Tüm alıştırma soruları

Soru 181Soru →

In a naval shipboard direct-current monitoring circuit, a $75\text{ }\Omega$ dummy load resistor dissipates electrical energy during transmitter testing. If a steady current of $4\text{ A}$ flows through this resistor, what is the total electrical power dissipated by the resistor, in watts?

Cevabı ve açıklamayı göster

Cevap: 1200

Cevap

The total electrical power dissipated by the resistor is

1200\text{ W}

.

According to Watt's Law, power dissipated in a resistor when current and resistance are known is calculated using the formula

P = I^2 R

. Squaring the current (

4\text{ A}

) gives

16\text{ A}^2

, and multiplying by the resistance of

75\text{ }\Omega

produces an electrical power dissipation of

1200\text{ W}

.

Adım Adım Çözüm

1

Identify the known circuit parameters

Current

I = 4\text{ A}

and resistance

R = 75\text{ }\Omega

These are the two independent circuit variables required to calculate electrical power using Watt's Law.

2

Apply Watt's power formula relating current and resistance

P = I^2 \times R

When voltage is not directly given, electrical power can be found directly from the square of the current multiplied by the resistance.

3

Compute the numerical power dissipation

P = (4\text{ A})^2 \times 75\text{ }\Omega = 16 \times 75 = 1200\text{ W}

Evaluating

(4)^2 = 16

and multiplying by

75

yields the total power in watts.

Anahtar Kavram

Electrical power dissipation in a resistive component using Watt's Law (

P = I^2 R

)

Tahmini Süre:1m 0s

Soru 182Soru →

A shipboard auxiliary alarm horn is connected across a $72\text{ V}$ direct-current (DC) power rail. When activated, the horn draws a steady current of $120\text{ mA}$ . Based on Ohm's Law, what is the total electrical resistance of the horn circuit in ohms ( $\Omega$ )?

Cevabı ve açıklamayı göster

Cevap: 600

Cevap

The total electrical resistance of the horn circuit is

600\ \Omega

.

According to Ohm's Law, resistance equals voltage divided by current (

R = \frac{V}{I}

). Converting

120\text{ mA}

to standard amperes gives

0.12\text{ A}

. Dividing

72\text{ V}

by

0.12\text{ A}

yields an electrical resistance of

600\ \Omega

.

Adım Adım Çözüm

1

Convert the current measurement from milliamperes to base amperes.

I = 120\text{ mA} = 0.12\text{ A}

Ohm's Law requires standard SI units (volts, amperes, and ohms) for direct substitution.

2

Rearrange Ohm's Law (

V = I \times R

) to isolate resistance (

R

).

R = \frac{V}{I}

The unknown quantity in this circuit problem is resistance.

3

Divide the applied voltage by the circuit current.

R = \frac{72\text{ V}}{0.12\text{ A}} = 600\ \Omega

Evaluating the division yields the equivalent circuit resistance in ohms.

Anahtar Kavram

Ohm's Law defines the proportional relationship between voltage, current, and resistance (

R = \frac{V}{I}

).

Tahmini Süre:45s

Soru 183Soru →

A bench technician uses a $100\text{ k}\Omega$ linear potentiometer as an adjustable control element in a circuit. If the wiper is adjusted to $75\%$ of its full mechanical travel away from the lower reference terminal, what is the resulting resistance between the wiper and the upper terminal in kilo-ohms ( $\text{k}\Omega$ )?

Cevabı ve açıklamayı göster

Cevap: 25

Cevap

25 kilo-ohms (

25\text{ k}\Omega

)

In a linear-taper potentiometer, the total end-to-end resistance (

100\text{ k}\Omega

) is distributed uniformly across the resistive track between the outer fixed terminals. When the wiper is moved

75\%

of the travel distance from the lower terminal, the remaining segment between the wiper and the upper terminal comprises

25\%

(

100\% - 75\%

) of the total resistance. Multiplying

100\text{ k}\Omega \times 0.25

gives

25\text{ k}\Omega

.

Adım Adım Çözüm

1

Find the percentage of the resistive element situated between the wiper contact and the upper terminal.

100\% - 75\% = 25\%

The total resistive track spans

100\%

of the component's resistance between its two outer end terminals.

2

Calculate the resistance across this upper portion of the track.

