Tüm alıştırma soruları

Soru 1941Soru →

In a standard vapor-compression refrigeration cycle, the condenser relies on a cooling fan to move ambient air across its coils. Based on thermodynamic principles, which of the following is the most likely consequence if the condenser cooling fan completely fails while the compressor continues to operate?

The high-pressure refrigerant will remain a gas instead of condensing into a liquid, because it cannot adequately dissipate thermal energy to the environment.

The system will automatically switch from convection to conduction, causing the expansion valve to absorb the excess heat directly from the compressor.

The trapped thermal energy will accelerate the phase change process, causing the high-pressure gas to condense into a liquid much faster than normal.

The hot gaseous refrigerant will rapidly become an incompressible fluid inside the coils, forcing the condenser to act as a secondary hydraulic pump.

Cevabı ve açıklamayı göster

Cevap: The high-pressure refrigerant will remain a gas instead of condensing into a liquid, because it cannot adequately dissipate thermal energy to the environment.

Cevap

The high-pressure refrigerant will remain a gas instead of condensing into a liquid, because it cannot adequately dissipate thermal energy to the environment.

In a vapor-compression refrigeration cycle, the condenser's primary job is to reject heat absorbed from the interior space (and heat added by the compressor) to the outside environment. It does this via forced convection using a cooling fan. When the high-pressure, high-temperature gas loses this heat, it condenses into a high-pressure liquid. If the fan fails, the heat cannot be dissipated into the ambient air. Consequently, the refrigerant retains its thermal energy and remains a gas, entirely disrupting the cooling cycle.

Adım Adım Çözüm

1

Identify the normal function of the condenser in the refrigeration cycle.

The condenser removes heat from the high-pressure, high-temperature gaseous refrigerant coming from the compressor.

Understanding baseline component function is necessary to analyze the system failure.

2

Determine the thermodynamic result of normal heat removal in the condenser.

As the gaseous refrigerant loses thermal energy to the cooler outside air, it undergoes a phase change (condenses) into a high-pressure liquid.

Phase changes are driven by the transfer of latent heat.

3

Analyze the impact of the cooling fan failure on heat transfer.

Without the fan blowing air across the coils, forced convection stops. Heat dissipation drops drastically.

Airflow is required to carry away the heat; still air acts as an insulator.

4

Conclude how the lack of heat transfer affects the state of the refrigerant.

Because the thermal energy cannot be adequately rejected to the environment, the refrigerant cannot shed enough heat to condense. It remains a hot, high-pressure gas as it exits the condenser.

A substance cannot condense into a liquid until sufficient thermal energy has been removed.

Anahtar Kavram

Thermodynamics of the Vapor-Compression Cycle

Soru 1942Soru →

A deck winch on a naval vessel applies a constant net horizontal force of $4,500 \text{ N}$ to drag a heavy supply pallet across a level deck. If the pallet has a mass of $1,500 \text{ kg}$ , what is the acceleration of the pallet?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The correct answer is 3.

By applying Newton's Second Law (

F = ma

) and rearranging for acceleration (

a = \frac{F}{m}

), we divide the net force of

4,500 \text{ N}

by the mass of

1,500 \text{ kg}

to find an acceleration of

3 \text{ m/s}^2

.

Adım Adım Çözüm

1

Identify the given information

Force (

F

) =

4,500 \text{ N}

, Mass (

m

) =

1,500 \text{ kg}

Extracting the known variables is the first step in solving a physics calculation problem.

2

Select the appropriate formula

F = ma

Newton's Second Law relates force, mass, and acceleration.

3

Rearrange the formula to solve for acceleration

a = \frac{F}{m}

We need to isolate the unknown variable, acceleration (

a

).

4

Substitute the values and calculate

a = \frac{4500}{1500} = 3 \text{ m/s}^2

Plugging in the given numbers yields the final numerical answer.

Anahtar Kavram

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (

F = ma

).

Soru 1943Soru →

Match each hydraulic jack scenario to its correctly calculated parameter based on Pascal's Principle.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Jack A matches to 160 lbs output force, Jack B matches to 3 inches output distance, Jack C matches to 4 in² input area, and Jack D matches to 30 psi fluid pressure.

Each hydraulic system operates on Pascal's Principle and the conservation of volume. By applying the formulas for pressure (

P = F/A

) and mechanical advantage (

MA = A_{out}/A_{in}

), the missing parameter for each jack can be calculated and uniquely matched.

Adım Adım Çözüm

1

Calculate the output force for Jack A.

