Tüm alıştırma soruları

Soru 1721Soru →

A manual winch is used to lift a $240 \text{ lb}$ engine block exactly $2 \text{ feet}$ vertically. The winch consists of a steering-wheel style control with a diameter of $3 \text{ feet}$ , which is rigidly attached to an axle drum with a radius of $3 \text{ inches}$ . Assuming an ideal system with no friction, what continuous effort force must be applied to the outer edge of the wheel, and what total distance must the effort force move along the wheel's rotation?

20 \text{ lbs}

of force;

24 \text{ feet}

of distance

480 \text{ lbs}

of force;

1 \text{ foot}

of distance

40 \text{ lbs}

of force;

12 \text{ feet}

of distance

1440 \text{ lbs}

of force;

1/3 \text{ foot}

of distance

Cevabı ve açıklamayı göster

Cevap: $40 \text{ lbs}$ of force; $12 \text{ feet}$ of distance

Cevap

The correct answer is

40 \text{ lbs}

of force and

12 \text{ feet}

of distance.

The system's Ideal Mechanical Advantage is determined by the ratio of the effort radius (18 inches, half of the 3-foot diameter) to the load radius (3 inches), which yields an IMA of 6. This means the required effort force is divided by 6 (

240 \text{ lbs} / 6 = 40 \text{ lbs}

), while the required effort distance is multiplied by 6 (

2 \text{ feet} \times 6 = 12 \text{ feet}

) to conserve work.

Adım Adım Çözüm

1

Convert all measurements to the same unit (inches).

Wheel diameter =

3 \text{ feet} = 36 \text{ inches}

.

Units must be identical to calculate a valid, dimensionless mechanical advantage ratio.

2

Identify the effort radius and the load radius.

Wheel radius (

R

) =

18 \text{ inches}

. Axle drum radius (

r

) =

3 \text{ inches}

.

The lever arms in a wheel and axle system are the distances from the central axis (the radii), not the diameters.

3

Calculate the Ideal Mechanical Advantage (IMA).

\text{IMA} = \frac{R}{r} = \frac{18}{3} = 6

.

This establishes that the system multiplies the user's force by a factor of 6.

4

Calculate the required effort force.

\text{Effort Force} = \frac{\text{Load}}{\text{IMA}} = \frac{240 \text{ lbs}}{6} = 40 \text{ lbs}

.

Because the machine provides a mechanical advantage of 6, the required input force is one-sixth of the load.

5

Calculate the required effort distance.

\text{Effort Distance} = \text{Load Distance} \times \text{IMA} = 2 \text{ feet} \times 6 = 12 \text{ feet}

.

According to the principle of work, whatever factor force is reduced by, distance must be multiplied by that same factor.

Anahtar Kavram

Ideal Mechanical Advantage (IMA) and Work in a Wheel and Axle

Tahmini Süre:1m 30s

Soru 1722Soru →

A sealed pneumatic cylinder initially contains air at a pressure of $40 \text{ psi}$ . A mechanical linkage forces the cylinder's internal volume to be reduced to exactly half ( $1/2$ ) of its original volume. Simultaneously, an external heat source causes the absolute temperature of the confined air to double. If this newly pressurized air is then directed into a separate pneumatic actuator with a piston surface area of $5 \text{ in}^2$ , what is the total theoretical force exerted by this actuator?

32 \text{ lbs}

200 \text{ lbs}

400 \text{ lbs}

800 \text{ lbs}

Cevabı ve açıklamayı göster

Cevap: $800 \text{ lbs}$

Cevap

The correct force is

800 \text{ lbs}

.

The correct answer accurately combines two gas law principles before applying fluid power mathematics. First, halving the volume of a gas doubles its pressure (Boyle's Law). Second, doubling the absolute temperature doubles that pressure again (Gay-Lussac's Law). This results in a final system pressure of

160 \text{ psi}

. When applied to a

5 \text{ in}^2

piston, the total force is

160 \text{ psi} \times 5 = 800 \text{ lbs}

.

Adım Adım Çözüm

1

Determine the effect of the volume change on the gas pressure using Boyle's Law (

P_1 \times V_1 = P_2 \times V_2

).

Since the volume is halved (

1/2

), the pressure must double.

40 \text{ psi} \times 2 = 80 \text{ psi}

.

In a compressible gas, pressure and volume are inversely proportional when temperature is held constant.

2

Determine the effect of the temperature change on the gas pressure using Gay-Lussac's Law.

Since the absolute temperature is doubled, the pressure must double again.

80 \text{ psi} \times 2 = 160 \text{ psi}

.

In a confined gas, absolute pressure is directly proportional to absolute temperature.

