Physical Science Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 2

Question 21Question →

A lunar exploration probe has a mass of $60\text{ kg}$ on Earth, where gravitational acceleration is $9.8\text{ m/s}^2$ . The probe is transported to the Moon, where gravitational acceleration is $1.6\text{ m/s}^2$ . A thruster applies a constant horizontal net force of $180\text{ N}$ to propel the probe along a frictionless test surface. What is the mass of the probe on the Moon, and what is the magnitude of its horizontal acceleration?

The mass is

10\text{ kg}

, and the acceleration is

18.0\text{ m/s}^2

.

The mass is

96\text{ kg}

, and the acceleration is

1.88\text{ m/s}^2

.

The mass is

60\text{ kg}

, and the acceleration is

3.0\text{ m/s}^2

.

The mass is

60\text{ kg}

, and the acceleration is

1.4\text{ m/s}^2

.

Show answer & explanation

Answer: The mass is $60\text{ kg}$ , and the acceleration is $3.0\text{ m/s}^2$ .

Answer

The probe's mass on the Moon is

60\text{ kg}

, and its horizontal acceleration is

3.0\text{ m/s}^2

.

Mass is a fundamental scalar quantity that measures an object's inertia (resistance to acceleration) and remains constant regardless of the gravitational environment. On the Moon, the probe retains its full mass of

60\text{ kg}

. By Newton's second law of motion, the horizontal acceleration is determined by dividing the net horizontal force by the mass:

a = \frac{F}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the mass of the probe on the Moon

The mass remains

60\text{ kg}

.

Mass measures the amount of matter in an object and its inertia; it does not change with the local gravitational field strength.

2

Apply Newton's second law of motion (

F_{\text{net}} = ma

) to find horizontal acceleration

a = \frac{F_{\text{net}}}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

The horizontal thrust provides the net horizontal force on a frictionless surface, accelerating the object's mass.

Key Concept

Mass is an invariant intrinsic property representing inertia, whereas acceleration depends solely on the net applied force divided by that mass according to Newton's Second Law (

F = ma

).

Estimated Time:1m 15s

Question 22Question →

A warehouse worker applies a constant horizontal force of $75\text{ N}$ to push a supply crate a distance of $8\text{ meters}$ across a smooth floor. What is the total amount of work done on the crate?

83\text{ J}

600\text{ J}

600\text{ W}

9.38\text{ J}

Show answer & explanation

Answer: $600\text{ J}$

Answer

600\text{ J}

Mechanical work is calculated using the equation

W = F \times d

, where

F

is the applied force in Newtons and

d

is the displacement in meters. Multiplying

75\text{ N}

by

8\text{ m}

gives

600\text{ Joules}

(

\text{J}

).

Step-by-Step Solution

1

Identify the given physical quantities and the formula for mechanical work.

Force

F = 75\text{ N}

, distance

d = 8\text{ m}

, and work formula

W = F \times d

.

Work is defined in physics as the product of the force applied to an object and the distance through which the force acts in the direction of motion.

2

Multiply the force by the distance to calculate the work done.

W = 75\text{ N} \times 8\text{ m} = 600\text{ J}

One Joule (

\text{J}

) is equal to one Newton-meter (

\text{N}\cdot\text{m}

).

Key Concept

Work is equal to force multiplied by displacement in the direction of the force (

W = Fd

), measured in Joules.

Estimated Time:45s

Question 23Question →

A test vehicle accelerating from rest to a speed of $10\text{ m/s}$ requires $50\text{ kJ}$ of net work. Assuming friction and air resistance are negligible, how much additional work must be done on the vehicle to increase its speed from $10\text{ m/s}$ to $20\text{ m/s}$ ?

50\text{ kJ}

100\text{ kJ}

150\text{ kJ}

200\text{ kJ}

Show answer & explanation

Answer: $150\text{ kJ}$

Answer

The additional work required is

150\text{ kJ}

.

According to the work-energy theorem, net work equals the change in kinetic energy (

W = \Delta KE

). Because kinetic energy is proportional to the square of velocity (

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

), accelerating from rest to

10\text{ m/s}

gives the vehicle

50\text{ kJ}

of kinetic energy. At

20\text{ m/s}

, the speed is doubled, which quadruples the total kinetic energy to

4 \times 50\text{ kJ} = 200\text{ kJ}

. The additional work required to increase the speed from

10\text{ m/s}

to

20\text{ m/s}

is therefore

200\text{ kJ} - 50\text{ kJ} = 150\text{ kJ}

.

Step-by-Step Solution

1

Use the work-energy theorem for the initial acceleration from rest to determine the mass-related factor of the vehicle.

W_1 = \Delta KE_1 = \frac{1}{2}m(v_1^2 - v_0^2) = \frac{1}{2}m(10^2 - 0) = 50m = 50{}000\text{ J} \implies m = 1{}000\text{ kg}

The net work done on an object equals its change in kinetic energy.

2

Calculate the total kinetic energy of the vehicle at the final speed of

20\text{ m/s}

.

KE_2 = \frac{1}{2}m v_2^2 = \frac{1}{2}(1{}000\text{ kg})(20\text{ m/s})^2 = \frac{1}{2}(1{}000)(400) = 200{}000\text{ J} = 200\text{ kJ}

Kinetic energy is directly proportional to the square of velocity.

3

Find the additional work by calculating the change in kinetic energy between

10\text{ m/s}

and

20\text{ m/s}

.

W_{\text{additional}} = KE_2 - KE_1 = 200\text{ kJ} - 50\text{ kJ} = 150\text{ kJ}

The additional work needed is the difference between final and intermediate energy states.

Key Concept

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

Estimated Time:1m 30s

Question 24Question →

Four electric winches perform mechanical work by lifting loads vertically at constant speed. Arrange the lifting tasks in order of the mechanical power delivered, from least power to greatest power.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from least power to greatest power is: Lifting

500\text{ N}

by

3\text{ m}

in

30\text{ s}

(

50\text{ W}

), Lifting

200\text{ N}

by

5\text{ m}

in

10\text{ s}

(

100\text{ W}

), Lifting

400\text{ N}

by

2\text{ m}

in

4\text{ s}

(

200\text{ W}

), and Lifting

150\text{ N}

by

4\text{ m}

in

2\text{ s}

(

300\text{ W}

).

Power is the rate at which work is performed:

P = \frac{F \times d}{t}

. Evaluating each winch: the

500\text{ N}

load lifted

3\text{ m}

in

30\text{ s}

produces

50\text{ W}

; the

200\text{ N}

load lifted

5\text{ m}

in

10\text{ s}

produces

100\text{ W}

; the

400\text{ N}

load lifted

2\text{ m}

in

4\text{ s}

produces

200\text{ W}

; and the

150\text{ N}

load lifted

4\text{ m}

in

2\text{ s}

produces

300\text{ W}

. Arranged from lowest to highest wattage, the sequence is

50\text{ W} \rightarrow 100\text{ W} \rightarrow 200\text{ W} \rightarrow 300\text{ W}

.

Step-by-Step Solution

1

Recall the formula for mechanical power in terms of force, distance, and time.

Power is defined as work divided by time:

P = \frac{W}{t} = \frac{F \times d}{t}

, measured in watts (

\text{W}

).

Power measures the rate at which work is accomplished rather than total energy expended.

2

Calculate the power output for each lifting task.

Task 1:

\frac{500\text{ N} \times 3\text{ m}}{30\text{ s}} = \frac{1500\text{ J}}{30\text{ s}} = 50\text{ W}

. Task 2:

\frac{200\text{ N} \times 5\text{ m}}{10\text{ s}} = \frac{1000\text{ J}}{10\text{ s}} = 100\text{ W}

. Task 3:

\frac{400\text{ N} \times 2\text{ m}}{4\text{ s}} = \frac{800\text{ J}}{4\text{ s}} = 200\text{ W}

. Task 4:

\frac{150\text{ N} \times 4\text{ m}}{2\text{ s}} = \frac{600\text{ J}}{2\text{ s}} = 300\text{ W}

.

Determines the exact numerical power rating for each winch.

3

Sort the values in ascending order from least to greatest.

50\text{ W} < 100\text{ W} < 200\text{ W} < 300\text{ W}

.

Satisfies the ordering criteria specified in the stem.

Key Concept

Mechanical power is the rate of doing work:

P = \frac{W}{t} = \frac{F \times d}{t}

.

Estimated Time:1m 30s

Question 25Question →

An electric winch with a power rating of $400\text{ W}$ is used to lift a $120\text{ kg}$ engine block vertically by a distance of $5\text{ meters}$ at a constant speed. Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , how much time does it take to complete the lift?

1.5\text{ seconds}

7.5\text{ seconds}

15\text{ seconds}

24\text{ seconds}

Show answer & explanation

Answer: $15\text{ seconds}$

Answer

15\text{ seconds}

The weight of the

120\text{ kg}

engine block is

F = mg = 120\text{ kg} \times 10\text{ m/s}^2 = 1{}200\text{ N}

. Lifting it

5\text{ meters}

requires

W = Fd = 1{}200\text{ N} \times 5\text{ m} = 6{}000\text{ J}

of work. Since power is the rate of work (

P = \frac{W}{t}

), the time required is

t = \frac{W}{P} = \frac{6{}000\text{ J}}{400\text{ W}} = 15\text{ seconds}

.

Step-by-Step Solution

1

Calculate the downward gravitational force (weight) of the engine block

F = m \times g = 120\text{ kg} \times 10\text{ m/s}^2 = 1{}200\text{ N}

Lifting the object at constant speed requires an upward force equal to its weight.

2

Calculate the total mechanical work performed to lift the engine

W = F \times d = 1{}200\text{ N} \times 5\text{ m} = 6{}000\text{ J}

Work is defined as force multiplied by displacement in the direction of the force.

3

Calculate the time required using the definition of power

t = \frac{W}{P} = \frac{6{}000\text{ J}}{400\text{ W}} = 15\text{ seconds}

Power is the rate of doing work (

P = \frac{W}{t}

), so time equals work divided by power.

Key Concept

Power as the rate of doing work (

P = \frac{W}{t}

) combined with gravitational potential work (

W = mgh

)

Estimated Time:1m 0s

Question 26Question →

Match each physical concept related to mechanics with its correct scientific definition.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Work matches the transfer of energy occurring when a force moves an object across a distance; Power matches the rate at which work is performed over time; Kinetic Energy matches the energy possessed by an object due to its motion; Gravitational Potential Energy matches the energy stored in an object due to its vertical position.

Each concept pairs directly with its foundational physics definition: Work is energy transferred by a force acting along a distance; Power is the time rate of doing work; Kinetic Energy is the energy of a body in motion; and Gravitational Potential Energy is energy stored by virtue of position in a gravitational field.

Step-by-Step Solution

1

Identify the definition of Work.

Work corresponds to a force exerted across a displacement (

W = Fd

).

Work represents mechanical energy transferred by applying force over distance.

2

Identify the definition of Power.

Power corresponds to the rate of doing work (

P = \frac{W}{t}

).

Power quantifies work completed per unit time.

3

Identify the definition of Kinetic Energy.

Kinetic energy corresponds to energy of motion (

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

).

Any mass in motion possesses kinetic energy.

4

Identify the definition of Gravitational Potential Energy.

Gravitational potential energy corresponds to energy stored by elevated position (

PE = mgh

).

An object's location in a gravitational field determines its stored gravitational potential energy.

Key Concept

Fundamental definitions and distinctions among work, power, kinetic energy, and potential energy

Estimated Time:45s

Question 27Question →

A technician observes several material transformations while working in a maintenance shop. Which of the following observations indicates that a chemical reaction has occurred to form a new compound?

Solid solder wire melting into a liquid puddle when touched with a hot iron

An iron bracket developing a reddish-brown layer of rust after exposure to humid air

Rubbing alcohol evaporating completely from a metal surface into vapor

A sheet of brass being hammered and shaped into a curved shield

Show answer & explanation

Answer: An iron bracket developing a reddish-brown layer of rust after exposure to humid air

Answer

An iron bracket developing a reddish-brown layer of rust after exposure to humid air

The formation of rust occurs when elemental iron reacts with oxygen in the presence of water to synthesize iron oxide (

Fe_2O_3

), a completely new chemical compound with distinct chemical and physical properties from the original metallic iron.

Step-by-Step Solution

1

Differentiate between physical transformations and chemical changes

Physical changes alter state, shape, or appearance without changing molecular structure, whereas chemical changes form entirely new substances with distinct chemical bonds and properties.

Understanding the fundamental definition of a chemical reaction is required to evaluate each scenario.

2

Analyze the formation of rust on iron

Iron (

Fe

) combines with oxygen (

O_2

) and moisture from the environment to synthesize iron(III) oxide (

Fe_2O_3

), which is a brand-new compound with different physical and chemical properties.

This transformation demonstrates a true chemical reaction (oxidation/synthesis).

3

Evaluate phase changes and mechanical shaping

Melting solder, evaporating alcohol, and shaping brass preserve the original chemical identities of the materials.

Eliminating physical state changes confirms the only chemical change.

Key Concept

Identification of Chemical Reactions and Compound Formation versus Physical Changes

Estimated Time:45s

Question 28Question →

In Newtonian mechanics and kinematics, distinct physical parameters govern the translational and curved motion of bodies. Match each mechanical quantity with its precise physical definition and governing mathematical relationship.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Impulse matches the force applied over a time interval causing a change in momentum (

J = F_{\text{avg}} \Delta t

); Centripetal Acceleration matches the inward rate of directional velocity change on a curve (

a_c = \frac{v^2}{r}

); Kinetic Friction Force matches the dissipative sliding resistance proportional to normal force (

f_k = \mu_k F_N

); and Instantaneous Velocity matches the time rate of change of position (

v = \frac{d\mathbf{r}}{dt}

).

Each mechanics quantity matches its exact standard definition and mathematical formula: Impulse represents force applied across time; Centripetal Acceleration measures inward radial turning acceleration; Kinetic Friction Force calculates contact resistance against sliding; and Instantaneous Velocity specifies the instantaneous vector rate of positional change.

Step-by-Step Solution

1

Identify the definition and formula for Impulse

Impulse equals

F_{\text{avg}} \Delta t = \Delta p

, representing force integrated over time.

According to the impulse-momentum theorem, impulse measures the total momentum transfer delivered by a force over an elapsed time.

2

Identify the definition and formula for Centripetal Acceleration

Centripetal acceleration equals

a_c = \frac{v^2}{r}

, oriented radially inward.

In circular and curvilinear dynamics, inward acceleration is required to change velocity direction without necessarily changing tangential speed.

3

Identify the definition and formula for Kinetic Friction Force

Kinetic friction force equals

f_k = \mu_k F_N

, opposing relative sliding.

Amontons' and Coulomb's laws of friction state that kinetic friction depends directly on the normal force pressing two surfaces together.

4

Identify the definition and formula for Instantaneous Velocity

Instantaneous velocity equals

v = \frac{d\mathbf{r}}{dt}

, establishing magnitude and directional vector heading.

Velocity is the first derivative of position with respect to time, distinguishing it from scalar speed by including direction.

Key Concept

Fundamental kinematic definitions and dynamic force-motion relationships in Newtonian mechanics.

Estimated Time:1m 30s

Question 29Question →

In the study of classical mechanics, fundamental terms describe the motion of objects and their response to forces. Match each mechanics term on the left with its correct scientific definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Velocity corresponds to the rate of change of position in a specified direction; Acceleration corresponds to the rate at which velocity changes over time; Inertia corresponds to an object's resistance to changes in its state of motion; and Momentum corresponds to the product of an object's mass and velocity.

The pairings correctly match each fundamental physical term to its scientific definition: Velocity is position change over time with direction; Acceleration is velocity change over time; Inertia is the intrinsic resistance of matter to motion changes; and Momentum is the product of mass and velocity.

Step-by-Step Solution

1

Define Velocity

Velocity is displacement divided by elapsed time (

v = \frac{\Delta x}{\Delta t}

), including direction.

It describes how rapidly an object changes its position in a particular direction.

2

Define Acceleration

Acceleration is the change in velocity divided by time (

a = \frac{\Delta v}{\Delta t}

).

It quantifies speeding up, slowing down, or changing direction.

3

Define Inertia

Inertia is proportional to mass and represents resistance to acceleration.

According to Newton's first law, a body maintains constant velocity unless acted upon by a net external force.

4

Define Momentum

Momentum (

p

) is calculated as mass times velocity (

p = mv

).

It represents the overall moving mass and determines the impact force needed to bring an object to rest.

Key Concept

Core kinematic and dynamic quantities in mechanics: velocity, acceleration, inertia, and momentum.

Estimated Time:45s

Question 30Question →

A diver stands completely stationary at the edge of a 10-meter platform above a swimming pool. Which statement best describes the diver's mechanical energy while resting at this highest point?

Kinetic energy is at its maximum value, and gravitational potential energy is zero.

Gravitational potential energy is at its maximum value, and kinetic energy is zero.

Both kinetic energy and gravitational potential energy are at their maximum values simultaneously.

Total mechanical energy is zero because the diver is not currently in motion.

Show answer & explanation

Answer: Gravitational potential energy is at its maximum value, and kinetic energy is zero.

Answer

Gravitational potential energy is at its maximum value, and kinetic energy is zero.

Gravitational potential energy (

PE = mgh

) is directly proportional to height. At the top of the 10-meter platform, elevation is at its peak, making potential energy maximum. Because the diver is stationary (

v = 0

), kinetic energy (

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

) is zero.

Step-by-Step Solution

1

Analyze the diver's state of motion to determine kinetic energy.

The diver is stationary (

v = 0\text{ m/s}

), so kinetic energy (

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

) is

0\text{ J}

.

Kinetic energy is the energy of motion and requires a non-zero velocity.

2

Analyze the diver's position to determine gravitational potential energy.

The diver is at the maximum height (

h = 10\text{ m}

), so gravitational potential energy (

PE = mgh

) is at its maximum.

Gravitational potential energy is directly proportional to elevation above the reference level.

3

Combine the energy states to describe total mechanical energy.

All mechanical energy exists as gravitational potential energy, with zero kinetic energy.

Total mechanical energy is the sum of kinetic and potential energies.

Key Concept

Gravitational potential energy depends on height, whereas kinetic energy depends on motion.

Estimated Time:45s

Question 31Question →

A $4\text{ kg}$ object is launched vertically upward from the ground. At a height of $20\text{ meters}$ , it is traveling at a speed of $5\text{ m/s}$ . Assuming acceleration due to gravity is $10\text{ m/s}^2$ and ignoring air resistance, what was the total mechanical energy of the object at the exact moment it was launched?

850\text{ J}

800\text{ J}

130\text{ J}

50\text{ J}

Show answer & explanation

Answer: $850\text{ J}$

Answer

The total mechanical energy at the exact moment it was launched is

850\text{ J}

.

According to the law of conservation of energy, the total mechanical energy remains constant throughout the object's flight in the absence of air resistance. Therefore, the total energy at launch equals the sum of its kinetic and potential energy at the

20\text{-meter}

mark. Calculating the potential energy (

mgh = 800\text{ J}

) and the kinetic energy (

\frac{1}{2}mv^2 = 50\text{ J}

) yields a total mechanical energy of

850\text{ J}

.

Step-by-Step Solution

1

Identify the relevant physical principle.

Total Mechanical Energy = Potential Energy + Kinetic Energy. This total is conserved.

By the law of conservation of energy, the total energy at launch is exactly equal to the total energy at the

20\text{ m}

height.

2

Calculate the gravitational potential energy (

PE

) at the

20\text{-meter}

height.

PE = m \times g \times h = 4 \times 10 \times 20 = 800\text{ J}

To determine the energy stored due to the object's height.

3

Calculate the kinetic energy (

KE

) at the

20\text{-meter}

height.

KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 4 \times 5^2 = 50\text{ J}

To determine the energy the object possesses due to its current upward motion.

4

Sum the

PE

and

KE

to find the total mechanical energy.

800\text{ J} + 50\text{ J} = 850\text{ J}

The total mechanical energy at this height equals the mechanical energy at the exact moment of launch.

Key Concept

Conservation of Mechanical Energy

Question 32Question →

In mechanical systems, energy exists in various forms and transitions through work and power. Match each physical scenario on the left with its corresponding energy classification or power characteristic on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The compressed spring matches with elastic potential energy stored through mechanical deformation; the cruising aircraft matches with simultaneous gravitational potential and kinetic energy; the friction brake pads match with the dissipation of kinetic energy into thermal energy; and the electric hoist lifting rate matches with a mechanical power delivery of 2 kilowatts.

Each scenario correctly illustrates a fundamental principle of work, energy, and power: deformation stores elastic potential energy; elevated motion embodies simultaneous kinetic and gravitational potential energy; frictional braking converts kinetic energy to heat; and a work rate of 2,000 joules per second represents 2,000 watts (2 kW) of power.

Step-by-Step Solution

1

Analyze the energy state of the compressed spring.

Identified as elastic potential energy stored by mechanical strain.

Potential energy is stored energy resulting from position or configuration, such as a compressed or stretched spring.

2

Analyze the mechanical state of the cruising aircraft.

Contains both gravitational potential energy (

mgh

) and kinetic energy (

\frac{1}{2}mv^2

).

The aircraft is elevated above ground level and simultaneously moving at a high velocity.

3

Analyze the energy transformation occurring during vehicle braking.

Conversion of mechanical kinetic energy into thermal energy via friction.

Non-conservative frictional forces do negative work on the wheel, dissipating motion into heat.

4

Calculate the power output of the electric hoist performing

2,000\text{ J}

of work per second.

P = \frac{2000\text{ J}}{1\text{ s}} = 2000\text{ W} = 2\text{ kW}

.

Power is the time rate at which work is performed or energy is converted (

1\text{ W} = 1\text{ J/s}

).

Key Concept

Classification of energy forms (kinetic, gravitational potential, elastic potential), energy dissipation via friction, and the calculation of power as the rate of doing work.

Estimated Time:1m 0s

Question 33Question →

An electric motor performs $4{}500\text{ J}$ of mechanical work in $15\text{ seconds}$ . What is the power output of the motor, in watts?

Show answer & explanation

Answer: 300

Answer

The power output of the motor is

300\text{ W}

.

Power is calculated by dividing work by time (

P = \frac{W}{t}

). Dividing

4{}500\text{ J}

by

15\text{ s}

yields

300\text{ W}

.

Step-by-Step Solution

1

Identify the relationship between power, work, and time.

P = \frac{W}{t}

Power is defined scientifically as the rate of doing work or transferring energy per unit time.

2

Substitute the given work (

4{}500\text{ J}

) and time (

15\text{ s}

) into the power equation.

P = \frac{4{}500\text{ J}}{15\text{ s}} = 300\text{ W}

Dividing total work in joules by elapsed time in seconds yields the power in watts (

1\text{ W} = 1\text{ J/s}

).

Key Concept

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

P = \frac{W}{t}

).

Estimated Time:45s

Question 34Question →

An industrial pump performs $72,000\text{ J}$ of work to circulate coolant through a cooling system in $2\text{ minutes}$ . What is the average power output of the pump?

36,000\text{ W}

600\text{ W}

144,000\text{ W}

72,000\text{ W}

Show answer & explanation

Answer: $600\text{ W}$

Answer

600\text{ W}

Power is defined as the rate at which work is done (

P = \frac{W}{t}

). The standard unit of power, the watt (

\text{W}

), equals one joule per second (

\text{J/s}

). Converting

2\text{ minutes}

gives

120\text{ seconds}

. Dividing

72,000\text{ J}

by

120\text{ s}

gives an average power output of

600\text{ W}

.

Step-by-Step Solution

1

Convert the elapsed time from minutes into the standard SI unit of seconds

2\text{ minutes} \times 60\text{ seconds/minute} = 120\text{ seconds}

The watt is defined as one joule per second, requiring time to be in seconds.

2

Apply the power formula

P = \frac{W}{t}

by dividing total work by time

P = \frac{72,000\text{ J}}{120\text{ s}} = 600\text{ W}

Power measures the rate at which work is performed over time.

Key Concept

Power as the Rate of Doing Work (

P = \frac{W}{t}

)

Estimated Time:1m 0s

Question 35Question →

Fill in the blank with the correct integer coefficient needed to balance the chemical equation.

Fill in the blanks below

In the complete combustion of methane, one molecule of methane reacts with oxygen to form carbon dioxide and water:

\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 +

\text{H}_2\text{O}

Show answer & explanation

Answer

2

According to the law of conservation of mass, the total number of atoms for each element must be equal before and after the reaction. The reactant side contains 1 carbon atom, 4 hydrogen atoms, and 4 oxygen atoms. On the product side,

\text{CO}_2

contains 1 carbon atom and 2 oxygen atoms. Placing a coefficient of 2 in front of

\text{H}_2\text{O}

provides the remaining 4 hydrogen atoms and 2 oxygen atoms, fully balancing the equation.

Step-by-Step Solution

1

Count the number of atoms of each element on the reactant side.

Reactants have 1 carbon atom, 4 hydrogen atoms (from

\text{CH}_4

), and 4 oxygen atoms (from

2\text{O}_2

).

The law of conservation of mass requires the number of atoms of each element to be identical on both sides of a balanced chemical equation.

2

Count the atoms present in the products and determine the coefficient needed for

\text{H}_2\text{O}

.

One molecule of

\text{CO}_2

contains 1 carbon atom and 2 oxygen atoms. To balance the 4 hydrogen atoms and remaining 2 oxygen atoms, 2 molecules of

\text{H}_2\text{O}

are required.

A coefficient of 2 provides

2 \times 2 = 4

hydrogen atoms and

2 \times 1 = 2

oxygen atoms, giving a total of 4 oxygen atoms on the product side.

Key Concept

Balancing chemical equations using conservation of mass

Estimated Time:45s

Question 36Question →

An industrial catapult uses a compressed mechanical spring that stores $1{}600\text{ J}$ of elastic potential energy. Upon release, all of this stored energy is converted entirely into kinetic energy to propel an $8\text{ kg}$ projectile horizontally across a frictionless launch track. What is the velocity of the projectile immediately after launch?

10\text{ m/s}

20\text{ m/s}

200\text{ m/s}

400\text{ m/s}

Show answer & explanation

Answer: $20\text{ m/s}$

Answer

20\text{ m/s}

According to the principle of conservation of mechanical energy, the

1{}600\text{ J}

of stored elastic potential energy is completely converted into kinetic energy (

KE = 1{}600\text{ J}

). Applying the kinetic energy formula

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

with

m = 8\text{ kg}

gives

1{}600 = \frac{1}{2}(8)v^2 = 4v^2

. Solving for velocity gives

v^2 = 400

, and taking the square root yields

v = 20\text{ m/s}

.

Step-by-Step Solution

1

Apply the law of conservation of mechanical energy to equate potential and kinetic energy.

KE = PE_{\text{elastic}} = 1{}600\text{ J}

Since the launch track is frictionless and energy is fully converted, initial potential energy equals final kinetic energy.

2

Substitute the known mass and kinetic energy into the kinetic energy equation.

1{}600 = \frac{1}{2} (8\text{ kg}) v^2

The standard formula for kinetic energy is

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

.

3

Simplify the equation to solve for

v^2

.

4v^2 = 1{}600 \implies v^2 = 400\text{ m}^2/\text{s}^2

Dividing both sides by 4 isolates the squared velocity term.

4

Take the square root of both sides to determine velocity.

v = \sqrt{400} = 20\text{ m/s}

The final velocity is the positive square root of

v^2

.

Key Concept

Conservation of Mechanical Energy and Kinetic Energy Calculation

Alternative Method

Express velocity algebraically first:

v = \sqrt{\frac{2E}{m}} = \sqrt{\frac{2 \times 1{}600}{8}} = \sqrt{\frac{3{}200}{8}} = \sqrt{400} = 20\text{ m/s}

.

Estimated Time:1m 0s

Question 37Question →

A technician performs $750\text{ J}$ of mechanical work while pushing a piece of machinery across a level workshop floor over a distance of $15\text{ meters}$ . Assuming the force is applied parallel to the direction of motion, what is the magnitude of the horizontal force applied, in newtons?

Show answer & explanation

Answer: 50

Answer

The magnitude of the applied horizontal force is

50\text{ N}

.

Mechanical work is defined as

W = F \times d

when force and displacement are in the same direction. Rearranging to solve for force gives

F = \frac{W}{d} = \frac{750\text{ J}}{15\text{ m}} = 50\text{ N}

.

Step-by-Step Solution

1

State the governing formula relating work, force, and displacement

W = F \times d

Work is defined as force multiplied by displacement in the direction of the force.

2

Rearrange the equation to isolate the unknown force variable (

F

)

F = \frac{W}{d}

Dividing both sides of the work formula by displacement yields force.

3

Substitute the given numerical quantities (

W = 750\text{ J}

,

d = 15\text{ m}

) and compute

F = \frac{750}{15} = 50\text{ N}

Carrying out the arithmetic yields the magnitude of the required force in newtons.

Key Concept

Work is the product of the magnitude of displacement and the component of force in the direction of displacement (

W = Fd

).

Estimated Time:1m 0s

Question 38Question →

A model electric car accelerates uniformly along a straight track from rest to a speed of $12\text{ m/s}$ in $4\text{ seconds}$ . What is the magnitude of the car's acceleration in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The magnitude of the acceleration is

3\text{ m/s}^2

.

Acceleration is defined as the change in velocity divided by the time elapsed (

a = \frac{\Delta v}{t}

). Since the car accelerates from

0\text{ m/s}

to

12\text{ m/s}

in

4\text{ s}

, the acceleration is

\frac{12 - 0}{4} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement

Initial velocity

v_i = 0\text{ m/s}

, final velocity

v_f = 12\text{ m/s}

, time

t = 4\text{ s}

Establishing known variables is necessary before selecting the appropriate kinematic relationship.

2

Apply the definition of constant linear acceleration:

a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}

Formula set up as

a = \frac{12\text{ m/s} - 0\text{ m/s}}{4\text{ s}}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute acceleration

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

Dividing

12

by

4

yields the constant acceleration magnitude.

Key Concept

Uniform Linear Acceleration

Alternative Method

Using the kinematic equation

v_f = v_i + at

, substitute

12 = 0 + a(4)

, which simplifies directly to

4a = 12

, yielding

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

.

Estimated Time:45s

Question 39Question →

During a laboratory experiment, a student mixes an aqueous solution of sodium carbonate ( $\text{Na}_2\text{CO}_3$ ) with an aqueous solution of calcium chloride ( $\text{CaCl}_2$ ). A solid white precipitate of calcium carbonate ( $\text{CaCO}_3$ ) immediately forms and settles at the bottom, while sodium chloride ( $\text{NaCl}$ ) remains dissolved. Which of the following statements best explains why this process is classified as a chemical reaction rather than a physical change?

The liquid solution underwent a physical phase change where dissolved particles froze into solid crystals due to temperature loss.

The substances formed a simple mechanical mixture in which both original compounds retain their identical chemical bonds.

Chemical bonds were broken and reformed to produce a new substance with different chemical properties from the original reactants.

New atoms of calcium and carbon were generated during the reaction to create the additional mass observed in the solid precipitate.

Show answer & explanation

Answer: Chemical bonds were broken and reformed to produce a new substance with different chemical properties from the original reactants.

Answer

Chemical bonds were broken and reformed to produce a new substance with different chemical properties from the original reactants.

A chemical reaction occurs when bonds within reactant molecules break and new bonds form to create one or more chemically distinct substances. The formation of solid calcium carbonate precipitate from aqueous sodium carbonate and calcium chloride demonstrates the synthesis of a new compound with unique solubility and chemical properties.

Step-by-Step Solution

1

Analyze the starting reactants and resulting products in the reaction.

Reactants are soluble

\text{Na}_2\text{CO}_3

and

\text{CaCl}_2

; products are solid

\text{CaCO}_3

precipitate and dissolved

\text{NaCl}

.

Identifying the initial and final chemical species confirms whether new substances were produced.

2

Distinguish between chemical transformations and physical changes.

The formation of a solid precipitate from two clear liquids via double displacement indicates bonds broke and reformed to yield a new insoluble compound.

A physical change alters form or state without changing chemical identity, whereas this reaction alters chemical identity and molecular structure.

3

Apply the Law of Conservation of Mass to verify atom balance.

The balanced equation is

\text{Na}_2\text{CO}_3\text{(aq)} + \text{CaCl}_2\text{(aq)} \rightarrow \text{CaCO}_3\text{(s)} + 2\text{NaCl}\text{(aq)}

, showing atom conservation rather than atom creation.

All atoms present in the products originate from the reactants; no atoms are generated or destroyed.

Key Concept

Chemical change involves breaking and forming chemical bonds to produce new substances, distinguished from physical phase changes and governed by the Law of Conservation of Mass.

Estimated Time:1m 0s

Question 40Question →

An automated conveyor belt pulls a heavy cargo container across a level $14\text{-meter}$ warehouse floor in $7\text{ seconds}$ by exerting a constant horizontal force of $250\text{ N}$ . What is the power output delivered by the conveyor belt to the container?

3{}500\text{ W}

125\text{ W}

500\text{ W}

24{}500\text{ W}

Show answer & explanation

Answer: $500\text{ W}$

Answer

The power output delivered by the conveyor belt is

500\text{ W}

.

Power is defined as work done divided by time (

P = \frac{W}{t}

). The conveyor belt performs

3{}500\text{ J}

of work (

250\text{ N} \times 14\text{ m}

). Over an interval of

7\text{ seconds}

, the power delivered is

\frac{3{}500\text{ J}}{7\text{ s}} = 500\text{ W}

.

Step-by-Step Solution

1

Calculate the mechanical work performed using

W = F \times d

.

W = 250\text{ N} \times 14\text{ m} = 3{}500\text{ J}

Work is the product of the applied force and the displacement in the direction of the force.

2

Calculate the power output by dividing work by time using

P = \frac{W}{t}

.

P = \frac{3{}500\text{ J}}{7\text{ s}} = 500\text{ W}

Power is defined as the time rate at which work is done or energy is transferred.

Key Concept

Mechanical Work and Power

Estimated Time:1m 0s

Physical Science

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