F_{out} = 160 \text{ lbs}

.

Using Pascal's principle, mechanical advantage is

12/3 = 4

.

F_{out} = 40 \times 4

.

2

Calculate the output distance for Jack B.

d_{out} = 3 \text{ inches}

.

Due to volume conservation,

d_{in} \times A_{in} = d_{out} \times A_{out}

.

15 \times 2 = d_{out} \times 10

.

3

Calculate the input area for Jack C.

A_{in} = 4 \text{ in}^2

.

Since pressure is equal across the system,

P = 180 / 24 = 7.5 \text{ psi}

.

A_{in} = 30 / 7.5

.

4

Calculate the fluid pressure for Jack D.

P = 30 \text{ psi}

.

Pressure equals force over area,

P = 45 / 1.5

.

Anahtar Kavram

Pascal's Principle, Fluid Volume Conservation, and Mechanical Advantage

Soru 1944Soru →

A heavy generator is suspended horizontally by two vertical cables, Cable X on the left and Cable Y on the right. The center of gravity of the generator is located closer to Cable Y. Which of the following describes the load distribution between the two cables?

Cable X carries more of the load than Cable Y.

Cable Y carries more of the load than Cable X.

Cable X and Cable Y carry equal amounts of the load.

The distribution depends entirely on the generator's total mass, not its center of gravity.

Cevabı ve açıklamayı göster

Cevap: Cable Y carries more of the load than Cable X.

Cevap

Cable Y carries more of the load than Cable X.

In mechanical comprehension, when a load is supported by multiple points, the support closer to the object's center of gravity must carry a proportionally larger share of the weight to maintain static equilibrium. Since the generator's center of gravity is closer to Cable Y, Cable Y bears the greater load.

Adım Adım Çözüm

1

Identify the location of the supports and the center of gravity.

Cable X is on the left, Cable Y is on the right, and the center of gravity is closer to Cable Y.

Understanding the geometry of the setup is the first step in determining load distribution.

2

Apply the principle of load distribution and equilibrium.

The support closer to the center of gravity must provide a larger upward reaction force to balance the weight.

The center of gravity acts as the specific point where the entire downward force of the object's mass is concentrated.

3

Determine which cable carries the greater load.

Cable Y carries a greater portion of the generator's weight.

Because Cable Y is physically closer to the concentration of the downward force, it must support more of the load than Cable X.

Anahtar Kavram

In a system with multiple supports, the support closest to the object's center of gravity carries the greatest proportion of the load.

Soru 1945Soru →

In an older gravity-fed residential heating system, a boiler in the basement heats water, which then travels up to radiators on the second floor. This system operates entirely without the use of a mechanical circulation pump. Which of the following best describes the primary mechanism causing this upward flow of water?

The heated water expands and decreases in density, allowing it to be displaced upward by cooler, denser water.

Heat transfers continuously through the solid metal pipes via direct contact, drawing the surrounding water upward.

The heated water contracts and increases in density, creating a pressure differential that pulls fluid toward the upper floors.

The boiler increases the weight of the water molecules, generating a greater buoyant force that pushes them up the pipes.

Cevabı ve açıklamayı göster

Cevap: The heated water expands and decreases in density, allowing it to be displaced upward by cooler, denser water.

Cevap

The heated water expands and decreases in density, allowing it to be displaced upward by cooler, denser water.

The correct answer accurately describes natural convection. When fluid is heated, its molecules move apart (thermal expansion). This decreases the fluid's density relative to the surrounding cooler fluid. Gravity pulls the denser, cooler fluid downward more strongly, which mechanically displaces the warmer, lighter fluid, pushing it upward.

Adım Adım Çözüm

1

Analyze the system described in the scenario.

A boiler heats water, which moves upward to radiators without a pump (natural flow).

Identifying the absence of mechanical force indicates the system relies on physical property changes in the fluid.

2

Identify the relevant physical principle acting on the fluid.

When a fluid is heated, it undergoes thermal expansion, increasing its volume and lowering its density.

Understanding thermal expansion is necessary to explain why the fluid's behavior changes.

3

Evaluate the resulting fluid dynamics.

The cooler, denser water from the radiators sinks due to gravity, displacing the warmer, less dense water and pushing it upward.

This describes the continuous convection loop that drives the gravity-fed system.

Anahtar Kavram

Natural Convection and Fluid Density

Tahmini Süre:1m 0s

Soru 1946Soru →

A $500\text{ kg}$ steel pipe is suspended by a vertical cable from a motorized overhead bridge crane. The crane carriage and the suspended pipe are traveling horizontally along a straight track at a constant speed of $2\text{ m/s}$ . If the crane operator suddenly engages the emergency brakes and the crane carriage stops instantly, what will initially happen to the suspended steel pipe?

It will continue moving forward, swinging in the original direction of travel, due to its inertia.

It will swing backward in the opposite direction of travel as a reaction to the crane's braking force.

It will stop moving horizontally, but its downward weight will momentarily increase.

It will stop immediately with the crane because its large mass causes it to naturally decelerate faster.

Cevabı ve açıklamayı göster

Cevap: It will continue moving forward, swinging in the original direction of travel, due to its inertia.

Cevap

The pipe will continue moving forward, swinging in the original direction of travel, due to its inertia.

According to Newton's First Law, an object in motion will stay in motion at a constant velocity unless acted upon by an external net force. The emergency brakes apply a stopping force to the crane carriage on the track, but not directly to the suspended pipe hanging below. Therefore, the pipe's mass strongly resists the change in velocity (inertia), causing it to continue moving forward and swing in its original direction of travel.

Adım Adım Çözüm

1

Identify the state of motion before the brakes are applied.

Both the crane carriage and the suspended pipe are moving horizontally at a steady speed of 2 m/s.

Establishing the initial conditions is necessary to properly apply Newton's First Law.

2

Determine where the stopping force is applied when the emergency brakes are engaged.

The braking force is applied directly to the crane carriage on the track, causing the carriage to stop abruptly.

To predict the motion of the suspended pipe, we must identify if an external horizontal force acts directly on it.

3

Apply Newton's First Law of Motion (Inertia) to the suspended pipe.

Because no direct horizontal stopping force is applied to the pipe, its inertia causes it to resist the change in motion and it attempts to continue moving forward at 2 m/s.

Newton's First Law states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

4

Evaluate the resulting physical behavior of the pipe.

Since the crane carriage stops but the pipe continues forward, the flexible cable allows the pipe's continued momentum to manifest as a forward swing, like a pendulum.

Visualizing the mechanical connection explains the exact physical outcome resulting from the object's inertia.

Anahtar Kavram

Newton's First Law (Inertia)

Soru 1947Soru →

A high-speed rail train is traveling at an initial velocity of $216 \text{ km/h}$ . To safely navigate a sharp curve, the train must reduce its velocity to $108 \text{ km/h}$ . If the train applies its braking system to produce a constant deceleration of $1.5 \text{ m/s}^2$ , how many seconds will it take to reach the required speed?

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

It will take 20 seconds for the train to reach the required speed.

The correct answer is found by first converting both velocities to meters per second to match the acceleration's units.

216 \text{ km/h}

is equivalent to

60 \text{ m/s}

, and

108 \text{ km/h}

is equivalent to

30 \text{ m/s}

. The change in velocity is

-30 \text{ m/s}

. Using the formula

t = \Delta v / a

, dividing

-30 \text{ m/s}

by the deceleration of

-1.5 \text{ m/s}^2

results in exactly

20 \text{ seconds}

.

Adım Adım Çözüm

1

Convert the initial velocity (

v_i

) from km/h to m/s.

216 \text{ km/h} \div 3.6 = 60 \text{ m/s}

Standardizing units to match the acceleration given in m/s^2 is required before calculation.

2

Convert the final velocity (

v_f

) from km/h to m/s.

108 \text{ km/h} \div 3.6 = 30 \text{ m/s}

All velocity variables must be in meters per second to be compatible with the acceleration.

3

Calculate the change in velocity (

\Delta v

).

\Delta v = 30 \text{ m/s} - 60 \text{ m/s} = -30 \text{ m/s}

Acceleration is the rate of change of velocity, so finding the total change is the necessary intermediate step.

4

Apply the acceleration formula

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

to solve for time (

t

).

t = \frac{-30 \text{ m/s}}{-1.5 \text{ m/s}^2} = 20 \text{ seconds}

Dividing the total change in velocity by the rate of deceleration yields the elapsed time.

Anahtar Kavram

Kinematics: Calculating time from constant acceleration and velocity change while managing unit conversions.

Soru 1948Soru →

A uniform wooden beam is $10$ feet long and weighs $50$ pounds. It rests horizontally on two sawhorses. Sawhorse A is placed $4$ feet from the left end, and Sawhorse B is placed $9$ feet from the left end. A $50$ -pound bag of cement is placed at the extreme right end of the beam ( $10$ feet from the left end). Assuming the system is in static equilibrium, what is the upward reaction force exerted by Sawhorse B?

30

pounds

50

pounds

60

pounds

70

pounds

Cevabı ve açıklamayı göster

Cevap: $70$ pounds

Cevap

The upward reaction force exerted by Sawhorse B is

70

pounds.

For the system to be in static equilibrium, the moments around any pivot point must sum to zero. Choosing Sawhorse A as the pivot: the beam's center of gravity (

5

ft mark) is

1

ft right of the pivot, creating

50 \times 1 = 50

ft-lbs of clockwise torque. The bag (

10

ft mark) is

6

ft right of the pivot, creating

50 \times 6 = 300

ft-lbs of clockwise torque. To balance the total

350

ft-lbs of clockwise torque, Sawhorse B (located

5

ft right of the pivot) must provide

350 / 5 = 70

pounds of upward force.

Adım Adım Çözüm

1

Identify the pivot point and the locations of all downward forces.

Using Sawhorse A (at

4

ft) as the pivot. The beam's weight (

50

lbs) acts at its center (

5

ft). The cement bag (

50

lbs) acts at the right end (

10

ft).

Choosing one support as the pivot eliminates its unknown force from the equilibrium equation.

2

Calculate the lever arm distances from the pivot for each force.

Beam weight lever arm:

5 - 4 = 1

ft. Cement bag lever arm:

10 - 4 = 6

ft. Sawhorse B lever arm:

9 - 4 = 5

ft.

Torque is determined by multiplying a force by its perpendicular distance from the pivot point.

3

Calculate the total clockwise torque acting on the beam.

Beam torque:

50 \text{ lbs} \times 1 \text{ ft} = 50 \text{ ft-lbs}

. Cement bag torque:

50 \text{ lbs} \times 6 \text{ ft} = 300 \text{ ft-lbs}

. Total clockwise torque =

350 \text{ ft-lbs}

.

Both the beam's weight and the cement bag push downward on the right side of the pivot, creating clockwise rotation.

4

Set the clockwise torque equal to the counterclockwise torque and solve for Sawhorse B's force.

F_B \times 5 \text{ ft} = 350 \text{ ft-lbs}

, which means

F_B = 350 / 5 = 70

pounds.

In static equilibrium, the torques must perfectly balance to prevent the beam from rotating.

Anahtar Kavram

Rotational Equilibrium and Center of Gravity

Alternatif Yöntem

You can verify this by calculating moments around Sawhorse B instead. The beam's center (

5

ft) is

4

ft to the left (CCW torque:

50 \times 4 = 200

). The cement bag (

10

ft) is

1

ft to the right (CW torque:

50 \times 1 = 50

). Sawhorse A is

5

ft to the left (CW torque:

F_A \times 5

). Balancing torques:

200 = 50 + 5(F_A) \rightarrow F_A = 30

lbs. Since total downward force is

100

lbs,

F_B

must be

100 - 30 = 70

lbs.

Tahmini Süre:2m 0s

Soru 1949Soru →

When used as a structural building material, timber can support a significantly heavier compressive load if the weight is applied perpendicular to its grain rather than parallel to its grain.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. Timber is much stronger in compression when loaded parallel to the grain.

The statement is false because the fibrous nature of timber means it acts like a series of vertical columns. It possesses its maximum compressive strength when loaded parallel to the grain, not perpendicular.

Adım Adım Çözüm

1

Analyze the physical structure of wood as a building material.

Wood consists of long, hollow cellulose fibers that are aligned in one primary direction, which forms the wood's grain.

Understanding the cellular structure is required to determine how the material handles mechanical stress.

2

Evaluate the effect of a compressive force relative to the grain orientation.

Compressing wood parallel to the grain pushes against the solid ends of the fibers, providing high load-bearing resistance. Compressing it perpendicular to the grain easily crushes the hollow fiber walls.

This physical behavior proves that the claim of higher strength perpendicular to the grain is incorrect.

Anahtar Kavram

Directional strength (anisotropy) and load-bearing properties of timber

Soru 1950Soru →

When a solid object is swung in a circular path on a tether and the tether suddenly snaps, the object will immediately fly directly outward, straight away from the center of the circle.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False

The statement is false because an object released from circular motion will follow a straight trajectory tangent to the circle, dictated by its instantaneous velocity, rather than flying radially outward.

Adım Adım Çözüm

1

Identify the forces acting on the object before the tether breaks.

The tether provides a continuous inward force (centripetal force) that constantly changes the object's direction, keeping it in a circular path.

Circular motion requires a net inward force directed toward the center of rotation.

2

Analyze the state of the system at the exact moment the tether snaps.

The physical connection is broken, causing the inward centripetal force to instantly drop to zero.

The tether is the only source of the inward force in this scenario.

3

Apply Newton's First Law of Motion (inertia) to determine the object's resulting path.

The object will travel in a straight line at a constant speed in the exact direction it was moving when the tether broke.

Without a net force acting upon it, an object in motion stays in motion in a straight line, which is mathematically tangent to the edge of the circle.

Anahtar Kavram

Inertia and Tangential Velocity in Circular Motion

Soru 1951Soru →

A common paint sprayer operates by blowing a stream of fast-moving air across the top of an open vertical tube, with the bottom of the tube submerged in a container of paint. Based on Bernoulli's principle, what is the primary reason the paint rises up the tube?

The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

The high-speed air creates a region of high static pressure at the top of the tube, which pulls the paint upward.

The stream of air compresses the fluid inside the vertical tube, reducing its volume and forcing it upward.

The fast-moving air decreases the weight of the displaced fluid, causing an upward buoyant force.

Cevabı ve açıklamayı göster

Cevap: The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

Cevap

The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

According to Bernoulli's principle, an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. The fast-moving air across the top of the tube creates a localized low-pressure area. The relatively higher atmospheric pressure pushing down on the surface of the paint in the container then forces the liquid up the tube.

Adım Adım Çözüm

1

Analyze the relationship between fluid speed and pressure.

The air moving quickly across the top of the tube has a higher velocity than the still air surrounding the container.

This scenario directly sets up an application of Bernoulli's principle.

2

Determine the pressure difference.

Due to its high velocity, the air stream creates an area of low static pressure directly above the open tube.

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in its static pressure.

3

Evaluate the effect on the fluid in the container.

The standard atmospheric pressure resting on the surface of the paint in the container is greater than the low pressure at the top of the tube, thus forcing the paint upward into the stream.

Fluids naturally move from areas of higher pressure to areas of lower pressure.

Anahtar Kavram

Bernoulli's principle establishes an inverse relationship between a fluid's velocity and its static pressure.

Tahmini Süre:45s

Soru 1952Soru →

A mason is pushing a solid, uniform rectangular clay brick across a horizontal wooden scaffold plank at a constant speed. Initially, the brick is positioned so it slides while resting flat on its widest face. If the mason stands the brick up so it slides on its narrowest face across the same section of the plank, how will the kinetic frictional resistance change?

It will remain unchanged because kinetic friction depends on normal force and surface materials, not contact area.

It will decrease because there is less surface area rubbing against the wooden plank.

It will increase because the brick's total weight becomes concentrated, increasing the total normal force.

It will decrease because altering the brick's orientation reduces its resistance to changes in motion.

Cevabı ve açıklamayı göster

Cevap: It will remain unchanged because kinetic friction depends on normal force and surface materials, not contact area.

Cevap

The kinetic frictional resistance will remain unchanged.

For standard rigid objects, the kinetic frictional force is determined solely by the nature of the materials in contact (the coefficient of friction) and the total force pressing them together (the normal force). Because the brick's mass and the materials involved do not change when it is rotated, the overall frictional resistance remains exactly the same, regardless of how much surface area is touching the plank.

Adım Adım Çözüm

1

Identify the formula for kinetic friction.

F_k = \mu_k \times N

To determine exactly which physical variables affect the frictional force.

2

Analyze the normal force (

N

).

The normal force equals the weight of the brick (

N = mg

), which remains constant regardless of its orientation.

To see if rotating the brick changes the total downward force pressing the surfaces together.

3

Analyze the coefficient of kinetic friction (

\mu_k

).

The coefficient remains constant because the materials (clay and wood) and their surface properties have not changed.

To verify that the fundamental physical interaction between the two specific surfaces remains the same.

4

Evaluate the effect of surface contact area.

Surface area is not a variable in the standard kinetic friction formula.

To conclusively confirm that resting the brick on a narrower face does not alter the total frictional resistance.

Anahtar Kavram

Independence of Friction from Surface Area

Soru 1953Soru →

A rigid, sealed cylindrical pontoon is pushed completely underwater in a testing pool, where it displaces $200 \text{ liters}$ of water. The empty pontoon weighs $400 \text{ N}$ . A technician then pulls the pontoon out, places $150 \text{ N}$ of solid lead weights inside it, seals it, and forces it completely back under the water. Which of the following best describes the change in the upward buoyant force acting on the completely submerged pontoon?

It remains exactly the same because the exterior volume of the pontoon displacing the water has not changed.

It increases by

150 \text{ N}

to directly counteract the additional weight of the lead inside.

It decreases because the overall density of the pontoon assembly has become significantly greater.

It increases due to the heavier pontoon creating a stronger downward force, which produces a larger upward reaction from the water.

Cevabı ve açıklamayı göster

Cevap: It remains exactly the same because the exterior volume of the pontoon displacing the water has not changed.

Cevap

The upward buoyant force remains exactly the same because the rigid exterior volume displacing the water does not change.

Archimedes' principle states that the buoyant force on a completely submerged object is equal to the weight of the fluid it displaces. Because the pontoon is rigid, its exterior volume does not change when lead weights are added inside. Since it displaces the exact same volume of water when forced completely underwater in both scenarios, the upward buoyant force acting on it remains perfectly constant, regardless of its increased internal weight.

Adım Adım Çözüm

1

Identify the factors that determine buoyant force according to Archimedes' Principle.

Buoyant force depends only on the density of the fluid and the volume of the fluid displaced by the object (

F_b = \rho \cdot V \cdot g

).

This establishes the fundamental physics rule needed to solve the problem.

2

Analyze what changes between the first and second scenario.

The total weight of the pontoon increases from

400 \text{ N}

to

550 \text{ N}

.

To see if any variables in the buoyant force equation have been affected.

3

Determine if the volume of displaced fluid changes.

Because the pontoon is rigid, its exterior dimensions do not expand or shrink. Since it is completely submerged in both cases, the displaced volume remains exactly

200 \text{ liters}

.

To calculate the final impact on the buoyant force.

4

Evaluate the final state of the buoyant force.

Since both the fluid (water) and the displaced volume (

200 \text{ liters}

) remain constant, the buoyant force remains identical.

To arrive at the final conceptual conclusion.

Anahtar Kavram

Archimedes' Principle states that buoyant force is equal to the weight of the fluid displaced, meaning it depends on the object's volume, not its mass.

Soru 1954Soru →

A municipal water treatment facility utilizes two open-air settling basins with flat bottoms. Basin Alpha is a wide rectangular pool with a base area of $50\text{ m}^2$ , currently holding $150\text{ m}^3$ of water. Basin Beta is a narrow cylindrical well with a base area of $5\text{ m}^2$ , currently holding $30\text{ m}^3$ of water. What is the ratio of the gauge hydrostatic pressure exerted on the bottom of Basin Alpha to the gauge hydrostatic pressure exerted on the bottom of Basin Beta?

1:2

5:1

10:1

2:1

Cevabı ve açıklamayı göster

Cevap: $1:2$

Cevap

The ratio is

1:2

, because gauge hydrostatic pressure depends exclusively on the vertical depth of the fluid, which is

3\text{ m}

in Basin Alpha and

6\text{ m}

in Basin Beta.

Hydrostatic pressure depends exclusively on the depth of the fluid, not the total volume or the base area. The depth of the water in Basin Alpha is

3\text{ m}

(

150\text{ m}^3 / 50\text{ m}^2

). The depth in Basin Beta is

6\text{ m}

(

30\text{ m}^3 / 5\text{ m}^2

). The ratio of these depths is

3:6

, which simplifies to

1:2

.

Adım Adım Çözüm

1

Calculate the depth of water in Basin Alpha.

h_{Alpha} = \frac{150\text{ m}^3}{50\text{ m}^2} = 3\text{ m}

Hydrostatic pressure is determined by fluid depth. Depth is found by dividing the total volume by the base area.

2

Calculate the depth of water in Basin Beta.

h_{Beta} = \frac{30\text{ m}^3}{5\text{ m}^2} = 6\text{ m}

The exact same volumetric relationship applies to find the vertical depth in the second basin.

3

Determine the ratio of their hydrostatic pressures.

Ratio =

3\text{ m} : 6\text{ m} = 1:2

Because both basins contain the same fluid (water) under the same gravitational force, the ratio of their bottom pressures is exactly equal to the ratio of their depths (

P = \rho g h

).

Anahtar Kavram

Hydrostatic pressure is completely independent of a container's shape, base area, or total fluid volume; it depends exclusively on fluid density, gravity, and vertical depth.

Tahmini Süre:1m 30s

Soru 1955Soru →

A footbridge spans a $20$ -foot wide creek, resting on a concrete pillar at each end (Left Pillar and Right Pillar). A person weighing $160$ pounds stands on the bridge, exactly $5$ feet from the Right Pillar. If we ignore the weight of the bridge itself, how many pounds of the person's weight are supported by the Left Pillar?

Cevabı ve açıklamayı göster

Cevap: 40

Cevap

40

The weight supported by the Left Pillar is inversely proportional to the load's distance from it. Since the person is

15

feet from the Left Pillar and

5

feet from the Right Pillar on a

20

-foot bridge, they are

3

times closer to the Right Pillar. Therefore, the Right Pillar carries

3/4

of the weight (

120

lbs) and the Left Pillar carries

1/4

of the weight (

40

lbs).

Adım Adım Çözüm

1

Determine the relevant distances along the bridge.

Total span =

20

ft. Distance to Right Pillar =

5

ft. Distance to Left Pillar =

15

ft.

To calculate the load on one support, we need the total distance and the distance to the opposite support.

2

Set up the load distribution calculation for the Left Pillar.

Load on Left Pillar = Total Weight

\times

(Distance to Right Pillar / Total Span)

The proportion of weight supported by one end of a beam is equal to the distance from the load to the opposite end, divided by the total length.

3

Calculate the supported weight using the values.

160 \times (5 / 20) = 160 \times (1 / 4) = 40

pounds.

Solving the equation gives the exact weight carried by the left support.

Anahtar Kavram

Load Distribution and Balancing

Alternatif Yöntem

You can also use the concept of torque (moments) in static equilibrium. Taking the Right Pillar as the pivot point: (Force of Left Pillar

\times

20

ft) = (

160

lbs

\times

5

ft). Therefore,

20 \times F_{left} = 800

, which means

F_{left} = 40

lbs.

Tahmini Süre:45s

Soru 1956Soru →

A combat engineer squad is using a motorized winch to pull a $2,500 \text{ kg}$ concrete barrier horizontally across rough ground to construct a defensive position. The winch applies a constant tension of $12,000 \text{ N}$ to the towing cable. If the friction between the barrier and the ground opposes the motion with a force of $7,000 \text{ N}$ , what is the acceleration of the barrier?

0.5 \text{ m/s}^2

2.0 \text{ m/s}^2

4.8 \text{ m/s}^2

0.2 \text{ m/s}^2

Cevabı ve açıklamayı göster

Cevap: $2.0 \text{ m/s}^2$

Cevap

2.0 \text{ m/s}^2

The correct answer is found by first calculating the net force, which is the applied tension minus the opposing friction (

12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

). Then, using Newton's Second Law (

a = \frac{F}{m}

), the net force is divided by the mass of the barrier (

\frac{5,000 \text{ N}}{2,500 \text{ kg}}

) to yield an acceleration of

2.0 \text{ m/s}^2

.

Adım Adım Çözüm

1

Identify the applied force and the opposing force acting on the barrier.

Applied Force =

12,000 \text{ N}

, Opposing Friction =

7,000 \text{ N}

.

To find the net force, all horizontal forces acting on the object must be accounted for.

2

Calculate the net force (

F_{net}

) acting on the concrete barrier.

F_{net} = 12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

.

Net force is the vector sum of all forces; opposite forces are subtracted.

3

Apply Newton's Second Law (

F = ma

) to find the acceleration.

a = \frac{F_{net}}{m} = \frac{5,000 \text{ N}}{2,500 \text{ kg}} = 2.0 \text{ m/s}^2

.

Acceleration is directly proportional to net force and inversely proportional to mass.

Anahtar Kavram

Newton's Second Law (F=ma) and Net Force

Soru 1957Soru →

When a person pushes forward against a stalled car to move it, the force the person exerts on the car is greater than the force the car exerts backward on the person.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False

The statement is false because Newton's Third Law states that the mutual forces of action and reaction between two interacting bodies are always equal in magnitude and opposite in direction. The person and the car exert exactly equal forces on each other.

Adım Adım Çözüm

1

Identify the two interacting objects in the given scenario.

The two interacting objects are the person pushing and the stalled car.

Newton's Third Law describes the mutual forces between two interacting bodies.

2

Determine the action and reaction forces occurring between the objects.

The action force is the person pushing forward on the car. The reaction force is the car pushing backward against the person's hands.

Identifying the specific action-reaction pair is necessary to evaluate their magnitudes.

3

Apply Newton's Third Law to compare the magnitudes of the two forces.

Newton's Third Law dictates that these two forces must be equal in magnitude and opposite in direction.

Because the forces must be equal, the statement claiming the person's force is greater is false.

Anahtar Kavram

Newton's Third Law (Action/Reaction)

Tahmini Süre:45s

Soru 1958Soru →

A worker operates a well crank (a wheel and axle mechanism) to lift a heavy bucket of water. The crank handle travels in a circle with a radius of $12 \text{ inches}$ . The lifting rope is wound around an axle that has a diameter of $6 \text{ inches}$ . What is the Ideal Mechanical Advantage (IMA) of this system?

4

2

1

0.5

Cevabı ve açıklamayı göster

Cevap: $4$

Cevap

The correct Ideal Mechanical Advantage (IMA) is

4

.

The correct answer is calculated by finding the ratio of the wheel's radius to the axle's radius. The wheel radius is given as

12 \text{ inches}

. The axle diameter is

6 \text{ inches}

, meaning its radius is

3 \text{ inches}

. Dividing

12

by

3

yields an IMA of

4

.

Adım Adım Çözüm

1

Identify the radius of the wheel (input distance).

The radius of the crank handle circle is

12 \text{ inches}

.

The IMA formula requires the radius of the wheel.

2

Calculate the radius of the axle (output distance).

The diameter is

6 \text{ inches}

, so the radius is

6 \div 2 = 3 \text{ inches}

.

The IMA formula requires the radius of the axle, not the diameter.

3

Calculate the Ideal Mechanical Advantage (IMA).

IMA = \frac{\text{Radius of Wheel}}{\text{Radius of Axle}} = \frac{12}{3} = 4

This ratio shows the mechanical advantage gained by applying force to the larger wheel to turn the smaller axle.

Anahtar Kavram

Ideal Mechanical Advantage of a Wheel and Axle

Tahmini Süre:45s

Soru 1959Soru →

A dull, dark-colored machinery housing will dissipate internal heat through thermal radiation faster than an identical housing with a highly polished, light-colored finish, assuming both are at the same operating temperature.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is true.

Dark, dull surfaces are excellent emitters of thermal radiation due to their high emissivity. As a result, they dissipate internal heat into the surrounding environment much faster than highly polished surfaces, which have low emissivity and act as poor radiators.

Adım Adım Çözüm

1

Identify the mode of heat transfer being tested.

The scenario focuses entirely on thermal radiation as the method of dissipating internal heat.

Understanding the heat transfer method determines which material properties are relevant to the problem.

2

Evaluate the effect of surface finish on thermal radiation.

Dark, dull surfaces have high emissivity, while shiny, light-colored surfaces have low emissivity.

Emissivity is the physical measure of a material's effectiveness in emitting thermal energy as electromagnetic radiation.

3

Determine which housing dissipates heat faster.

The dull, dark-colored housing will radiate heat faster than the polished housing.

A higher emissivity value means thermal energy is radiated away from the object at a significantly greater rate.

Anahtar Kavram

Surface Emissivity and Thermal Radiation

Tahmini Süre:45s

Soru 1960Soru →

An automated cargo tug applies a forward thrust of $24,000 \text{ N}$ to a $1,000 \text{ kg}$ supply sled. If the ground surface creates a constant opposing frictional force of $4,000 \text{ N}$ , what is the resulting acceleration of the sled?

20 \text{ m/s}^2

24 \text{ m/s}^2

2 \text{ m/s}^2

0.05 \text{ m/s}^2

Cevabı ve açıklamayı göster

Cevap: $20 \text{ m/s}^2$

Cevap

20 \text{ m/s}^2

The sled experiences a forward thrust of

24,000 \text{ N}

and a backward frictional force of

4,000 \text{ N}

, resulting in a net force of

20,000 \text{ N}

. Using Newton's Second Law (

F = ma

), dividing the net force (

20,000 \text{ N}

) by the mass (

1,000 \text{ kg}

) gives an acceleration of

20 \text{ m/s}^2

.

Adım Adım Çözüm

1

Calculate the net force acting on the sled.

F_{\text{net}} = 24,000 \text{ N} - 4,000 \text{ N} = 20,000 \text{ N}

Acceleration is determined by the net force, which is the applied force minus any opposing forces like friction.

2

Apply Newton's Second Law (

F = ma

) to find the acceleration.

a = \frac{F_{\text{net}}}{m} = \frac{20,000 \text{ N}}{1,000 \text{ kg}} = 20 \text{ m/s}^2

Rearranging the formula to solve for acceleration gives

a = \frac{F}{m}

.

Anahtar Kavram

Newton's Second Law (

F = ma

)

Tahmini Süre:45s

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap