in the question.

The bowling ball is actively rolling along the lane, which means it is in motion.

Determining whether an object is stationary (storing energy) or moving is the key to identifying the form of mechanical energy.

2

Apply the definition of mechanical energy categories to the moving object.

Energy associated directly with the motion of an object is defined as kinetic energy (

KE = \frac{1}{2}mv^2

).

Potential energy accounts for stored energy of position, whereas kinetic energy specifically measures energy of motion.

Key Concept

Kinetic Energy and Motion

Estimated Time:30s

Question 42Question →

Match each physical scenario on the left with its correct energy transformation or work-power principle on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The electric crane matches delivering 9,800 W steady power with constant kinetic energy; the descending elevator matches tension doing negative work to remove potential energy; the pneumatic piston matches stored potential energy doing positive work to become kinetic energy; and the skidding vehicle matches friction doing negative work to convert kinetic energy into thermal energy.

Each match correctly links mechanical principles: the crane requires steady power calculated via

P = Fv = (mg)v = 9{}800\text{ W}

; lowering a load under tension performs negative work because force opposes displacement; expanding gas does positive work converting potential energy to kinetic energy; and sliding friction performs negative work converting kinetic energy into thermal energy.

Step-by-Step Solution

1

Analyze the electric crane lifting at constant speed to determine force and power.

Force

F = mg = 500\text{ kg} \times 9.8\text{ m/s}^2 = 4{}900\text{ N}

, Power

P = Fv = 4{}900\text{ N} \times 2\text{ m/s} = 9{}800\text{ W}

. Because velocity is constant,

\Delta KE = 0

.

When velocity is constant, acceleration is zero, so applied upward force equals gravitational force, and instantaneous power equals force multiplied by velocity.

2

Evaluate the work done by tension on the descending elevator.

Upward cable tension is opposite to downward displacement (

180^\circ

), so work is negative (

W < 0

). Potential energy decreases while kinetic energy is unchanged.

Forces directed opposite to displacement extract mechanical energy by doing negative work.

3

Analyze the expanding pneumatic piston accelerating the projectile.

Internal potential energy exerts a force along the direction of motion, doing net positive work (

W > 0

) that becomes kinetic energy.

According to the work-energy theorem, positive net work performed on a mass increases its kinetic energy.

4

Determine the energy transition for the braking vehicle.

Friction acts opposite to displacement, doing negative work to dissipate initial kinetic energy into heat.

Non-conservative frictional forces convert macroscopic kinetic energy into microscopic thermal energy.

Key Concept

Work-energy theorem, rate of energy transfer (power as P = Fv), sign conventions of mechanical work, and conservative versus dissipative energy transformations.

Estimated Time:1m 30s

Question 43Question →

A $3\text{ kg}$ object moving at $20\text{ m/s}$ along a frictionless horizontal surface collides with and sticks to a stationary $7\text{ kg}$ object. Immediately after the collision, the combined mass slides onto a rough surface with a coefficient of kinetic friction of $0.3$ . Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , how many meters will the combined mass slide before coming to a complete stop?

Show answer & explanation

Answer: 6

Answer

6

The problem is solved in two phases. Phase 1 is the perfectly inelastic collision, where momentum is conserved:

p_i = p_f \Rightarrow (3)(20) = (10)v

, which gives a shared velocity of

6\text{ m/s}

. Phase 2 is the sliding on a rough surface, where the only horizontal force is kinetic friction. The acceleration is

a = -\mu_k g = -(0.3)(10) = -3\text{ m/s}^2

. Finally, using the kinematic equation

v_f^2 = v_i^2 + 2ad

(where

v_f = 0

), we get

0 = 36 + 2(-3)d

, yielding

d = 6\text{ meters}

.

Step-by-Step Solution

1

Apply the law of conservation of momentum to find the velocity of the combined mass immediately after the collision.

v = 6\text{ m/s}

In a perfectly inelastic collision, momentum is conserved (

m_1v_1 + m_2v_2 = (m_1+m_2)v

). Therefore,

3(20) + 7(0) = 10v

.

2

Calculate the deceleration of the combined mass due to kinetic friction.

a = -3\text{ m/s}^2

The net force is kinetic friction (

F_k = \mu_k m g

). Using Newton's second law, acceleration

a = -F_k / m = -\mu_k g = -0.3(10)

.

3

Use kinematics to find the distance required for the mass to come to a stop.

d = 6\text{ m}

Using the time-independent kinematic equation

v_f^2 = v_i^2 + 2ad

with

v_f = 0\text{ m/s}

,

v_i = 6\text{ m/s}

, and

a = -3\text{ m/s}^2

.

