Work, Energy, and Power Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

Four mobile systems are evaluated during performance trials on a flat testing course. Arrange the systems in order of their kinetic energy, from least to greatest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

From least to greatest kinetic energy: the

500\text{ kg}

cargo transport (

4{}000\text{ J}

), the

10\text{ kg}

automated inspection rover (

4{}500\text{ J}

), the

40\text{ kg}

tracked reconnaissance unit (

8{}000\text{ J}

), and the

2\text{ kg}

calibration projectile (

10{}000\text{ J}

).

Applying the kinetic energy formula

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

to each system yields

4{}000\text{ J}

for the

500\text{ kg}

transport at

4\text{ m/s}

,

4{}500\text{ J}

for the

10\text{ kg}

rover at

30\text{ m/s}

,

8{}000\text{ J}

for the

40\text{ kg}

unit at

20\text{ m/s}

, and

10{}000\text{ J}

for the

2\text{ kg}

projectile at

100\text{ m/s}

. Arranging these values from smallest to largest produces the correct sequence.

Adım Adım Çözüm

1

Identify 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 is directly proportional to mass and proportional to the square of velocity.

2

Calculate the kinetic energy for each of the four systems.

Cargo transport:

\frac{1}{2}(500)(4^2) = 250 \times 16 = 4{}000\text{ J}

; Inspection rover:

\frac{1}{2}(10)(30^2) = 5 \times 900 = 4{}500\text{ J}

; Reconnaissance unit:

\frac{1}{2}(40)(20^2) = 20 \times 400 = 8{}000\text{ J}

; Calibration projectile:

\frac{1}{2}(2)(100^2) = 1 \times 10{}000 = 10{}000\text{ J}

.

Quantitative values allow direct comparison across all systems.

3

Arrange the resulting energy values in ascending sequence.

4{}000\text{ J} < 4{}500\text{ J} < 8{}000\text{ J} < 10{}000\text{ J}

.

Orders the systems from least kinetic energy to greatest kinetic energy as required.

Anahtar Kavram

Kinetic energy is calculated as

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

, meaning velocity has a quadratic effect compared to the linear effect of mass.

Tahmini Süre:1m 30s

Soru 2Soru →

A pendulum bob is pulled to its highest point and released from rest. As the bob swings downward toward the lowest point of its path, which of the following energy transformations occurs?

Kinetic energy is converted into gravitational potential energy.

Gravitational potential energy is converted into kinetic energy.

Chemical energy is converted into thermal energy.

Gravitational potential energy and kinetic energy both decrease simultaneously.

Cevabı ve açıklamayı göster

Cevap: Gravitational potential energy is converted into kinetic energy.

Cevap

Gravitational potential energy is converted into kinetic energy.

At the highest point of its swing, the pendulum bob possesses maximum gravitational potential energy due to its position and zero kinetic energy because its velocity is zero. As it falls downward toward the lowest point, gravity accelerates the bob, converting its stored gravitational potential energy into kinetic energy.

Adım Adım Çözüm

1

Identify the initial energy state at the highest point of the swing.

At the peak, the pendulum bob has maximum gravitational potential energy (

PE = mgh

) and zero kinetic energy (

KE = 0

) because it is momentarily stationary.

Gravitational potential energy depends on the height of the object above its reference level.

2

Analyze the energy change as the bob descends toward the lowest point.

The bob loses height, which decreases its gravitational potential energy, and accelerates downward, increasing its kinetic energy (

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

).

By the law of conservation of mechanical energy, the lost potential energy transforms directly into kinetic energy.

Anahtar Kavram

Conservation and Transformation of Mechanical Energy

Tahmini Süre:45s

Soru 3Soru →

A roller coaster car is released from rest at the top of a hill and coasts without friction along a track. Place the following track locations in order from LEAST kinetic energy to GREATEST kinetic energy.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

Starting crest (highest elevation) → Halfway down the slope → Near the bottom of the incline → Lowest point of the track (ground level)

By the conservation of energy, gravitational potential energy is continuously converted into kinetic energy as the car moves downhill. Since the car starts from rest at the highest elevation, its initial kinetic energy is zero. As it descends, its speed increases, reaching maximum kinetic energy at the lowest point of the track.

Adım Adım Çözüm

1

Identify the initial energy state and energy transformation mechanism

At rest at the highest point, kinetic energy is zero (

E_k = 0

) and potential energy is at its maximum.

Kinetic energy depends on speed (

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

), so an object at rest has zero kinetic energy.

2

Apply the law of conservation of mechanical energy as the car descends

As elevation decreases, gravitational potential energy is converted into kinetic energy, increasing the speed of the car.

In a frictionless system, total mechanical energy is conserved (

E_{total} = E_p + E_k

).

3

Rank the positions from lowest to highest kinetic energy based on elevation

Elevation from highest to lowest directly corresponds to kinetic energy from least to greatest: crest (

0\text{ J}

) < halfway down < near bottom < lowest point (maximum).

Lower elevation yields lower potential energy and higher kinetic energy.

Anahtar Kavram

Conservation of Mechanical Energy and Potential-to-Kinetic Energy Transformation

Tahmini Süre:45s

Soru 4Soru →

A roller coaster cart begins from rest at the top of a track with $50{}000\text{ J}$ of gravitational potential energy. Assuming no energy is lost to friction, what is the cart's kinetic energy when its potential energy decreases to $15{}000\text{ J}$ ?

15{}000\text{ J}

50{}000\text{ J}

35{}000\text{ J}

65{}000\text{ J}

Cevabı ve açıklamayı göster

Cevap: $35{}000\text{ J}$

Cevap

35{}000\text{ J}

According to the Law of Conservation of Energy, the total mechanical energy in a frictionless system remains constant. Since the cart starts with

50{}000\text{ J}

of potential energy and zero kinetic energy, the total energy is

50{}000\text{ J}

. When potential energy drops to

15{}000\text{ J}

, the lost potential energy (

50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

) is entirely converted into kinetic energy.

Adım Adım Çözüm

1

Determine the total initial mechanical energy of the cart.

E_{\text{total}} = 50{}000\text{ J}

Since the cart starts from rest, its initial kinetic energy is zero, making total mechanical energy equal to initial potential energy.

2

Apply the Law of Conservation of Mechanical Energy at the lower height.

E_{\text{total}} = PE + KE \implies 50{}000\text{ J} = 15{}000\text{ J} + KE

In a frictionless system, the sum of kinetic and potential energy remains constant at all points.

3

Subtract the remaining potential energy from the total mechanical energy to solve for kinetic energy.

KE = 50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

The decrease in gravitational potential energy directly converts into an equal increase in kinetic energy.

Anahtar Kavram

Conservation of Mechanical Energy

Tahmini Süre:1m 0s

Soru 5Soru →

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 6Soru →

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 7Soru →

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 8Soru →

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 9Soru →

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 10Soru →

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 11Soru →

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 12Soru →

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 13Soru →

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 14Soru →

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 15Soru →

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}

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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 16Soru →

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?

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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 17Soru →

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

Soru 18Soru →

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

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Cevap: Kinetic energy

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Kinetic Energy and Motion

Tahmini Süre:30s

Soru 19Soru →

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

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

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Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:1m 30s

Soru 20Soru →

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.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

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).

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:45s

Work, Energy, and Power

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