100\text{ k}\Omega \times 0.25 = 25\text{ k}\Omega

Because the potentiometer is linear, resistance is directly proportional to the physical position of the wiper along the track.

Anahtar Kavram

Linear potentiometer terminal division and wiper position relationships

Alternatif Yöntem

Calculate the resistance from the lower terminal to the wiper first (

100\text{ k}\Omega \times 0.75 = 75\text{ k}\Omega

), and subtract that value from the total resistance:

100\text{ k}\Omega - 75\text{ k}\Omega = 25\text{ k}\Omega

.

Tahmini Süre:45s

Soru 184Soru →

A direct-current sensor heating element has an internal resistance of $12\text{ }\Omega$ and carries a steady current of $2.5\text{ A}$ . What is the electrical power dissipated by the heating element, in watts?

Cevabı ve açıklamayı göster

Cevap: 75

Cevap

The electrical power dissipated by the heating element is

75\text{ W}

.

Electrical power dissipated by a resistive element is calculated using Watt's Law as

P = I^2 R

. Squaring the current of

2.5\text{ A}

yields

6.25\text{ A}^2

, and multiplying by the resistance of

12\text{ }\Omega

results in

75\text{ W}

.

Adım Adım Çözüm

1

Identify the known circuit parameters

I = 2.5\text{ A}

and

R = 12\text{ }\Omega

These are the two direct measurements provided for the resistive load.

2

Select the appropriate power formula

P = I^2 R

Watt's Law specifies that power dissipation through a resistance carrying a known current equals the square of the current multiplied by the resistance.

3

Calculate the power dissipation

P = (2.5\text{ A})^2 \times 12\text{ }\Omega = 6.25 \times 12 = 75\text{ W}

Squaring

2.5

gives

6.25

, and multiplying

6.25

by

12

produces

75

watts.

Anahtar Kavram

Calculating electrical power using current and resistance (

P = I^2 R

)

Tahmini Süre:1m 0s

Soru 185Soru →

An avionics technician is troubleshooting a direct-current (DC) audio preamplifier circuit. The circuit is powered by an $18\text{ V}$ DC source and draws a steady current of $2.5\text{ mA}$ . What is the total resistance of the circuit in kilohms ( $\text{k}\Omega$ )?

Cevabı ve açıklamayı göster

Cevap: 7.2

Cevap

7.2 kΩ

According to Ohm's Law, resistance is determined by dividing voltage by current (

R = \frac{V}{I}

). Converting

2.5\text{ mA}

to

0.0025\text{ A}

and dividing

18\text{ V}

by

0.0025\text{ A}

yields

7200\ \Omega

, which equals

7.2\text{ k}\Omega

.

Adım Adım Çözüm

1

Convert the current measurement from milliamperes (mA) to base amperes (A)

I = 2.5\text{ mA} = 0.0025\text{ A}

Ohm's Law formulas require electrical quantities to be in standard base units (volts, amperes, and ohms) before computation.

2

Apply Ohm's Law rearranged to solve for resistance (

R = \frac{V}{I}

)

R = \frac{18\text{ V}}{0.0025\text{ A}} = 7200\ \Omega

Resistance equals the electromotive force divided by the resulting current flow.

3

Convert the calculated resistance from ohms (Ω) to kilohms (kΩ)

R = \frac{7200\ \Omega}{1000\ \Omega/\text{k}\Omega} = 7.2\text{ k}\Omega

The question specifically requests the final numerical value in kilohms.

Anahtar Kavram

Ohm's Law (

R = \frac{V}{I}

) with metric prefix conversion (

1\text{ mA} = 10^{-3}\text{ A}

and

1\text{ k}\Omega = 10^{3}\ \Omega

)

Tahmini Süre:45s

Soru 186Soru →

A supply sergeant is organizing a crate of $150$ signal flares. The crate contains $50$ red flares, $40$ green flares, $36$ yellow flares, and the remaining flares are white. If a recruit randomly selects one flare from the crate without looking, what is the probability that they select a white flare? Express your answer as a decimal.

Cevabı ve açıklamayı göster

Cevap: 0.16

Cevap

0.16

The correct probability is found by first determining the number of white flares (

150 - 126 = 24

), and then dividing that number by the total number of flares to find the probability of a single event (

24 \div 150 = 0.16

).

Adım Adım Çözüm

1

Calculate the total number of red, green, and yellow flares.

50 + 40 + 36 = 126

This is required to find out how many flares are in the known color categories.

2

Calculate the number of white flares.

150 - 126 = 24

Subtracting the other flares from the total gives the remaining white flares.

3

Calculate the probability of selecting a white flare.

\frac{24}{150}

Probability is the number of favorable outcomes (white flares) divided by the total number of possible outcomes (total flares).

4

Convert the fraction to a decimal.

\frac{24}{150} = \frac{4}{25} = 0.16

The question specifically asks for the answer to be expressed as a decimal.

Anahtar Kavram

Single Event Probability

Tahmini Süre:1m 0s

Soru 187Soru →

A carbon-film resistor has four distinct color bands in sequence: Red, Violet, Orange, and Gold. What is the minimum acceptable resistance of this resistor in kilohms ( $\text{k}\Omega$ ) based on its color code and tolerance rating?

Cevabı ve açıklamayı göster

Cevap: 25.65

Cevap

The minimum acceptable resistance is 25.65 kilohms (kΩ).

According to the standard EIA 4-band resistor color code, Red = 2, Violet = 7, Orange = multiplier 10^3 (1,000), and Gold = ±5% tolerance. The nominal resistance is 27 × 1,000 Ω = 27,000 Ω = 27 kΩ. The allowable variation is 5% of 27 kΩ, which is 1.35 kΩ. Subtracting this from the nominal value gives a minimum acceptable resistance of 27 kΩ - 1.35 kΩ = 25.65 kΩ.

Adım Adım Çözüm

1

Identify the significant digits from the first two color bands.

Red represents 2 and Violet represents 7, forming the base number 27.

In standard 4-band resistor color codes, the first two bands represent the first two significant figures.

2

Apply the decimal multiplier from the third color band and convert to kilohms.

Orange represents a multiplier of 10^3 (1,000), giving a nominal value of 27 × 1,000 Ω = 27,000 Ω = 27 kΩ.

The third band indicates the power of ten by which the significant digits are multiplied.

3

Calculate the tolerance value based on the fourth band.

Gold indicates a ±5% tolerance. 5% of 27 kΩ is 0.05 × 27 kΩ = 1.35 kΩ.

The fourth band specifies the allowable percentage deviation from the nominal resistance value.

4

Compute the lower limit of the allowable resistance range.

27 kΩ - 1.35 kΩ = 25.65 kΩ.

The minimum acceptable value is obtained by subtracting the allowable tolerance from the nominal resistance.

Anahtar Kavram

Four-Band Resistor Color Code and Tolerance Calculation

Alternatif Yöntem

Calculate the minimum multiplier directly: 27 kΩ × (1 - 0.05) = 27 kΩ × 0.95 = 25.65 kΩ.

Tahmini Süre:45s

Soru 188Soru →

A technician is using a standard dial caliper to measure the outside diameter of a steel sleeve. The main beam graduated in tenths of an inch shows a reading of $2.300\text{ inches}$ , and the dial indicator reads $0.045\text{ inches}$ . What is the total measured outside diameter of the sleeve in inches?

Cevabı ve açıklamayı göster

Cevap: 2.345

Cevap

The total measured outside diameter of the steel sleeve is

2.345\text{ inches}

.

To determine the total dimension on a dial caliper, the value from the main beam scale is added directly to the value shown on the dial indicator. Adding

2.300\text{ inches}

from the beam to

0.045\text{ inches}

from the dial indicator gives a total reading of

2.345\text{ inches}

.

Adım Adım Çözüm

1

Read the measurement indicated on the main beam scale

Main beam reading is

2.300\text{ inches}

The main beam of a dial caliper provides the coarse measurement in inches and tenths of an inch.

2

Read the measurement indicated on the dial face

Dial indicator reading is

0.045\text{ inches}

The dial needle indicates thousandths of an inch to provide precision beyond the beam scale.

3

Add the beam scale reading to the dial indicator reading

2.300\text{ inches} + 0.045\text{ inches} = 2.345\text{ inches}

Total measurement on a dial caliper is the direct sum of the beam graduation and the dial pointer value.

Anahtar Kavram

Reading and summing values from a dial caliper beam and dial indicator

Tahmini Süre:45s

Soru 189Soru →

An aircraft pitot tube heating element has an internal electrical resistance of $40\text{ }\Omega$ and connects directly to a $120\text{ V}$ direct-current (DC) power system. What is the electrical power dissipated by the heater, in watts ( $\text{W}$ )?

Cevabı ve açıklamayı göster

Cevap: 360

Cevap

The heating element dissipates

360\text{ W}

of electrical power.

Electrical power (

P

) dissipated by a resistive element when voltage (

V

) and resistance (

R

) are known is given by Watt's Law:

P = \frac{V^2}{R}

. Substituting

V = 120\text{ V}

and

R = 40\text{ }\Omega

gives

P = \frac{120^2}{40} = \frac{14{}400}{40} = 360\text{ W}

.

Adım Adım Çözüm

1

State the given circuit parameters

V = 120\text{ V}

,

R = 40\text{ }\Omega

These are the known electrical quantities provided in the problem stem.

2

Select the appropriate power formula derived from Ohm's Law and Watt's Law

P = \frac{V^2}{R}

Power can be directly calculated from voltage and resistance without needing to solve for current first.

3

Substitute the values into the formula and solve for power

P = \frac{(120)^2}{40} = \frac{14{}400}{40} = 360\text{ W}

Carrying out the arithmetic yields the total electrical power converted into thermal energy.

Anahtar Kavram

Calculating electrical power from voltage and resistance using Watt's Law (

P = \frac{V^2}{R}

)

Tahmini Süre:1m 0s

Soru 190Soru →

A four-band resistor has color bands in the following sequence: Orange, White, Red, and Silver. Based on this color code, what is the maximum acceptable resistance value for this component in ohms ( $\Omega$ )?

Cevabı ve açıklamayı göster

Cevap: 4290

Cevap

The maximum acceptable resistance value for the resistor is

4290\ \Omega

.

The first band (Orange) equals 3, the second band (White) equals 9, and the third band (Red) represents a multiplier of 100 (

10^2

), giving a nominal resistance of

3900\ \Omega

. The fourth band (Silver) specifies a

\pm 10\%

tolerance. Ten percent of

3900\ \Omega

is

390\ \Omega

, so the maximum acceptable resistance value is

3900 + 390 = 4290\ \Omega

.

Adım Adım Çözüm

1

Decode the first two significant digit color bands.

Orange = 3, White = 9, giving base digits 39.

Standard four-band resistors use the first two bands to establish the two most significant digits.

2

Apply the multiplier from the third color band.

Red =

10^2 = 100

, so

R_{\text{nominal}} = 39 \times 100 = 3900\ \Omega

.

The third band indicates the power of ten multiplier applied to the significant digits.

3

Calculate the upper limit of the resistance range using the tolerance band.

Silver =

\pm 10\%

. Maximum limit

= 3900 + (0.10 \times 3900) = 3900 + 390 = 4290\ \Omega

.

The fourth band specifies the allowable percentage deviation from nominal resistance, and the maximum limit requires adding the tolerance value.

Anahtar Kavram

Standard four-band resistor color code decoding and percentage tolerance range calculation.

Tahmini Süre:45s

Soru 191Soru →

A supply room contains 25 identical-looking computer mice, of which 10 are wireless and 15 are wired. If an IT technician randomly selects two mice from the room one after the other without replacement, what is the probability that both selected mice are wireless? (Express your answer as a decimal.)

Cevabı ve açıklamayı göster

Cevap: 0.15

Cevap

0.15

The correct answer is found by multiplying the probability of the first event by the conditional probability of the second event. First draw:

\frac{10}{25}

. Second draw:

\frac{9}{24}

. Multiplying these gives

\frac{90}{600}

, which simplifies exactly to

0.15

.

Adım Adım Çözüm

1

Determine the probability of the first event.

The probability of drawing the first wireless mouse is

\frac{10}{25}

.

There are 10 target items (wireless mice) out of 25 total items.

2

Determine the probability of the second event given the first event occurred.

The probability of drawing a second wireless mouse is

\frac{9}{24}

.

Because the selection is without replacement, one wireless mouse has been removed, leaving 9 wireless mice out of 24 total mice.

3

Calculate the compound probability.

\frac{10}{25} \times \frac{9}{24} = 0.15

For dependent events occurring in sequence, multiply the probability of the first event by the conditional probability of the second event.

Anahtar Kavram

Compound Probability (Dependent Events)

Tahmini Süre:1m 0s

Soru 192Soru →

A carpenter is calculating material quantities for a framing project. What is the total number of board feet in a single piece of lumber measuring $2\text{ inches}$ thick, $6\text{ inches}$ wide, and $10\text{ feet}$ long?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10 board feet

The correct answer is 10 board feet. Applying the standard trade formula

\text{Board Feet} = \frac{\text{Thickness (in.)} \times \text{Width (in.)} \times \text{Length (ft.)}}{12}

gives

\frac{2 \times 6 \times 10}{12} = \frac{120}{12} = 10\text{ board feet}

.

Adım Adım Çözüm

1

State the standard board foot calculation formula when length is measured in feet.

\text{Board Feet} = \frac{\text{Thickness (inches)} \times \text{Width (inches)} \times \text{Length (feet)}}{12}

One board foot represents a volume of 144 cubic inches (equivalent to a board 1 inch thick, 12 inches wide, and 1 foot long).

2

Substitute thickness = 2 in., width = 6 in., and length = 10 ft into the formula.

\text{Board Feet} = \frac{2 \times 6 \times 10}{12} = \frac{120}{12}

Calculates the total cross-sectional area and length ratio to convert to board feet.

3

Divide 120 by 12.

10 board feet

Completes the arithmetic evaluation.

Anahtar Kavram

Calculating board footage of dimensional lumber

Tahmini Süre:45s

Soru 193Soru →

In a small vehicle's hydraulic braking system, a driver applies an input force of $30 \text{ lbs}$ to the master cylinder piston. The master cylinder piston has a cross-sectional area of $1 \text{ in}^2$ . If the brake caliper piston has a cross-sectional area of $4 \text{ in}^2$ , what is the resulting output force applied by the brake caliper piston?

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

120

According to Pascal's Principle, pressure is transmitted equally throughout an enclosed fluid. Because the brake caliper piston has an area 4 times larger than the master cylinder piston, it will multiply the input force by a factor of 4, resulting in 120 lbs of output force.

Adım Adım Çözüm

1

Calculate the fluid pressure created by the master cylinder.

P = \frac{30 \text{ lbs}}{1 \text{ in}^2} = 30 \text{ psi}

Pressure is defined as force divided by area.

2

Calculate the output force at the brake caliper using Pascal's Principle.

F_2 = 30 \text{ psi} \times 4 \text{ in}^2 = 120 \text{ lbs}

Pascal's Principle states that the 30 psi pressure is transmitted undiminished to the 4 sq in output piston.

Anahtar Kavram

Pascal's Principle and Mechanical Advantage in Hydraulics

Tahmini Süre:45s

Soru 194Soru →

A hiker accidentally knocks a rock off the edge of a steep cliff. Assuming there is no air resistance and the acceleration due to gravity is $10\text{ m/s}^2$ , how fast is the rock traveling exactly $3$ seconds after it begins to fall?

Cevabı ve açıklamayı göster

Cevap: 30

Cevap

30

In free fall with no air resistance, an object's speed increases by the acceleration of gravity each second. After

3

seconds of accelerating at

10\text{ m/s}^2

, the speed is exactly

30\text{ m/s}

.

Adım Adım Çözüm

1

Identify the relevant formula

v = gt

The rock starts from rest, so its speed depends only on gravitational acceleration multiplied by the elapsed time.

2

Substitute the given values into the formula

v = 10 \times 3 = 30

Gravity accelerates the object by

10\text{ m/s}^2

for every second it falls.

Anahtar Kavram

Velocity of an object in free fall increases linearly with time based on gravitational acceleration.

Soru 195Soru →

A lead screw on a lathe has 8 threads per inch (TPI). How far, in inches, will the carriage move if the screw is turned exactly 12 full revolutions?

Cevabı ve açıklamayı göster

Cevap: 1.5

Cevap

1.5

Because the screw has 8 threads per inch, completing one full revolution advances the screw exactly 1/8 of an inch (0.125 inches). Turning the screw 12 times results in a total linear movement of 12 * 0.125 = 1.5 inches.

Adım Adım Çözüm

1

Determine the pitch of the screw.

Pitch = 1 / 8 = 0.125 inches per revolution.

Pitch is the linear distance a screw travels in one complete revolution, which is the inverse of the TPI (Threads Per Inch).

2

Calculate the total linear distance traveled.

Distance = 0.125 inches/revolution * 12 revolutions = 1.5 inches.

Total distance is the product of the distance per revolution and the number of full revolutions.

Anahtar Kavram

The relationship between Threads Per Inch (TPI), pitch, and linear travel distance of a screw mechanism.

Alternatif Yöntem

Set up a proportion based on the definition of TPI: If 8 revolutions move the carriage 1 inch (since there are 8 threads in one inch), then 12 revolutions will move it 12 / 8 = 1.5 inches.

Tahmini Süre:45s

Soru 196Soru →

A delivery crew needs to load a $600\text{ lb}$ safe into the back of a moving truck that sits $4\text{ ft}$ above the ground. They deploy a straight, uniform ramp that is $16\text{ ft}$ long. Assuming friction is negligible, what is the ideal effort force, in pounds, required to push the safe up the ramp?

Cevabı ve açıklamayı göster

Cevap: 150

Cevap

150

By using a ramp, the distance over which the force is applied increases, which proportionally decreases the required force. A 16-foot ramp lifting an object 4 feet provides a mechanical advantage of 4 (16 divided by 4). Therefore, pushing a 600-pound load requires only one-quarter of the weight in force, which is 150 pounds.

Adım Adım Çözüm

1

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

IMA = 16 / 4 = 4

The mechanical advantage of an inclined plane is the ratio of its length to its vertical height.

2

Calculate the ideal effort force required to move the load.

Effort Force = 600 / 4 = 150 lbs

The required effort force is the total load divided by the mechanical advantage.

Anahtar Kavram

Ideal Mechanical Advantage of an Inclined Plane

Soru 197Soru →

A logistics team needs to roll a heavy generator weighing $900\text{ lbs}$ from the ground onto a raised platform that is $5\text{ feet}$ high. If the team can apply a maximum combined push force of $150\text{ lbs}$ parallel to the ramp surface, what is the minimum ramp length required to accomplish this task? Assume ideal conditions with zero friction.

Cevabı ve açıklamayı göster

Cevap: 30

Cevap

The minimum ramp length required is

30\text{ feet}

.

In an ideal frictionless system, the ratio of the load force to the effort force equals the ratio of the ramp length to its height. A load of

900\text{ lbs}

requiring only

150\text{ lbs}

of effort means the system needs a mechanical advantage of

6

. Since the height is

5\text{ feet}

, the ramp must be

6

times longer than the height, which is

30\text{ feet}

.

Adım Adım Çözüm

1

Calculate the required Ideal Mechanical Advantage (IMA).

IMA = \frac{\text{Load}}{\text{Effort}} = \frac{900\text{ lbs}}{150\text{ lbs}} = 6

The mechanical advantage indicates how many times the machine multiplies the effort force. We need a mechanical advantage of 6 to move the

900\text{ lbs}

load with only

150\text{ lbs}

of force.

2

Calculate the required ramp length using the IMA and the given height.

IMA = \frac{\text{Length}}{\text{Height}} \Rightarrow 6 = \frac{\text{Length}}{5\text{ feet}} \Rightarrow \text{Length} = 6 \times 5 = 30\text{ feet}

For an inclined plane in ideal conditions, the mechanical advantage is also the ratio of the ramp's length to its vertical height.

Anahtar Kavram

The relationship between effort force, load, ramp length, and vertical height on an ideal inclined plane (Ideal Mechanical Advantage).

Tahmini Süre:1m 30s

Soru 198Soru →

A hydraulic theater stage lift is used to raise a heavy set piece. The output piston supporting the stage has a cross-sectional area of $120 \text{ in}^2$ , while the input piston connected to the control system has an area of $8 \text{ in}^2$ . If the set piece and stage exert a combined downward force of $2,400 \text{ lbs}$ on the output piston, how much input force, in pounds, must be applied to the input piston to hold the stage steady?

Cevabı ve açıklamayı göster

Cevap: 160

Cevap

160

Based on Pascal's Principle, an enclosed fluid transmits pressure equally. The stage creates a pressure of

20 \text{ psi}

(

2,400 \text{ lbs} / 120 \text{ in}^2

). Because this

20 \text{ psi}

is transmitted to the input piston, which has an area of

8 \text{ in}^2

, the required force is

20 \text{ psi} \times 8 \text{ in}^2 = 160 \text{ lbs}

.

Adım Adım Çözüm

1

State Pascal's Principle for the system.

P_{in} = P_{out}

, meaning

\frac{F_{in}}{A_{in}} = \frac{F_{out}}{A_{out}}

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

2

Calculate the pressure at the output piston.

P = \frac{2,400 \text{ lbs}}{120 \text{ in}^2} = 20 \text{ psi}

This establishes the uniform pressure throughout the entire hydraulic system.

3

Calculate the required input force.

F_{in} = P \times A_{in} = 20 \text{ psi} \times 8 \text{ in}^2 = 160 \text{ lbs}

Applying the system pressure to the smaller area of the input piston yields the necessary input force.

Anahtar Kavram

Pascal's Principle and Mechanical Advantage

Soru 199Soru →

In a specialized heavy-duty hydraulic system, the master cylinder has a piston diameter of $2 \text{ cm}$ and the lifting cylinder has a piston diameter of $10 \text{ cm}$ . If the master cylinder piston is pushed through a total stroke distance of $75 \text{ cm}$ , how far, in cm, will the lifting cylinder piston move?

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Cevap: 3

Cevap

3

In a closed hydraulic system, the volume of fluid displaced by the input piston must equal the volume of fluid that moves the output piston. Because volume is the product of the piston's cross-sectional area and its stroke distance (

V = A \times d

), and area is proportional to the square of the diameter (

A \propto D^2

), the distance moved is inversely proportional to the square of the diameter. The lifting cylinder has a diameter

5

times larger than the master cylinder (

10 / 2 = 5

), which means its area is

25

times larger (

5^2 = 25

). Therefore, to conserve fluid volume, the lifting piston will move

1/25

of the distance of the master piston. Dividing the master piston's distance of

75 \text{ cm}

by

25

gives an output distance of

3 \text{ cm}

.

Adım Adım Çözüm

1

State the principle of volume conservation for incompressible fluids.

V_{in} = V_{out}

In a closed hydraulic system, the volume of fluid pushed by the input piston must equal the volume displacing the output piston.

2

Express volume in terms of piston diameter and stroke distance.

V \propto D^2 \times d

Volume equals cross-sectional area times distance, and area is proportional to the square of the diameter.

3

Set up the equation using the given values.

2^2 \times 75 = 10^2 \times d_{out}

Substituting

D_{in} = 2

,

d_{in} = 75

, and

D_{out} = 10

allows us to solve for the unknown output distance.

4

Simplify and solve for the output distance.

300 = 100 \times d_{out} \rightarrow d_{out} = 3

Basic algebra isolates the variable to find the final distance.

Anahtar Kavram

Hydraulic volumetric conservation and area-distance tradeoffs

Soru 200Soru →

A construction worker on a tall scaffolding accidentally drops a heavy steel wrench. Assuming there is no air resistance and the acceleration due to gravity is $32\text{ ft/s}^2$ , the wrench hits the ground after exactly $4$ seconds. What is the height from which the wrench was dropped, in feet?

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Cevap: 256

Cevap

The wrench was dropped from a height of 256 feet.

The height of the drop is found by calculating the total distance the wrench falls in 4 seconds under the continuous influence of gravity. Using the standard kinematic equation for an object dropped from rest,

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

, and the given gravitational acceleration of

32\text{ ft/s}^2

, the calculation is

0.5 \times 32 \times (4^2) = 16 \times 16 = 256

feet.

Adım Adım Çözüm

1

Identify the known variables from the problem statement.

Initial velocity

v_i = 0

, time

t = 4\text{ s}

, gravity

g = 32\text{ ft/s}^2

.

Establishing the knowns is required to select the appropriate kinematic formula for free fall.

2

Select the correct formula for calculating the distance fallen.

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

This formula calculates distance when an object accelerates uniformly from rest.

3

Substitute the known values into the equation and perform the calculation.

d = 0.5 \times 32 \times 16 = 256

To compute the final numerical distance.

Anahtar Kavram

Calculating distance in free fall using gravitational acceleration

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