3

Calculate the force exerted by the actuator using the final pressure and the piston area (

F = P \times A

).

160 \text{ psi} \times 5 \text{ in}^2 = 800 \text{ lbs}

.

Force is defined as pressure applied over a specific surface area.

Anahtar Kavram

The Combined Gas Law allows simultaneous evaluation of pressure, volume, and temperature changes in a pneumatic system, which is then used to calculate mechanical force.

Soru 1723Soru →

A maintenance crew is selecting a hydraulic jack to lift a heavy machinery component. The load must be lifted exactly $2 \text{ inches}$ . Different jacks have different input (pump) and output (lifting) cylinder areas.

Match each hydraulic jack's specifications to the distance its input piston must be pushed down to achieve the $2 \text{-inch}$ output lift.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

To find the input distance, calculate the mechanical advantage (Output Area / Input Area) and multiply it by the desired output distance (

2 \text{ inches}

). Jack Alpha requires

10 \text{ inches}

, Jack Beta requires

8 \text{ inches}

, Jack Gamma requires

12 \text{ inches}

, and Jack Delta requires

4 \text{ inches}

.

Each correct match is found by calculating the mechanical advantage (Output Area divided by Input Area) and multiplying that ratio by the desired

2\text{-inch}

output lift. This ensures the volume of fluid pushed by the pump equals the volume required to lift the load.

Adım Adım Çözüm

1

Determine the mathematical relationship for distance in a closed hydraulic system.

\text{Input Area} \times \text{Input Distance} = \text{Output Area} \times \text{Output Distance}

Because liquids are essentially incompressible, the volume of fluid displaced by the input piston must equal the volume of fluid pushing up the output piston.

2

Rearrange the formula to solve for the required Input Distance.

\text{Input Distance} = \text{Output Distance} \times (\frac{\text{Output Area}}{\text{Input Area}})

This isolates the unknown variable, making it easier to plug in the given values for each jack.

3

Calculate the required input distance for Jack Alpha.

2 \text{ inches} \times (\frac{10}{2}) = 2 \times 5 = 10 \text{ inches}

.

Applying the specific area measurements of Jack Alpha to the derived formula.

4

Apply the same formula to the remaining jacks to find their respective input distances.

Beta:

2 \times (\frac{12}{3}) = 8 \text{ inches}

. Gamma:

2 \times (\frac{24}{4}) = 12 \text{ inches}

. Delta:

2 \times (\frac{10}{5}) = 4 \text{ inches}

.

Completing the required calculations to find all corresponding values.

Anahtar Kavram

In a hydraulic system, the distance an input piston must travel is proportional to the ratio of the output area to the input area. A larger mechanical advantage requires a proportionally larger input distance to conserve the total volume of displaced fluid.

Soru 1724Soru →

Match each gear system configuration with its resulting mechanical properties.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The simple train multiplies torque by 4 and reverses direction. The idler train quadruples speed and keeps the same direction. The compound train provides a mechanical advantage of 6 and keeps the same direction. The rack and pinion converts rotational motion to linear motion.

Each specific gear arrangement produces distinct mechanical outcomes based on the ratio of teeth between the driving and driven gears, the number of intermediary gears, and the physical shape of the gears involved.

Adım Adım Çözüm

1

Determine the mechanical properties of the simple train.

Matches with: Torque is multiplied by 4; rotational direction is reversed.

A 15-tooth gear driving a 60-tooth gear has a ratio of 4:1. The driven gear is 4 times larger, multiplying torque by 4. Two meshing gears turn in opposite directions.

2

Determine the mechanical properties of the idler train.

Matches with: Output speed is 4 times the input speed; rotational direction is unchanged.

The 25-tooth idler gear does not change the ratio. The 60-tooth drive gear directly relates to the 15-tooth driven gear, meaning the output is 1/4 the size and spins 4 times as fast. An odd number of gears (3) preserves the rotational direction.

3

Determine the mechanical properties of the compound train.

Matches with: Overall mechanical advantage is 6; final gear rotates in the same direction as the input gear.

Calculate the ratio of each pair: 40/20 = 2, and 30/10 = 3. Multiply them: 2 * 3 = 6. This is the mechanical advantage. There are two gear meshes, causing the direction to reverse twice, returning to the original input direction.

4

Determine the mechanical properties of the rack and pinion.

Matches with: Rotational motion is converted into linear motion.

A round pinion turning against a straight rack is the standard mechanism for converting rotational motion into linear motion.

Anahtar Kavram

Calculating gear ratios and tracking rotational direction across simple, idler, compound, and rack-and-pinion trains.

Soru 1725Soru →

A dentist adjusts a patient's hydraulic examination chair. The system's input piston has a cross-sectional area of $8 \text{ in}^2$ , and the lifting piston beneath the chair has an area of $64 \text{ in}^2$ . If the dentist applies $35 \text{ lbs}$ of force to the input piston, how much upward force is generated by the lifting piston?

Cevabı ve açıklamayı göster

Cevap: 280

Cevap

280

The hydraulic system provides a mechanical advantage equal to the ratio of the two piston areas (

64 / 8 = 8

). Multiplying the input force of

35 \text{ lbs}

by this mechanical advantage yields a total lifting force of

280 \text{ lbs}

.

Adım Adım Çözüm

1

Identify the given variables.

Input area

A_1 = 8 \text{ in}^2

, output area

A_2 = 64 \text{ in}^2

, and input force

F_1 = 35 \text{ lbs}

.

These variables are required to apply Pascal's Principle.

2

Calculate the mechanical advantage (area ratio) of the hydraulic system.

\frac{A_2}{A_1} = \frac{64}{8} = 8

.

The ratio of the output area to the input area determines how much the input force will be multiplied.

3

Calculate the generated output force.

F_2 = F_1 \times \text{Area Ratio} = 35 \text{ lbs} \times 8 = 280 \text{ lbs}

.

Pascal's Principle states that pressure is transmitted equally throughout an enclosed fluid, meaning force increases proportionally with area.

Anahtar Kavram

According to Pascal's Principle, pressure applied to an enclosed fluid is transmitted equally in all directions. In a hydraulic system, this means the ratio of output force to input force is equal to the ratio of output area to input area (

F_1/A_1 = F_2/A_2

).

Tahmini Süre:45s

Soru 1726Soru →

A worker uses a uniform $60$ -inch steel pry bar to lift a $150\text{ lb}$ concrete block. The worker places a pivot exactly $20$ inches from the load end of the bar, configuring it as a first-class lever. If the pry bar itself weighs $20\text{ lbs}$ , how much downward vertical force must the worker apply at the opposite end of the bar to perfectly balance the concrete block?

75\text{ lbs}

300\text{ lbs}

70\text{ lbs}

80\text{ lbs}

Cevabı ve açıklamayı göster

Cevap: $70\text{ lbs}$

Cevap

The correct force required is

70\text{ lbs}

.

To achieve equilibrium, the torques around the pivot must balance. The concrete block creates a counter-clockwise torque of

3000\text{ in-lbs}

(

150\text{ lbs} \times 20\text{ inches}

). The pry bar's weight acts at its center (

30

inches from the end), which places it

10

inches from the pivot on the effort side. This provides an assisting clockwise torque of

200\text{ in-lbs}

(

20\text{ lbs} \times 10\text{ inches}

). The effort force is applied at the very end,

40

inches from the pivot. The equilibrium equation is

3000 = 200 + (F \times 40)

, resolving to

2800 = F \times 40

, which means the required force is

70\text{ lbs}

.

Adım Adım Çözüm

1

Calculate the counter-clockwise torque generated by the concrete block.

150\text{ lbs} \times 20\text{ inches} = 3000\text{ in-lbs}

.

The load is placed

20

inches from the pivot, creating the primary rotational force to overcome.

2

Determine the location of the pry bar's center of gravity and its resulting torque.

The center of the

60

-inch bar is at

30

inches. Since the pivot is at

20

inches, the center of gravity is

10

inches from the pivot on the effort side. Torque =

20\text{ lbs} \times 10\text{ inches} = 200\text{ in-lbs}

(clockwise).

A uniform bar's weight acts at its exact center. Because this center is on the same side of the pivot as the worker's effort, it provides an assisting clockwise torque.

3

Set up the torque equilibrium equation to find the required effort force.

Counter-clockwise Torque = Clockwise Torque

3000 = 200 + (F \times 40)

For the lever to balance, the sum of opposing torques must be equal. The effort arm is the total length minus the load arm (

60 - 20 = 40

inches).

4

Solve the equation for the effort force (

F

).

2800 = F \times 40

, which simplifies to

F = 70\text{ lbs}

.

Isolating

F

gives the exact supplemental force the worker needs to apply to achieve balance.

Anahtar Kavram

Torque Equilibrium Involving Lever Mass

Soru 1727Soru →

Arrange the following material handling tasks in order from the LEAST amount of effort force required to the GREATEST amount of effort force required. (Assume frictionless ramps)

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from least to greatest effort force is: Task A (

30\text{ lbs}

), Task D (

40\text{ lbs}

), Task C (

50\text{ lbs}

), Task B (

60\text{ lbs}

).

Task A requires

30\text{ lbs}

of force, Task D requires

40\text{ lbs}

, Task C requires

50\text{ lbs}

, and Task B requires

60\text{ lbs}

. Ordering these mathematically from lowest to highest yields Task A, Task D, Task C, and Task B.

Adım Adım Çözüm

1

Calculate the Ideal Mechanical Advantage (IMA) for each ramp.

Task A:

12/3 = 4

. Task B:

6/2 = 3

. Task C:

8/4 = 2

. Task D:

5/1 = 5

.

The IMA determines how much the ramp multiplies the applied force, calculated as the length of the ramp divided by its height.

2

Calculate the required effort force for each task.

Task A:

120/4 = 30\text{ lbs}

. Task B:

180/3 = 60\text{ lbs}

. Task C:

100/2 = 50\text{ lbs}

. Task D:

200/5 = 40\text{ lbs}

.

Effort force equals the load's total weight divided by the IMA of the ramp.

3

Order the tasks from least effort to greatest effort.

Task A (

30\text{ lbs}

) < Task D (

40\text{ lbs}

) < Task C (

50\text{ lbs}

) < Task B (

60\text{ lbs}

).

The question specifically asks for the sequence starting with the lowest force and ending with the highest.

Anahtar Kavram

Ideal Mechanical Advantage and Effort Force on an Inclined Plane

Soru 1728Soru →

A homeowner needs to move a $300\text{ lb}$ refrigerator onto a porch that is $2\text{ feet}$ above ground level. They place a straight, frictionless wooden ramp that is $6\text{ feet}$ long from the ground to the porch edge. How much effort force is required to push the refrigerator up the ramp?

150\text{ lbs}

300\text{ lbs}

100\text{ lbs}

900\text{ lbs}

Cevabı ve açıklamayı göster

Cevap: $100\text{ lbs}$

Cevap

100\text{ lbs}

To find the force required to push an object up a frictionless ramp, first find the ramp's Ideal Mechanical Advantage (IMA). The IMA is the ramp's length divided by its vertical height (

6\text{ ft} / 2\text{ ft} = 3

). The effort force needed is the object's weight divided by this mechanical advantage (

300\text{ lbs} / 3 = 100\text{ lbs}

).

Adım Adım Çözüm

1

Calculate the Ideal Mechanical Advantage (IMA) of the ramp.

\text{IMA} = \frac{\text{Length}}{\text{Height}} = \frac{6\text{ ft}}{2\text{ ft}} = 3

The IMA tells us how many times easier the ramp makes the task compared to lifting the object straight up.

2

Calculate the required effort force.

\text{Effort Force} = \frac{\text{Weight}}{\text{IMA}} = \frac{300\text{ lbs}}{3} = 100\text{ lbs}

An inclined plane reduces the necessary force by a factor equal to its mechanical advantage.

Anahtar Kavram

Ideal Mechanical Advantage and Effort Force of an Inclined Plane

Tahmini Süre:1m 0s

Soru 1729Soru →

A worker uses a steel wedge to split a large block of ice. If the worker switches to a longer wedge that has the exact same maximum thickness, which of the following statements correctly describes the result?

It decreases the effort force required to split the ice.

It decreases the total amount of work required to split the ice.

It increases the total frictional force resisting the wedge due to the larger surface area.

It requires a greater effort force because the wedge must be driven a longer distance.

Cevabı ve açıklamayı göster

Cevap: It decreases the effort force required to split the ice.

Cevap

It decreases the effort force required to split the ice.

The ideal mechanical advantage of a wedge is its length divided by its thickness. By increasing the length while keeping the thickness the same, the mechanical advantage increases, which reduces the effort force needed to do the job.

Adım Adım Çözüm

1

Recall the formula for the ideal mechanical advantage (IMA) of a wedge.

IMA = Length / Thickness

This relationship determines how much a wedge multiplies the applied force.

2

Analyze the change in the wedge's dimensions described in the scenario.

The length increases, while the thickness remains exactly the same.

Understanding the variables helps determine the new mechanical advantage.

3

Determine the effect on the effort force.

Since the numerator (length) is larger and the denominator (thickness) is constant, the IMA increases. A higher IMA means less effort force is needed.

An increased mechanical advantage trades a longer distance for a reduced effort force requirement.

Anahtar Kavram

Mechanical Advantage of Wedges

Soru 1730Soru →

A solid machine part is suspended from a spring scale. In the air, the scale reads $60 \text{ N}$ . When the part is completely submerged in water, the scale reads $40 \text{ N}$ . The part is then removed, dried, and completely submerged in a vat of unknown oil, where the scale reads $45 \text{ N}$ . Based on these readings, what is the density of the oil compared to the density of water?

0.75 times the density of water

1.33 times the density of water

0.25 times the density of water

1.13 times the density of water

Cevabı ve açıklamayı göster

Cevap: 0.75 times the density of water

Cevap

The oil is 0.75 times the density of water.

According to Archimedes' principle, buoyant force equals the weight of the displaced fluid (

F_b = \rho \cdot V \cdot g

). The buoyant force in water is

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

. The buoyant force in the oil is

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

. Because the part is fully submerged in both instances, the displaced volume (

V

) is identical. Therefore, the buoyant forces are directly proportional to the fluid densities. The ratio of the oil's density to the water's density is the ratio of their buoyant forces:

15 \text{ N} / 20 \text{ N} = 0.75

.

Adım Adım Çözüm

1

Calculate the buoyant force exerted by the water.

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

The buoyant force is equal to the object's true weight in air minus its apparent weight when submerged.

2

Calculate the buoyant force exerted by the oil.

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

To compare the lifting effect of the two fluids, we need to know the specific buoyant force each exerts on the identical volume.

3

Calculate the ratio of the oil's density to the water's density.

15 \text{ N} / 20 \text{ N} = 0.75

Because the same object is completely submerged in both fluids, the displaced volume is constant. Therefore, the buoyant forces are directly proportional to the densities of the fluids.

Anahtar Kavram

Apparent weight and Archimedes' Principle

Soru 1731Soru →

A steel construction beam has a mass of $120 \text{ kg}$ on Earth, where the gravitational acceleration is approximately $10 \text{ m/s}^2$ . The beam is subsequently transported to a lunar outpost, where the local gravitational acceleration is $1.6 \text{ m/s}^2$ . What is the mass of the beam on the lunar outpost?

19.2 \text{ kg}

192 \text{ kg}

120 \text{ kg}

192 \text{ N}

Cevabı ve açıklamayı göster

Cevap: $120 \text{ kg}$

Cevap

120 \text{ kg}

The correct answer is

120 \text{ kg}

because mass represents the physical amount of matter in the steel beam. This property is invariant and does not change when moved to a different gravitational environment, unlike weight.

Adım Adım Çözüm

1

Identify the quantity requested in the problem.

The question specifically asks for the mass of the beam on the Moon.

Carefully distinguishing between requested mass and weight prevents calculation errors based on gravity.

2

Recall the definition and properties of mass.

Mass is the amount of matter in an object and is an invariant property, meaning it does not change based on location.

Unlike weight, which is a force dependent on the local gravitational acceleration (

W = mg

), mass remains constant universally.

3

Determine the mass on the Moon based on its initial mass.

Since the mass on Earth is

120 \text{ kg}

, the mass on the Moon remains exactly

120 \text{ kg}

.

The change in gravitational acceleration from

10 \text{ m/s}^2

to

1.6 \text{ m/s}^2

affects only the weight of the object, not its mass.

Anahtar Kavram

Mass is an intrinsic, invariant property of an object (measured in kilograms), whereas weight is the location-dependent gravitational force exerted on that mass (measured in Newtons).

Soru 1732Soru →

A technician is analyzing the thread specifications of four different fasteners to determine their linear travel. Assuming all fasteners have single-start threads, arrange them in order from the LEAST to the GREATEST linear distance they will travel into a fixed base for each full $360^\circ$ rotation.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from least to greatest linear travel per rotation is: the machine screw (20 TPI), the wood screw (1/16 inch pitch), the lag bolt (10 TPI), and finally the power screw (0.125 inch lead).

The sequence correctly calculates and compares the linear travel per rotation for each fastener. By converting all specifications to decimal inches (

0.05

in,

0.0625

in,

0.10

in, and

0.125

in), they can be accurately ordered from least to greatest.

Adım Adım Çözüm

1

Define the relationship between threads per inch (TPI), pitch, lead, and linear travel.

For single-start threads, the linear travel per rotation equals the lead, which is equal to the pitch. Pitch can be calculated as

1 \div \text{TPI}

.

Establishing the mathematical formulas is necessary to compare different types of thread specifications on a single scale.

2

Calculate the decimal linear travel for the fasteners specified in TPI.

The machine screw travels

1 \div 20 = 0.05

inches per rotation. The lag bolt travels

1 \div 10 = 0.10

inches per rotation.

Converting TPI into decimal pitch allows for direct numerical comparison.

3

Convert the fractional pitch of the wood screw to a decimal.

The wood screw travels

1 \div 16 = 0.0625

inches per rotation. The power screw is already given as

0.125

inches.

Decimals provide a consistent format for sequential ordering.

4

Compare all decimal values and arrange them from least to greatest.

0.05

(machine screw)

< 0.0625

(wood screw)

< 0.10

(lag bolt)

< 0.125

(power screw).

Finalizes the sequence according to the explicit instructions in the stem.

Anahtar Kavram

The linear distance a screw travels in one full rotation is determined by its lead. For single-start threads, the lead equals the pitch, and the pitch is the reciprocal of the threads per inch (

P = 1 / \text{TPI}

).

Soru 1733Soru →

A special effects crew is dropping various props into a deep gorge for a movie scene. Assuming air resistance is negligible, arrange the following drops in order from the shortest time in the air to the longest time in the air before hitting the bottom.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from shortest to longest fall time is: the 100 kg safe (5 m), the 2 kg camera (20 m), the 50 kg sandbag (45 m), and finally the 10 kg stunt dummy (80 m).

The time an object spends in free fall from rest is determined entirely by the height from which it is dropped, according to the kinematic equation

t = \sqrt{\frac{2d}{g}}

. Because air resistance is negligible in this scenario, the mass of the objects is completely irrelevant. Therefore, arranging the objects from shortest to longest fall time is identical to arranging them from lowest to highest drop height:

5\text{ m}

(safe),

20\text{ m}

(camera),

45\text{ m}

(sandbag), and

80\text{ m}

(dummy).

Adım Adım Çözüm

1

Identify the relevant formula for the time of free fall from rest.

d = \frac{1}{2}gt^2

, which rearranges to

t = \sqrt{\frac{2d}{g}}

.

To determine which variables affect the time an object spends in the air.

2

Analyze the role of mass in the free fall equation.

Mass (

m

) does not appear in the equation.

In the absence of air resistance, all objects accelerate toward Earth at the exact same rate (

g

), regardless of how heavy they are.

3

Compare the heights from which the objects are dropped.

The heights are

5\text{ m}

,

20\text{ m}

,

45\text{ m}

, and

80\text{ m}

.

Since fall time is entirely dependent on the initial height (

d

), the object dropped from the lowest height hits the ground first.

4

Order the objects based on their drop heights from shortest to highest.

Safe (

5\text{ m}

) < Camera (

20\text{ m}

) < Sandbag (

45\text{ m}

) < Dummy (

80\text{ m}

).

A shorter fall distance results in a shorter amount of time spent in the air.

Anahtar Kavram

In a vacuum or when air resistance is negligible, the acceleration due to gravity is constant for all objects. Therefore, the time it takes to fall depends only on the initial height, not the mass.

Soru 1734Soru →

A marine vessel is cruising forward at a constant speed. Its propulsion system uses an internal engine to drive a solid steel shaft, which extends out the rear of the hull to turn the propeller. A heavy-duty thrust bearing inside the ship absorbs the forward driving force generated by the propeller. During this forward motion, what primary combination of internal stresses is the section of the shaft located between the propeller and the thrust bearing experiencing?

Torsion and compression

Torsion and tension

Shear and tension

Shear and compression

Cevabı ve açıklamayı göster

Cevap: Torsion and compression

Cevap

Torsion and compression

The correct answer is torsion and compression because the engine twists the shaft to rotate the propeller (creating torsion), and the forward thrust generated by the propeller pushes the shaft into the internal thrust bearing (creating compression).

Adım Adım Çözüm

1

Identify the stress caused by power transmission.

The engine applies a rotational force to turn the propeller against water resistance, resulting in twisting, which is torsional stress.

Rotational power transmission through a solid shaft always induces torsion.

2

Determine the direction of the thrust force.

To move the ship forward, the propeller pushes water backward. According to Newton's Third Law, the water exerts an equal forward reaction force on the propeller.

Thrust requires an opposing reaction force to generate motion.

3

Analyze how the thrust force affects the shaft.

The forward reaction force on the propeller pushes the shaft forward into the thrust bearing inside the hull. This squeezes the section of the shaft between them, creating compressive stress.

A structural member being squeezed inward from opposite ends is under compression.

Anahtar Kavram

Internal stresses induced by combined rotational and axial loads.

Soru 1735Soru →

A mechanic uses a simple hydraulic lift to raise a motorcycle. The system's input piston has a cross-sectional area of $5 \text{ in}^2$ , and the output (lifting) piston has a cross-sectional area of $50 \text{ in}^2$ . If the mechanic applies a downward force of $40 \text{ lbs}$ on the input piston, what is the upward force exerted by the output piston?

4 \text{ lbs}

40 \text{ lbs}

200 \text{ lbs}

400 \text{ lbs}

Cevabı ve açıklamayı göster

Cevap: $400 \text{ lbs}$

Cevap

The upward force exerted by the output piston is

400 \text{ lbs}

.

According to Pascal's Principle, pressure is transmitted equally throughout a confined fluid. The pressure generated at the input piston is

40 \text{ lbs} / 5 \text{ in}^2 = 8 \text{ psi}

. This exact same pressure acts on the larger

50 \text{ in}^2

output piston, resulting in an upward force of

8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

. Alternatively, using the mechanical advantage ratio:

50 / 5 = 10

, so the output force is

10 \times 40 = 400 \text{ lbs}

.

Adım Adım Çözüm

1

Calculate the pressure exerted by the input piston.

P = \frac{F_{in}}{A_{in}} = \frac{40 \text{ lbs}}{5 \text{ in}^2} = 8 \text{ psi}

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted equally in all directions.

2

Calculate the output force by applying the pressure to the output piston's area.

F_{out} = P \times A_{out} = 8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

The output force is the product of the constant fluid pressure and the area of the output piston.

Anahtar Kavram

Pascal's Principle and Hydraulic Multiplication

Tahmini Süre:45s

Soru 1736Soru →

A motorized mixer uses two meshing gears to adjust the mixing speed. The driving gear, which is attached to the motor, has $12$ teeth and spins at $150$ RPM. It meshes directly with a driven gear that has $36$ teeth. What is the rotational speed of the driven gear in RPM?

Cevabı ve açıklamayı göster

Cevap: 50

Cevap

50

The driven gear has three times as many teeth as the driving gear (

36

vs

12

). Because gears have an inverse relationship between size and speed, the larger driven gear will rotate at one-third the speed of the driving gear (

150 \div 3 = 50

RPM).

Adım Adım Çözüm

1

State the gear speed formula

T_1 \times S_1 = T_2 \times S_2

To establish the inverse relationship between the number of gear teeth and rotational speed

2

Substitute the given values into the formula

12 \times 150 = 36 \times S_2

To set up the equation with the known tooth counts and driving speed

3

Solve for the unknown driven speed (

S_2

)

S_2 = \frac{1800}{36} = 50

To find the final RPM of the driven gear

Anahtar Kavram

The rotational speed of meshing gears is inversely proportional to their number of teeth.

Soru 1737Soru →

An engineer is designing a solid metal support bracket to connect a high-temperature engine block to a heat-sensitive electronic sensor. The primary goal is to minimize the rate of heat transfer through conduction from the engine block to the sensor. Which design modification will best achieve this goal?

Increasing the length of the metal bracket between the engine and the sensor

Increasing the cross-sectional thickness of the metal bracket

Allowing heated engine fluids to circulate directly around the sensor housing

Selecting a metal for the bracket that contracts instead of expands when heated

Cevabı ve açıklamayı göster

Cevap: Increasing the length of the metal bracket between the engine and the sensor

Cevap

Increasing the length of the metal bracket between the engine and the sensor

Increasing the length of the material increases the physical distance over which the temperature drops. Because the rate of heat conduction is inversely proportional to the length of the conductive path, a longer bracket slows down the direct transfer of thermal energy to the sensor.

Adım Adım Çözüm

1

Identify the mode of heat transfer being targeted in the scenario.

The scenario requires minimizing heat transfer via conduction through a solid metal bracket.

Different modes of heat transfer (conduction, convection, radiation) require different physical mitigation strategies.

2

Analyze the physical factors that affect the rate of thermal conduction.

The rate of conduction depends on the material's thermal conductivity, its cross-sectional area, and its length (distance).

Fourier's law of heat conduction dictates these physical relationships.

3

Evaluate how dimensional changes impact the conduction rate.

Increasing length decreases the rate of conduction, whereas increasing cross-sectional area increases the rate of conduction.

A greater length reduces the temperature gradient across the material, slowing the transfer of thermal energy.

Anahtar Kavram

Factors Affecting Thermal Conduction

Tahmini Süre:1m 0s

Soru 1738Soru →

A barber chair uses a closed hydraulic lift mechanism to raise customers. The barber operates a foot pedal connected to an input cylinder with a cross-sectional area of $4 \text{ in}^2$ . The chair is mounted on a larger output cylinder with a cross-sectional area of $80 \text{ in}^2$ . If the total weight of the chair and the customer is $320 \text{ lbs}$ , how much downward force must the barber apply to the input cylinder to lift the load?

4 \text{ lbs}

16 \text{ lbs}

1280 \text{ lbs}

6400 \text{ lbs}

Cevabı ve açıklamayı göster

Cevap: $16 \text{ lbs}$

Cevap

The barber must apply

16 \text{ lbs}

of force.

The correct answer applies Pascal's Principle, which indicates that the mechanical advantage of a hydraulic system is determined by the ratio of the piston areas. The output cylinder is

20

times larger than the input cylinder (

80 / 4 = 20

). Therefore, the input force only needs to be

1/20

th of the output load. Dividing the

320 \text{ lbs}

load by

20

yields an input force requirement of

16 \text{ lbs}

.

Adım Adım Çözüm

1

Identify the given values for the hydraulic system.

Input area (

A_1

) =

4 \text{ in}^2

, Output area (

A_2

) =

80 \text{ in}^2

, Output force/load (

F_2

) =

320 \text{ lbs}

.

Organizing known variables is the first step in solving a Pascal's Principle problem.

2

State Pascal's Principle equation relating force and area.

\frac{F_1}{A_1} = \frac{F_2}{A_2}

Pascal's Principle dictates that pressure is transmitted equally throughout a confined incompressible fluid.

3

Rearrange the formula to solve for the unknown input force (

F_1

).

F_1 = F_2 \times \left(\frac{A_1}{A_2}\right)

Isolating

F_1

prepares the equation for direct substitution.

4

Substitute the known values and calculate.

F_1 = 320 \times \left(\frac{4}{80}\right) = 320 \times \left(\frac{1}{20}\right) = 16 \text{ lbs}

.

Performing the arithmetic reveals the exact force required at the pedal.

Anahtar Kavram

Pascal's Principle states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid. In a hydraulic system, a small force applied over a small area can lift a large weight over a proportionally larger area.

Soru 1739Soru →

A carpenter uses a wooden wedge as a doorstop to hold a heavy door open. The wedge has a length of $15\text{ cm}$ and a maximum thickness of $3\text{ cm}$ . What is the ideal mechanical advantage (IMA) of this wedge?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The ideal mechanical advantage is 5.

The ideal mechanical advantage of a wedge is found by dividing its length (the distance the wedge penetrates) by its maximum thickness (the distance the object is separated). For a wedge with a length of

15\text{ cm}

and a thickness of

3\text{ cm}

, the mechanical advantage is calculated as

15 / 3 = 5

.

Adım Adım Çözüm

1

Identify the given dimensions of the wedge.

Length (

L

) =

15\text{ cm}

, Thickness (

t

) =

3\text{ cm}

.

These values are required to calculate the mechanical advantage.

2

Apply the formula for the ideal mechanical advantage of a wedge.

IMA = \frac{L}{t} = \frac{15}{3} = 5

.

The IMA is the ratio of the effort distance (length) to the resistance distance (thickness).

Anahtar Kavram

Ideal Mechanical Advantage of a Wedge

Soru 1740Soru →

A rigid horizontal strut extends outward from a vertical building wall to support a heavy sign. The outer end of the strut is supported by a diagonal steel cable anchored to the wall above. The inner end of the strut is connected to a wall bracket using a heavy-duty steel pin. When the sign's weight is applied to the outer end of the strut, what primary types of internal mechanical stress are experienced by the diagonal cable, the horizontal strut, and the steel pin, respectively?

Cable: Tension; Strut: Compression; Pin: Shear

Cable: Tension; Strut: Tension; Pin: Compression

Cable: Compression; Strut: Tension; Pin: Shear

Cable: Tension; Strut: Compression; Pin: Tension

Cevabı ve açıklamayı göster

Cevap: Cable: Tension; Strut: Compression; Pin: Shear

Cevap

The correct answer identifies the cable under tension, the strut under compression, and the pin under shear.

The correct answer accurately evaluates the stress on all three components. The diagonal cable must stretch to hold up the heavy sign, placing it under tension. This tension has an inward horizontal pull, which squeezes the horizontal strut against the wall, creating compressive stress. Finally, the downward weight acting on the wall bracket tries to slide or slice perpendicularly across the steel pin, subjecting it to shear stress.

Adım Adım Çözüm

1

Analyze the forces acting on the diagonal cable.

The cable must pull upward and backward toward the wall to support the downward weight of the sign.

Supporting a downward load from above requires an upward pulling force, which stretches the material and creates tension.

2

Analyze the forces acting on the horizontal strut.

The inward horizontal component of the cable's tension pulls the outer end of the strut firmly against the wall.

Because the strut is being squeezed between the cable's attachment point and the wall bracket, it experiences compressive stress.

3

Analyze the forces acting on the wall bracket pin.

The downward weight of the strut and load pushes perpendicularly against the cross-section of the connecting pin.

Forces acting parallel to the cross-section of a fastener, trying to slice through it, cause shear stress.

Anahtar Kavram

Identifying applied structural loads (Tension, Compression, Shear)

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