Key Concept

Conservation of Momentum and Kinematics

Question 44Question →

A student performs several classroom experiments to study how substances interact. Which of the following processes represents a chemical change?

Melting an ice cube into liquid water

Crushing a solid piece of chalk into fine powder

Baking bread dough into a loaf of bread

Dissolving granulated sugar in warm water

Show answer & explanation

Answer: Baking bread dough into a loaf of bread

Answer

Baking bread dough into a loaf of bread represents a chemical change.

Baking bread is a chemical change because thermal energy causes chemical reactions among ingredients (such as gas production and protein structural changes), resulting in new substances that cannot be converted back by simple physical means.

Step-by-Step Solution

1

Recall the distinction between chemical and physical changes.

A chemical change results in the formation of one or more new substances through the breaking and forming of chemical bonds, whereas a physical change alters only the form, state, or appearance of matter without changing its chemical identity.

This criterion allows accurate categorization of each observed process.

2

Evaluate each choice against the definition of a chemical change.

Melting ice, crushing chalk, and dissolving sugar all preserve the original chemical composition of the materials. In contrast, baking bread involves heat-driven chemical reactions that form completely new compounds.

Only baking creates new substances with distinct chemical properties.

Key Concept

Differentiating chemical changes (which form new chemical substances) from physical changes (which alter physical state or appearance without changing molecular composition).

Estimated Time:45s

Question 45Question →

A skier slides down a hill from the starting gate at the summit to the finish line at the flat base. Arrange the following positions along the slope in order of the skier's gravitational potential energy, from greatest to least.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from greatest to least gravitational potential energy is: at the starting gate at the summit, one-quarter of the way down the slope, three-quarters of the way down the slope, and at the finish line at the flat base.

Gravitational potential energy is calculated as

PE = mgh

, where

m

is mass,

g

is the acceleration due to gravity, and

h

is height. Because potential energy is directly proportional to height, the position with the greatest elevation (the summit) has the most potential energy, and potential energy decreases continuously as the skier moves toward the lowest elevation (the flat base).

Step-by-Step Solution

1

Identify the formula for gravitational potential energy

PE = mgh

Gravitational potential energy is directly proportional to height above the reference level when mass and gravity are constant.

2

Rank the vertical heights of the given positions along the hill

Summit > One-quarter down > Three-quarters down > Flat base

As the skier descends the slope, vertical elevation continuously decreases.

3

Order the positions according to potential energy magnitude

pos_summit, pos_quarter, pos_three_quarter, pos_base

Higher elevations correspond directly to greater amounts of gravitational potential energy.

Key Concept

Gravitational potential energy depends directly on an object's vertical height above a reference point.

Estimated Time:45s

Question 46Question →

Arrange the following mechanical systems in order of their average power output, from lowest power to highest power. Assume ideal conditions and use $g = 10\text{ m/s}^2$ .

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from lowest to highest power is: the linear accelerator sled (

400\text{ W}

), the hydraulic press (

600\text{ W}

), the forklift (

800\text{ W}

), and the motorized winch (

1,200\text{ W}

).

The linear sled produces

400\text{ W}

(from a

1,600\text{ J}

change in kinetic energy over

4\text{ s}

). The hydraulic press produces

600\text{ W}

(

18,000\text{ J} / 30\text{ s}

). The forklift produces

800\text{ W}

(

200\text{ N} \times 4\text{ m/s}

). The motorized winch produces

1,200\text{ W}

(from a

6,000\text{ J}

change in potential energy over

5\text{ s}

). This results in the correct ascending sequence.

Step-by-Step Solution

1

Calculate the average power of the linear accelerator sled.

Power =

400\text{ W}

Calculate the change in kinetic energy

\Delta KE = \frac{1}{2}m(v_f^2 - v_i^2)

and divide by time.

\Delta KE = 0.5 \times 100 \times (36 - 4) = 1600\text{ J}

.

1600\text{ J} / 4\text{ s} = 400\text{ W}

.

2

Calculate the average power of the hydraulic press.

Power =

600\text{ W}

Use the direct power formula

P = W / t

.

18,000\text{ J} / 30\text{ s} = 600\text{ W}

.

3

Calculate the average power of the forklift.

Power =

800\text{ W}

Since the speed is constant, the applied force equals the kinetic friction force. Use

P = F \times v

.

200\text{ N} \times 4\text{ m/s} = 800\text{ W}

.

4

Calculate the average power of the motorized winch.

Power =

1,200\text{ W}

Calculate the change in gravitational potential energy

\Delta PE = mgh

and divide by time.

60 \times 10 \times 10 = 6000\text{ J}

.

6000\text{ J} / 5\text{ s} = 1200\text{ W}

.

5

Arrange the resulting power values in ascending order.

Sled (

400\text{ W}

), Press (

600\text{ W}

), Forklift (

800\text{ W}

), Winch (

1,200\text{ W}

).

The prompt requires ordering from lowest to highest average power output.

Key Concept

Calculating average power output by integrating different energy formulas (kinetic energy, potential energy, direct work, and force-velocity).

Question 47Question →

In an industrial wastewater neutralization facility, aqueous calcium hydroxide [ $Ca(OH)_2$ ] reacts with aqueous phosphoric acid [ $H_3PO_4$ ] to yield an insoluble calcium phosphate [ $Ca_3(PO_4)_2$ ] precipitate and liquid water [ $H_2O$ ]. When the chemical equation for this reaction is completely balanced using the lowest whole-number coefficients, what is the sum of all stoichiometric coefficients, and which fundamental type of chemical reaction is demonstrated?

Total sum of

11

; synthesis reaction

Total sum of

6

; single replacement reaction

Total sum of

12

; double replacement reaction

Total sum of

12

; physical dissolution change

Show answer & explanation

Answer: Total sum of $12$ ; double replacement reaction

Answer

Total sum of

12

; double replacement reaction

The balanced chemical reaction is

3Ca(OH)_2 + 2H_3PO_4 \rightarrow Ca_3(PO_4)_2 + 6H_2O

. Summing all stoichiometric coefficients yields

3 + 2 + 1 + 6 = 12

. Because the cations and anions of two reacting compounds trade partners to produce two new substances (an insoluble precipitate and water), the process is classified as a double replacement reaction.

Step-by-Step Solution

1

Write the unbalanced skeleton equation for the described chemical reaction.

Ca(OH)_2 + H_3PO_4 \rightarrow Ca_3(PO_4)_2 + H_2O

Establishing the correct chemical formulas of reactants and products is the necessary starting point for stoichiometry.

2

Balance the metal cations, polyatomic phosphate ions, and remaining hydrogen and oxygen atoms.

3Ca(OH)_2 + 2H_3PO_4 \rightarrow 1Ca_3(PO_4)_2 + 6H_2O

Balancing calcium requires

3Ca(OH)_2

, balancing phosphate requires

2H_3PO_4

, which yields

6

hydrogen atoms from hydroxide and

6

from acid, forming

6H_2O

and satisfying the Law of Conservation of Mass.

3

Calculate the sum of all stoichiometric coefficients in the balanced equation.

3 + 2 + 1 + 6 = 12

Every term in the balanced equation has a coefficient, where an unwritten coefficient represents exactly

1

.

4

Classify the reaction mechanism based on atomic and ionic reorganization.

Double replacement (acid-base neutralization and precipitation)

The calcium cations and hydrogen ions exchange their respective polyatomic anion partners (

OH^-

and

PO_4^{3-}

), which defines a double replacement reaction.

Key Concept

Balancing chemical equations and classifying chemical reaction types

Estimated Time:1m 30s

Question 48Question →

A mechanical test cart accelerates horizontally from rest to a speed of $v$ , requiring $400\text{ J}$ of net work. How much additional net work must be performed on the cart to further increase its speed from $v$ to $3v$ ?

1,200\text{ J}

3,600\text{ J}

3,200\text{ J}

800\text{ J}

Show answer & explanation

Answer: $3,200\text{ J}$

Answer

An additional

3,200\text{ J}

of net work is required.

According to the Work-Energy Theorem, the net work performed on an object equals its change in kinetic energy (

W_{\text{net}} = \Delta \text{KE}

). Accelerating from rest to speed

v

requires

400\text{ J}

, meaning

\frac{1}{2}mv^2 = 400\text{ J}

. At triple the speed (

3v

), the total kinetic energy becomes

\frac{1}{2}m(3v)^2 = 9\left(\frac{1}{2}mv^2\right) = 9 \times 400\text{ J} = 3,600\text{ J}

. The additional work needed to increase speed from

v

to

3v

is the difference between these two energy states:

3,600\text{ J} - 400\text{ J} = 3,200\text{ J}

.

Step-by-Step Solution

1

Express the initial kinetic energy and relate it to initial work done.

\text{KE}_1 = \frac{1}{2}mv^2 = 400\text{ J}

By the Work-Energy Theorem, the net work done on an object starting from rest equals its final kinetic energy.

2

Calculate the total kinetic energy of the cart when its speed reaches

3v

.

\text{KE}_2 = \frac{1}{2}m(3v)^2 = 9\left(\frac{1}{2}mv^2\right) = 9 \times 400\text{ J} = 3,600\text{ J}

Kinetic energy depends on the square of velocity, so tripling the velocity increases kinetic energy by a factor of

3^2 = 9

.

3

Determine the additional net work needed to transition from speed

v

to

3v

.

W_{\text{additional}} = \text{KE}_2 - \text{KE}_1 = 3,600\text{ J} - 400\text{ J} = 3,200\text{ J}

The additional work required equals the change in kinetic energy between the two states.

Key Concept

Work-Energy Theorem and Velocity-Squared Relationship of Kinetic Energy

Estimated Time:1m 15s

Question 49Question →

In chemistry, chemical reactions are categorized by the pattern in which reactants rearrange to form new substances. Match each chemical reaction equation with its correct classification type.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The reaction

2H_2 + O_2 \rightarrow 2H_2O

matches Synthesis reaction;

2H_2O_2 \rightarrow 2H_2O + O_2

matches Decomposition reaction;

C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O

matches Combustion reaction; and

HCl + NaOH \rightarrow NaCl + H_2O

matches Neutralization reaction.

Each chemical reaction matches its respective classification based on the fundamental pattern of atomic rearrangement: synthesis combines multiple reactants into one product; decomposition splits a single reactant into multiple products; combustion oxidizes a fuel with oxygen to form carbon dioxide and water; and neutralization combines an acid with a base to produce salt and water.

Step-by-Step Solution

1

Analyze the number and structure of reactants and products in

2H_2 + O_2 \rightarrow 2H_2O

.

Two distinct reactant molecules join together to form a single product species (

H_2O

).

When multiple simple reactants unite into a single compound (

A + B \rightarrow AB

), the process is classified as synthesis.

2

Examine the reactant and products in

2H_2O_2 \rightarrow 2H_2O + O_2

.

A single reactant species (

H_2O_2

) splits into two distinct product species (

H_2O

and

O_2

).

When one complex substance breaks apart into simpler components (

AB \rightarrow A + B

), the process is classified as decomposition.

3

Examine the chemical species participating in

C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O

.

A hydrocarbon fuel (

C_3H_8

) reacts rapidly with oxygen gas (

O_2

) to yield

CO_2

and

H_2O

.

Oxidation of a hydrocarbon fuel producing carbon dioxide and water vapor is the hallmark of a combustion reaction.

4

Identify the nature of the reactants in

HCl + NaOH \rightarrow NaCl + H_2O

.

An acid (

HCl

) reacts with a strong base (

NaOH

) to produce an ionic salt (

NaCl

) and liquid water (

H_2O

).

An acid-base double replacement yielding salt and water is specifically classified as a neutralization reaction.

Key Concept

Classification of Chemical Reactions

Estimated Time:45s

Question 50Question →

A heavy boulder rests motionless on the edge of a high cliff overlooking a valley. Which form of energy does the boulder primarily possess due to its elevated position?

Thermal energy

Gravitational potential energy

Kinetic energy

Chemical energy

Show answer & explanation

Answer: Gravitational potential energy

Answer

Gravitational potential energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. Because the boulder is elevated high above the ground and held stationary, all of its mechanical energy is stored as gravitational potential energy.

Step-by-Step Solution

1

Analyze the state of motion and spatial position of the object.

The boulder is motionless at an elevated height above the ground.

Identifying motion and position determines whether mechanical energy is active or stored.

2

Apply the definition of mechanical energy forms.

Energy stored by virtue of an object's height in a gravitational field is gravitational potential energy (

PE = mgh

).

Stationary objects at a height possess potential energy rather than kinetic energy.

Key Concept

Gravitational Potential Energy

Estimated Time:35s

Question 51Question →

When solid baking soda (sodium bicarbonate) is mixed with liquid vinegar (acetic acid), vigorous bubbling occurs as carbon dioxide gas is released. Which of the following statements correctly classifies and explains this transformation?

It is a physical change because the vinegar underwent rapid boiling caused by mixing.

It is a chemical change because bonds are broken and rearranged to form new substances with different properties.

It is a physical change because dissolving a solid into a liquid only separates molecules without creating new substances.

It is a physical change because the solid baking soda simply melted into a liquid state upon contact with the vinegar.

Show answer & explanation

Answer: It is a chemical change because bonds are broken and rearranged to form new substances with different properties.

Answer

It is a chemical change because bonds are broken and rearranged to form new substances with different properties.

The reaction between baking soda and vinegar is a chemical change because the original substances react to form entirely new compounds (carbon dioxide gas, water, and dissolved sodium acetate) with properties distinct from the starting materials.

Step-by-Step Solution

1

Analyze the observed interaction and identify products.

Mixing sodium bicarbonate (

\text{NaHCO}_3

) and acetic acid (

\text{HC}_2\text{H}_3\text{O}_2

) generates carbon dioxide gas (

\text{CO}_2

), water (

\text{H}_2\text{O}

), and sodium acetate (

\text{NaC}_2\text{H}_3\text{O}_2

).

The production of a new gas and temperature change serve as clear evidence of a chemical transformation.

2

Classify the type of change based on chemical identity.

The process is classified as a chemical change rather than a physical change.

In a chemical change, atoms are rearranged and chemical bonds are broken and formed, creating entirely new chemical substances with distinct chemical and physical properties.

Key Concept

Chemical vs. Physical Changes

Estimated Time:45s

Question 52Question →

Four different objects are moving horizontally across a testing facility floor. Arrange these objects in order of their kinetic energy, from least kinetic energy to greatest kinetic energy.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from least to greatest kinetic energy is: the

4\text{ kg}

bowling ball at

2\text{ m/s}

(

8\text{ J}

), the

1\text{ kg}

drone at

6\text{ m/s}

(

18\text{ J}

), the

2\text{ kg}

robotic vehicle at

5\text{ m/s}

(

25\text{ J}

), and the

8\text{ kg}

utility cart at

3\text{ m/s}

(

36\text{ J}

).

Kinetic energy is calculated using the formula

KE = \frac{1}{2}mv^2

. Computing each value yields

8\text{ J}

for the bowling ball,

18\text{ J}

for the drone,

25\text{ J}

for the robotic vehicle, and

36\text{ J}

for the utility cart. Arranging these values in ascending order produces the correct sequence.

Step-by-Step Solution

1

Recall the formula for kinetic energy

KE = \frac{1}{2}mv^2

, where

m

is mass in kilograms and

v

is velocity in meters per second.

Kinetic energy depends directly on mass and the square of velocity.

2

Calculate the kinetic energy of each moving object

Bowling ball:

\frac{1}{2}(4)(2^2) = 8\text{ J}

; Drone:

\frac{1}{2}(1)(6^2) = 18\text{ J}

; Robotic vehicle:

\frac{1}{2}(2)(5^2) = 25\text{ J}

; Utility cart:

\frac{1}{2}(8)(3^2) = 36\text{ J}

.

Determine the exact numerical energy value for each scenario.

3

Order the computed values from smallest to largest

8\text{ J} < 18\text{ J} < 25\text{ J} < 36\text{ J}

Satisfies the stem requirement to arrange from lowest to highest kinetic energy.

Key Concept

Kinetic Energy Calculation (

KE = \frac{1}{2}mv^2

)

Estimated Time:1m 0s

Question 53Question →

In physical science, work, energy, and power describe how forces interact with matter over distance and time. Match each physical quantity with its correct scientific definition.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Work corresponds to the energy transferred across a distance; Kinetic Energy corresponds to the energy of an object in motion; Power corresponds to the rate of doing work per unit time; Gravitational Potential Energy corresponds to the energy stored due to elevated position.

Each quantity maps directly to its fundamental physical definition: Work is force exerted over a distance, Kinetic Energy is the energy of motion, Power is work per unit time, and Gravitational Potential Energy is stored energy from elevated position.

Step-by-Step Solution

1

Identify the definition of Work

Work is the product of force and distance (

W = Fd

), representing energy transfer.

Work measures how much energy is mechanically transferred when a force moves an object.

2

Identify the definition of Kinetic Energy

Kinetic energy is the energy of a moving object (

KE = \frac{1}{2}mv^2

).

Motion is the defining physical attribute of kinetic energy.

3

Identify the definition of Power

Power is the rate at which work is done over time (

P = \frac{W}{t}

).

Power accounts for time, measuring how fast work is completed.

4

Identify the definition of Gravitational Potential Energy

Gravitational potential energy is stored energy based on height (

PE = mgh

).

Position in a gravitational field determines stored gravitational potential energy.

Key Concept

Fundamental definitions and relationships among work, kinetic energy, potential energy, and power in mechanics.

Estimated Time:45s

Question 54Question →

A motorized conveyor system applies a constant horizontal net force of $80\text{ N}$ to a container, causing it to accelerate along a smooth surface at $4\text{ m/s}^2$ . What is the mass of the container?

320\text{ kg}

20\text{ kg}

20\text{ N}

0.05\text{ kg}

Show answer & explanation

Answer: $20\text{ kg}$

Answer

The mass of the container is

20\text{ kg}

.

According to Newton's second law of motion (

F = ma

), mass is equal to net force divided by acceleration (

m = \frac{F}{a}

). Dividing

80\text{ N}

by

4\text{ m/s}^2

gives

20\text{ kg}

.

Step-by-Step Solution

1

Identify the given physical quantities and the relevant equation.

Net Force

F = 80\text{ N}

, Acceleration

a = 4\text{ m/s}^2

, and Newton's Second Law is

F = ma

.

Newton's second law relates net force, mass, and acceleration.

2

Rearrange the equation to solve for mass (

m

) and substitute the given values.

m = \frac{F}{a} = \frac{80\text{ N}}{4\text{ m/s}^2} = 20\text{ kg}

.

Dividing both sides of

F = ma

by

a

isolates the unknown mass

m

.

Key Concept

Newton's Second Law of Motion (

F = ma

)

Estimated Time:45s

Question 55Question →

In emergency life-support systems, oxygen is generated through the chemical breakdown of solid sodium chlorate ( $NaClO_3$ ) into solid sodium chloride ( $NaCl$ ) and oxygen gas ( $O_2$ ) according to the balanced chemical equation:

2NaClO_3(s) \rightarrow 2NaCl(s) + 3O_2(g)

Fill in the blanks to identify the reaction type and calculate the total moles of oxygen produced.

Fill in the blanks below

Because a single reactant compound breaks apart to form multiple simpler products, this transformation is classified as a reaction. Furthermore, based on the stoichiometric coefficients in the balanced equation, the complete reaction of

6

moles of

NaClO_3

produces moles of

O_2

gas.

Show answer & explanation

Answer

The chemical process is classified as a decomposition reaction, and 6 moles of sodium chlorate produce 9 moles of oxygen gas.

A chemical reaction in which a single compound decomposes into two or more simpler elements or compounds is a decomposition reaction. According to the balanced equation

2NaClO_3(s) \rightarrow 2NaCl(s) + 3O_2(g)

, every

2

moles of

NaClO_3

consumed produce

3

moles of

O_2

. Therefore, reacting

6

moles of

NaClO_3

yields

6 \times \frac{3}{2} = 9

moles of

O_2

.

Step-by-Step Solution

1

Analyze the reactant and product patterns to determine the reaction classification.

The reaction is classified as a decomposition reaction.

A single complex reactant (

NaClO_3

) breaks down into two distinct, simpler substances (

NaCl

and

O_2

).

2

Identify the stoichiometric molar ratio between

NaClO_3

and

O_2

from the balanced equation.

The molar ratio is

2\text{ moles } NaClO_3 : 3\text{ moles } O_2

.

The coefficients preceding

NaClO_3

and

O_2

in the balanced equation are

2

and

3

, respectively.

3

Calculate the moles of

O_2

produced from

6

moles of

NaClO_3

.

6\text{ mol } NaClO_3 \times \frac{3\text{ mol } O_2}{2\text{ mol } NaClO_3} = 9\text{ moles of } O_2

.

Multiplying the given quantity by the stoichiometric conversion factor yields the theoretical product amount.

Key Concept

Reaction classification criteria and stoichiometric molar ratio calculations from balanced chemical equations

Estimated Time:1m 30s

Question 56Question →

In everyday physical interactions, distinct forces and kinematic principles govern how objects start, change, or cease their motion. Which pairs correctly match each physical observation on the left with its primary governing principle on the right?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match the sliding toolbox with frictional force, the lurching passenger with inertia, the falling wrench with gravitational attraction, and the harder-to-stop loaded cart with momentum.

Each observation directly matches the defining characteristic of its governing principle: surface resistance causing slowing is friction, resistance to change in motion is inertia, downward acceleration is gravity, and mass-dependent difficulty in stopping a moving object is momentum.

Step-by-Step Solution

1

Analyze the cause of stopping motion for sliding surfaces.

Identify friction as the contact force resisting sliding between the toolbox and deck.

Friction opposes sliding motion parallel to contacting surfaces.

2

Examine the tendency of a passenger to keep moving forward during sudden braking.

Identify inertia as the property of matter resisting changes in velocity.

Newton's First Law explains that objects in motion stay in motion unless acted upon by a net external force.

3

Determine the downward pull on unsupported falling objects.

Identify gravity as the non-contact attractive force pulling mass downward.

Earth's gravity accelerates falling objects toward the ground at approximately

9.8\text{ m/s}^2

.

4

Evaluate why a heavier cart at equal speed is harder to bring to rest.

Identify momentum (

p = mv

) as the quantity dependent on mass and speed that dictates stopping effort.

Greater mass at the same speed yields larger momentum, requiring greater impulse to stop.

Key Concept

Fundamental mechanical principles including friction, inertia, gravity, and momentum governing the motion and interaction of objects.

Estimated Time:45s

Question 57Question →

A laboratory technician analyzes a uniform metal alloy sample with a mass of $160\text{ g}$ and a volume of $20\text{ cm}^3$ . The sample is cut into Piece A ( $40\text{ g}$ ) and Piece B ( $120\text{ g}$ ), after which Piece B is transported to a high-altitude research station where gravitational pull is weaker. Which statement correctly describes the physical properties and behavior of these samples?

Cutting the original metal alloy represents a chemical change that alters the melting point and density of Piece A.

Piece B experiences a decrease in mass due to the reduced gravitational pull at the high-altitude facility.

Both pieces have an identical density of

8\text{ g/cm}^3

, and Piece B maintains a constant mass of

120\text{ g}

despite weighing less at high altitude.

Piece B has a higher density than Piece A because density is an extensive property that increases proportionally with the mass of a sample.

Show answer & explanation

Answer: Both pieces have an identical density of $8\text{ g/cm}^3$ , and Piece B maintains a constant mass of $120\text{ g}$ despite weighing less at high altitude.

Answer

Both pieces have an identical density of

8\text{ g/cm}^3

, and the larger piece maintains a constant mass of

120\text{ g}

despite weighing less at high altitude.

Density is an intensive property calculated as

\frac{160\text{ g}}{20\text{ cm}^3} = 8\text{ g/cm}^3

, which remains identical for any piece cut from the homogeneous alloy. Furthermore, mass is an intrinsic measure of matter that remains

120\text{ g}

anywhere in the universe, whereas weight decreases at higher altitudes due to reduced gravitational force.

Step-by-Step Solution

1

Calculate the density of the original metal alloy

\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{160\text{ g}}{20\text{ cm}^3} = 8\text{ g/cm}^3

Density is defined as mass per unit volume.

2

Determine the density of the separated pieces

Both Piece A and Piece B retain a density of

8\text{ g/cm}^3

.

Density is an intensive physical property of uniform matter and does not change when a sample is divided.

3

Evaluate the effect of altitude and gravity on mass versus weight

Mass remains exactly

120\text{ g}

, while weight decreases.

Mass measures the amount of matter and is invariant with location, while weight (

W = mg

) depends directly on local gravitational acceleration.

4

Classify the separation process

Cutting is a physical change.

Dividing a material modifies physical dimensions but does not alter chemical bonds or intrinsic constants like melting point.

Key Concept

Density as an intensive physical property, physical vs. chemical changes, and mass vs. weight invariance under varying gravity.

Estimated Time:1m 0s

Question 58Question →

A maintenance technician drops a $4\text{-kilogram}$ mechanical component from an elevated platform located $5\text{ meters}$ above the workshop floor. Assuming air resistance is negligible and the acceleration due to gravity is $9.8\text{ m/s}^2$ , how much kinetic energy does the component possess immediately before striking the floor?

0\text{ J}

39.2\text{ J}

196\text{ J}

20\text{ J}

Show answer & explanation

Answer: $196\text{ J}$

Answer

The kinetic energy immediately before impact is

196\text{ J}

.

According to the principle of conservation of energy, the mechanical energy in an isolated system remains constant. As the component falls, its initial gravitational potential energy (

PE = mgh

) is entirely converted into kinetic energy (

KE

) right before impact:

KE = 4\text{ kg} \times 9.8\text{ m/s}^2 \times 5\text{ m} = 196\text{ J}

.

Step-by-Step Solution

1

Calculate the initial gravitational potential energy at the release height.

PE = mgh = 4\text{ kg} \times 9.8\text{ m/s}^2 \times 5\text{ m} = 196\text{ J}

At the moment of release from rest, all mechanical energy of the component is stored as gravitational potential energy.

2

Apply the law of conservation of mechanical energy.

KE_{\text{final}} = PE_{\text{initial}} = 196\text{ J}

In the absence of non-conservative forces like air resistance, total mechanical energy is conserved, meaning all potential energy converts into kinetic energy at ground level (

h = 0

).

Key Concept

Conservation of Mechanical Energy

Estimated Time:1m 0s

Question 59Question →

Chemical compounds are identified by specific chemical formulas and possess distinct everyday applications and properties. Match each chemical compound on the left with its corresponding description and practical use on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Calcium carbonate matches the primary mineral compound in limestone, marble, and antacids; Sodium hydroxide matches the strong alkaline base lye used in soap making and drain cleaning; Hydrochloric acid matches the corrosive acid found in gastric juices and muriatic acid; Methane matches the simple hydrocarbon gas that serves as the primary component of natural gas.

Each compound correctly corresponds to its standardized chemical formula, common name, and primary practical usage: Calcium carbonate (

\text{CaCO}_3

) is limestone/antacid; Sodium hydroxide (

\text{NaOH}

) is lye/drain cleaner; Hydrochloric acid (

\text{HCl}

) is stomach acid/muriatic acid; Methane (

\text{CH}_4

) is natural gas fuel.

Step-by-Step Solution

1

Analyze the formula and chemical nature of Calcium carbonate (

\text{CaCO}_3

).

Identify it as an insoluble ionic salt that constitutes limestone and marble, frequently used to neutralize stomach acids.

Connecting chemical formula to geological presence and antacid utility.

2

Analyze the formula and chemical nature of Sodium hydroxide (

\text{NaOH}

).

Identify it as a soluble, highly caustic alkali base commonly called lye.

Distinguishing hydroxide bases and their commercial cleaning roles.

3

Analyze the formula and chemical nature of Hydrochloric acid (

\text{HCl}

).

Identify it as a strong binary acid present in the stomach and sold as muriatic acid.

Matching common commercial acid names with biological roles.

4

Analyze the formula and chemical nature of Methane (

\text{CH}_4

).

Identify it as a simple flammable hydrocarbon that makes up the majority of natural gas.

Classifying organic fuel compounds by molecular formula.

Key Concept

Nomenclature, chemical formulas, and practical applications of common household and industrial compounds

Estimated Time:1m 0s

Question 60Question →

Complete the statement and equation for the reaction between solid magnesium metal and hydrochloric acid. What coefficient balances the acid reactant, and what classification describes this reaction?

Fill in the blanks below

When solid magnesium reacts with aqueous hydrochloric acid, it forms dissolved magnesium chloride and hydrogen gas according to the equation: $\text{Mg} + \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2$. Because an uncombined element takes the place of another element in a compound, this process is classified as a replacement reaction.

Show answer & explanation

Answer

The balanced coefficient for

\text{HCl}

is

2

, and the reaction type is single replacement.

According to the Law of Conservation of Mass, matter is neither created nor destroyed during a chemical reaction. On the product side,

\text{MgCl}_2

contains two chlorine atoms and

\text{H}_2

contains two hydrogen atoms. Therefore, a coefficient of

2

in front of

\text{HCl}

is necessary to supply two hydrogen and two chlorine atoms from the reactants. Furthermore, because elemental magnesium displaces hydrogen from hydrochloric acid to yield magnesium chloride and free hydrogen, the reaction is by definition a single replacement (displacement) reaction.

Step-by-Step Solution

1

Count the atoms of each element on the product side of the equation

The products

\text{MgCl}_2 + \text{H}_2

contain

1

magnesium atom,

2

chlorine atoms, and

2

hydrogen atoms.

The Law of Conservation of Mass requires the number of atoms of each element to be identical on both sides of a chemical equation.

2

Determine the coefficient needed for

\text{HCl}

on the reactant side

Placing a coefficient of

2

in front of

\text{HCl}

gives

2

hydrogen atoms and

2

chlorine atoms, balancing

1\text{Mg} + 2\text{HCl} \rightarrow 1\text{MgCl}_2 + 1\text{H}_2

.

Changing coefficients balances the total atom counts without altering chemical identities.

3

Classify the reaction mechanism based on reactant and product structures

The reaction is classified as a single replacement (or single displacement) reaction.

Free magnesium metal (

\text{Mg}

) displaces hydrogen (

\text{H}

) from hydrochloric acid (

\text{HCl}

) to form a new compound and release elemental hydrogen gas.

Key Concept

Balancing chemical equations by conserving atoms and identifying single replacement reaction patterns.

Estimated Time:45s

Physical Science

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept