Physical Science Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 2

Soru 21Soru →

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

.

Cevabı ve açıklamayı göster

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

Cevap

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

.

Adım Adım Çözüm

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.

Anahtar Kavram

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

).

Tahmini Süre:1m 15s

Soru 22Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $600\text{ J}$

Cevap

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}

).

Adım Adım Çözüm

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}

).

Anahtar Kavram

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

W = Fd

), measured in Joules.

Tahmini Süre:45s

Soru 23Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $150\text{ kJ}$

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:1m 30s

Soru 24Soru →

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.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

Mechanical power is the rate of doing work:

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

.

Tahmini Süre:1m 30s

Soru 25Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $15\text{ seconds}$

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

Power as the rate of doing work (

P = \frac{W}{t}

) combined with gravitational potential work (

W = mgh

)

Tahmini Süre:1m 0s

Soru 26Soru →

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

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:45s

Soru 27Soru →

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

Cevabı ve açıklamayı göster

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

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Identification of Chemical Reactions and Compound Formation versus Physical Changes

Tahmini Süre:45s

Soru 28Soru →

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.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:1m 30s

Soru 29Soru →

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.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:45s

Soru 30Soru →

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.

Cevabı ve açıklamayı göster

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

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:45s

Soru 31Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $850\text{ J}$

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

Conservation of Mechanical Energy

Soru 32Soru →

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.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

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.

Adım Adım Çözüm

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}

).

Anahtar Kavram

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

Tahmini Süre:1m 0s

Soru 33Soru →

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?

Cevabı ve açıklamayı göster

Cevap: 300

Cevap

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}

.

Adım Adım Çözüm

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}

).

Anahtar Kavram

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

P = \frac{W}{t}

).

Tahmini Süre:45s

Soru 34Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $600\text{ W}$

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

Power as the Rate of Doing Work (

P = \frac{W}{t}

)

Tahmini Süre:1m 0s

Soru 35Soru →

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

Aşağıdaki boşlukları doldurun

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}

Cevabı ve açıklamayı göster

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Balancing chemical equations using conservation of mass

Tahmini Süre:45s

Soru 36Soru →

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}

Cevabı ve açıklamayı göster

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

Cevap

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}

.

Adım Adım Çözüm

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

.

Anahtar Kavram

Conservation of Mechanical Energy and Kinetic Energy Calculation

Alternatif Yöntem

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}

.

Tahmini Süre:1m 0s

Soru 37Soru →

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?

Cevabı ve açıklamayı göster

Cevap: 50

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

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

W = Fd

).

Tahmini Süre:1m 0s

Soru 38Soru →

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 ( $\text{m/s}^2$ )?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

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

.

Adım Adım Çözüm

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.

Anahtar Kavram

Uniform Linear Acceleration

Alternatif Yöntem

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

.

Tahmini Süre:45s

Soru 39Soru →

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.

Cevabı ve açıklamayı göster

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

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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.

Tahmini Süre:1m 0s

Soru 40Soru →

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}

Cevabı ve açıklamayı göster

Cevap: $500\text{ W}$

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

Mechanical Work and Power

Tahmini Süre:1m 0s

Physical Science

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