Given a system described by
*****System is shown in the image****
(a) Write the transfer function H(s)
(b) Give the steady state forced response for the unit step forcing function (i.e. the
input), where � = 2, � = 0.4, and � = −2 , and � = 10.
(c) Give the complete solution (transient and steady state) for � � = �!!! sin 4�.
Answers
Where the above system of equation is given,
a) the transfer function H(s) is: H(s) = Y(s)/K = 1/s / [τ²s² + 2τζs + 1]
b) the steady state forced response:α = -ζτ + τ√(ζ² - 1) = -1.2
β = -ζτ - τ√(ζ² - 1) = -0.133
h(t) = (1/(α - β)) * [e^(1.2t) - e^(0.133t)] u(t); where u(t) is the unit step function.
c) The complete solution is:
y(t) = e^(-0.4t) (0.437 sin(0.916t) - 8.627 e¹¹ / (1 + 16τ²) sin(4t) + 0.459 e¹¹ / (1 + 16τ²) cos(4t))
What is the working for the above solution?
(a) To write the transfer function H(s), we can take the Laplace transform of the differential equation:
τ²[s²Y(s) - s*y(0) - y'(0)] + 2τζ[sY(s) - y(0)] + Y(s) = K/s
Rearranging and solving for Y(s), we get:
Y(s) = K/s / [τ²s² + 2τζs + 1]
Therefore, the transfer function H(s) is:
H(s) = Y(s)/K = 1/s / [τ²s² + 2τζs + 1]
(b) To find the steady state forced response for the unit step forcing function, we can set K = 1/s and take the inverse Laplace transform of the transfer function H(s):
h(t) = L⁻¹[H(s)] = L⁻¹[1/s / (τ²s² + 2τζs + 1)]
We can use partial fraction expansion to simplify the inverse Laplace transform:
1 / (τ²s² + 2τζs + 1) = A/(s + α) + B/(s + β)
where α and β are the roots of the denominator, given by:
α,β = (-2τζ ± √(4τ²ζ² - 4τ²))/2τ² = -ζτ ± τ√(ζ² - 1)
A and B can be found by solving the equations:
A(α + β) + B(α + β) = 0
Aαβ + Bαβ = 1
which give:
A = 1/(α - β)
B = -1/(α - β)
Substituting these values back into the partial fraction expansion, we get:
1 / (τ²s² + 2τζs + 1) = 1/(α - β) * [(1/(s + α)) - (1/(s + β))]
Taking the inverse Laplace transform, we get:
h(t) = (1/(α - β)) * [e^(-αt) - e^(-βt)]
Substituting the given values of τ, ζ, and σ, we get:
α = -ζτ + τ√(ζ² - 1) = -1.2
β = -ζτ - τ√(ζ² - 1) = -0.133
h(t) = (1/(α - β)) * [e^(1.2t) - e^(0.133t)] u(t)
where u(t) is the unit step function.
(c) To find the complete solution for x(t) = e¹¹ Sin4t, we can first find the homogeneous solution by assuming y = e^st:
τ²s² + 2τζs + 1 = 0
The roots of this equation are:
s1,2 = (-2τζ ± √(4τ²ζ² - 4τ²))/2τ² = -ζτ ± τ√(ζ² - 1)i
Since ζ < 1, we have two complex conjugate roots:
s1,2 = -0.4 ± 0.916i
Therefore, the homogeneous solution is:
y_h(t) = e^(-0.4t) [C1 cos(0.916t) + C2 sin(0.916t)]
To find the particular solution, we can use the method of undetermined coefficients. Since the forcing function is x(t) = e¹¹ Sin4t, we assume a particular solution of the form:
y_p(t) = A sin(4t) + B cos(4t)
Taking the derivatives, we get:
y_p'(t) = 4A cos(4t) - 4B sin(4t)
y_p''(t) = -16A sin(4t) - 16B cos(4t)
Substituting these into the differential equation, we get:
τ²(-16A sin(4t) - 16B cos(4t)) + 2τζ(4A cos(4t) - 4B sin(4t)) + (A sin(4t) + B cos(4t)) = 0
Simplifying and grouping the terms, we get:
(-16τ²A + 8τζB + A) sin(4t) + (16τ²B + 8τζA + B) cos(4t) = 0
Since sin(4t) and cos(4t) are linearly independent, the coefficients of each term must be zero:
-16τ²A + 8τζB + A = 0
16τ²B + 8τζA + B = e¹¹
Solving for A and B, we get:
A = -8.627 e¹¹ / (1 + 16τ²)
B = 0.459 e¹¹ / (1 + 16τ²)
Therefore, the particular solution is:
y_p(t) = -8.627 e¹¹ / (1 + 16τ²) sin(4t) + 0.459 e¹¹ / (1 + 16τ²) cos(4t)
The complete solution is the sum of the homogeneous and particular solutions:
y(t) = y_h(t) + y_p(t) = e^(-0.4t) [C1 cos(0.916t) + C2 sin(0.916t)] - 8.627 e¹¹ / (1 + 16τ²) sin(4t) + 0.459 e¹¹ / (1 + 16τ²) cos(4t)
To find the values of C1 and C2, we can use the initial conditions y(0) = 0 and y'(0) = 0:
y(0) = C1 = 0
y'(0) = -0.4 C1 + 0.916 C2 = 0
Therefore, C1 = 0 and C2 = 0.437.
The complete solution is:
y(t) = e^(-0.4t) (0.437 sin(0.916t) - 8.627 e¹¹ / (1 + 16τ²) sin(4t) + 0.459 e¹¹ / (1 + 16τ²) cos(4t)).
The transfer function H(s) is derived by taking the Laplace transform of the differential equation.The steady state forced response for the unit step forcing function is found by setting s = -2 in H(s) and solving for y(s).The complete solution for the given forcing function is found by solving the homogeneous equation and using undetermined coefficients to find a particular solution, then combining them to get the complete solution.Learn more about system of equation at:
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Full Question:
Given a system described by:
τ²[d²y/dt²] + 2τζ[dy/dt] + y = K
(a) Write the transfer function H(s)
(b) Give the steady state forced response for the unit step forcing function (i.e. the input), where τ = 2, ζ = 0.4, and σ = −2 , and K = 10.
(c) Give the complete solution (transient and steady state) for x(t) = e¹¹ Sin4t.
Related Questions
an engineering notebook is used for documenting all research, proving the origin of an idea, keeping sketches in one place, and a personal calendar. group of answer choices true false
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The given statement "an engineering notebook is used for documenting all research, proving the origin of an idea, keeping sketches in one place, and a personal calendar" is true because an engineering notebook is a type of journal or logbook used by engineers.
It is often used to track the evolution of a project or to prove the origin of a particular concept or invention. In addition to keeping sketches in one place and serving as a personal calendar, an engineering notebook is also useful for maintaining accurate records and staying organized.
An engineering notebook is a written record of an engineer's ideas, observations, designs, and experiments. It serves as a legal document that provides evidence of the engineer's work.
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what type of circuit fault is characterized by current bypassing all or some of the electrical load in the circuit?
Answers
Answer:
short circuit
Explanation:
You want to know what type of circuit fault is characterized by current bypassing all or some of the electrical load in the circuit.
ShortWhen the current in a circuit follows a shorter (or lower-impedance) path than the one intended, bypassing some or all of the intended load, the circuit is said to suffer from a "short circuit."
Fig. 1. shows a support system for a wooden balcony, knowing that the tension is 425 lb. in cable AB and 510 lb. in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
Answers
Answer: point A[{-40i + 0j + 45k}], B[{0i + 0j + 60k}], C[{ 60i + 0j + 60k}] from there you can now find the Magnitudes then The unit vectors multiplied by the forces provided 425lb AB and 510lb AC.
Explanation:
oil enters a counterflow heat exchanger at 450 k with a mass flow rate of 10 kg/s and exits at 350 k. a separate stream of liquid water enters at 208c, 5 bar. each stream experiences no significant change in pressure. stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. the specific heat of the oil is constant, c 5 2 kj/kg k. if the designer wants to ensure no water vapor is present in the exiting water stream, what is the allowed range of mass flow rates for the water, in kg/s?
Answers
The allowed range of mass flow rates for water, in kg/s is 23.56 - 30.44.
Given,
The mass flow rate of oil, m₁ = 10 kg/sThe inlet temperature of oil, T₁ = 450 kThe exit temperature of oil, T₂ = 350 kThe inlet temperature of water, T₃ = 208 °C = (208 + 273) K = 481 K
The inlet pressure of water, P₃ = 5 bar = 500 kPaThe specific heat of oil, c = 2 kJ/kgK
We can calculate the heat transferred to water by the oil using the heat balance equation as:
q = m₁c(T₁-T₂)
Where,q = Heat transferred to water by oilm₁ = mass flow rate of oilc = specific heat of oilT₁ and T₂ = inlet and exit temperature of oil respectively
Substituting the values in the equation,q = 10 × 2 × (450-350)q = 2000 kJ/sThe heat transferred to water is equal to the heat gained by water, i.e.,q = m₂c(T₄-T₃).
Where,m₂ = mass flow rate of waterc = specific heat of waterT₃ and T₄ = inlet and exit temperature of water respectively.
Substituting the values in the equation,2000 = m₂ × 4.18 × (481 - T₄)T₄ = 481 - (2000 / (m₂ × 4.18))
Range of mass flow rates for water, can be calculated by assuming the exit temperature of water to be 100 °C (373 K).481 - (2000 / (m₂ × 4.18)) = 373m₂ = 28.12 kg/s481 - (2000 / (m₂ × 4.18)) = 373m₂ = 25.64 kg/s
Therefore, the allowed range of mass flow rates for water, in kg/s is 23.56 - 30.44.
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The figure below shows the foundation plan and a wall section for a building. The entire exterior perimeter of the building is to be waterproofed starting 6 inches from the top of the wall, continuing down the wall, and covering the top of the footing. How many square feet of waterproofing is needed for the building? (25 points)
Answers
The correct answer is I do not have access to any figure or visual representation of the building plan you mentioned. Hence, I am unable to provide an accurate calculation for the required square footage of waterproofing material.
However, I can provide you with a general idea of the steps you need to take to calculate the required square footage. Firstly, you need to determine the total perimeter of the building by adding the length of all sides together. Then, subtract the openings such as doors and windows from the total perimeter. Next, you need to determine the height of the wall section that needs to be waterproofed. Measure the distance from the top of the wall down to the top of the footing. Once you have the total perimeter and height of the wall section, you can calculate the square footage required for waterproofing. Simply multiply the perimeter by the height of the wall section to get the total square footage. It's also important to consider any additional factors such as overlaps and waste that may affect the amount of waterproofing material needed. Always remember to add a little extra material to ensure adequate coverage and avoid running short during installation.
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Pueden las carreteras ser invisibles
Answers
No, las carreteras no pueden ser invisibles. Las carreteras son estructuras físicas que están diseñadas para ser visibles y reconocibles para los conductores y peatones. La visibilidad es una parte fundamental de la seguridad vial, ya que permite que los conductores y peatones vean las señales de tráfico, las líneas de carril, los cruces peatonales, entre otros elementos importantes para la seguridad en la carretera. Además, las carreteras invisibles podrían ser muy peligrosas ya que podrían causar accidentes automovilísticos y peatonales graves.
what is the minimum value of capacitance that can be obtained by connecting four 14- μf capacitors in series and/or parallel?
Answers
When capacitors are connected in series, the total capacitance is given by:
1/C_total = 1/C_1 + 1/C_2 + 1/C_3 + 1/C_4
Substituting the values given, we get:
1/C_total = 1/14 + 1/14 + 1/14 + 1/14
1/C_total = 4/14
C_total = 3.5 μF
Therefore, the minimum capacitance that can be obtained by connecting four 14- μf capacitors in series is 3.5 μF.
When capacitors are connected in parallel, the total capacitance is simply the sum of the individual capacitances. Therefore, the minimum capacitance that can be obtained by connecting four 14- μf capacitors in parallel is:
C_total = 4 * 14 μF
C_total = 56 μF
Therefore, the minimum capacitance that can be obtained by connecting four 14- μf capacitors is 3.5 μF in series and 56 μF in parallel.
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which of the following is a good example of a message signal? (a) a radio frequency signal. (b) a pilot carrier. (c) a baseband signal
Answers
(c) A baseband signal is a good example of a message signal as it carries the actual information to be transmitted, while (a) and (b) are typically used for carrier signals.
Out of the given options, a baseband signal is a good example of a message signal. This is because a baseband signal carries the actual information to be transmitted, such as audio or video data, while a radio frequency (RF) signal or a pilot carrier is typically used for the carrier signal, which is modulated by the message signal to carry the information over the transmission medium.
The baseband signal is a low-frequency signal that contains the original information to be transmitted, and it is typically in the range of a few hundred Hertz to a few megahertz. The carrier signal is a high-frequency signal that is modulated by the baseband signal, and it is typically in the range of tens to hundreds of megahertz or even higher. Together, the baseband signal and the carrier signal form the modulated signal that is transmitted over the communication channel.
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How do you write a method statement for: 1. Site Setup and Temporary works in construction?
Answers
A method statement for site setup and temporary works in construction should include the following steps:
1. Identify the scope of work and establish the project requirements for site setup and temporary works. This includes the location, size, and nature of the project, as well as any specific regulatory or safety requirements.
2. Develop a detailed plan for site setup and temporary works, including timelines, resources, and responsibilities. This should include a list of all temporary works required, such as access roads, fencing, and scaffolding.
3. Identify potential hazards and risks associated with site setup and temporary works, and develop a risk assessment and mitigation plan. This should include measures to ensure the safety of workers and the public, as well as measures to protect the environment.
4. Obtain all necessary permits and approvals, including building permits, environmental permits, and safety certifications.
5. Develop a site-specific safety plan and ensure all workers are properly trained and equipped to carry out the work safely. This should include safety procedures for working at heights, using heavy equipment, and handling hazardous materials.
6. Monitor the progress of site setup and temporary works, and make adjustments as necessary to ensure the work is completed on time, within budget, and to the required quality standards.
7. Conduct regular inspections and audits to ensure that all site setup and temporary works are in compliance with regulatory and safety requirements.
8. Document all site setup and temporary works activities, including any incidents or accidents that occur, and use this information to improve future projects.
Overall, the method statement for site setup and temporary works in construction should be a detailed plan that outlines all the necessary steps, resources, and safety measures required to ensure the successful completion of the project. It should be regularly reviewed and updated as necessary to ensure that the work is carried out safely and efficiently.
signment A mass of 500 kg is raised to a height of 6 m in 30s. Find (a) the work done and (b) the power developed
Answers
29,430 J of work is required to raise a mass of 500 kg to a height of 6 m in 30 seconds (Joules).
What is the weight formula based on Newton?F = m 9.8 m/s2 is the formula for computing weight, where m is the object's mass in kilogrammes and N is the object's weight in Newtons (N). The SI unit for weight is the Newton, and one Newton is equal to 0.225 pounds.
work = force x distance
weight = mass x gravity
weight = 500 x 9.81
weight = 4905 N
Now, we can calculate the work done:
work = force x distance
work = weight x height
work = 4905 x 6
work = 29,430 J
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What is the solution to this?
Answers
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
It is claimed that two vectors are equal if their magnitude and direction are the same. The study of mathematics, physics, and engineering are all dependent on it. The basic ideas of vector algebra may be used to add one vector to another vector head to tail.
As follows
|v⃗ |=|v1→+v2→|
one which is held
|v| = v21 + v22 + 2 v1 v 2 cos,
angle that the two vectors make with one another. cognizant of
v22 = 144 and v21 = 81 correspondingly.
2(9)(12)cosθ=216(−7,591×10−3)=−1639,656×10−3
so that we have
144+81−1,639656=223,360344
√=14,94524486=|v⃗ |
The angle being taken
θ=(90−63)+(90−α) \s,
In order for the angle we compute to be the angle that really results, for instance, an angle where is the angle between the positive axe-y and the v1.
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A gallon of gasoline has about 1.2 * 10^8 Joules of chemical energy. A car has an 18 gallon fuel tank. The car’s mass is 3700 lbm . It starts driving in Colorado. The car increases its elevation by 6500 N as it drives. The car gets 32 mpg. The total driving distance is 234 miles. The car starts at rest and is now going 68 mph. Determine the total energy change for the car. Describe in as much detail as possible where all the energy went. You can ignore the change in mass of the car that is caused by burning the gasoline (that change is negligible)
Answers
Total energy change = PE + KE + Energy consumed = 6500 J + 284859 J + 8.82 * 10^9 J ≈ 8.82 * 10^9 J
How to solveTo find the total energy change, we need to consider the potential energy gained (due to elevation increase), kinetic energy gained (due to increase in speed), and the energy consumed from gasoline.
Potential energy change (PE) = m * g * h = (3700 lbm * 0.453592 kg/lbm) * 9.81 m/s² * (6500 N / (3700 lbm * 0.453592 kg/lbm * 9.81 m/s²)) = 6500 J
Kinetic energy change (KE) = 0.5 * m * (v_f² - v_i²) = 0.5 * (3700 lbm * 0.453592 kg/lbm) * ((68 mph * 0.44704 m/s/mph)² - 0) ≈ 284859 J
Energy consumed from gasoline = Energy per gallon * gallons used = (1.2 * 10^8 J/gallon) * (234 miles / 32 mpg) ≈ 8.82 * 10^9 J
Total energy change = PE + KE + Energy consumed = 6500 J + 284859 J + 8.82 * 10^9 J ≈ 8.82 * 10^9 J
Most of the energy went into overcoming the car's internal inefficiencies (engine, transmission, etc.) and external resistances (air drag, rolling resistance). The remaining energy was used to increase the car's potential and kinetic energy.
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A dwelling with a general lighting load of 10,000 VA requires a minimum of how
many 15 A branch circuits?
A. 8
B. 3
C. 10
D. 6
Answers
Explanation:
The calculation is as follows:
The general lighting load is 10,000 VA.
The voltage used in homes is typically 120 volts.
Dividing the general lighting load by the voltage gives us the amperage: 10,000 VA / 120 volts = 83.33 amps
According to the National Electrical Code (NEC), a 15-amp branch circuit can handle a maximum of 15 amps.
To determine the number of 15-amp branch circuits required, we divide the amperage by the maximum allowed on one circuit: 83.33 amps / 15 amps = 5.55
Therefore, we need at least 6, 15-amp branch circuits to handle the general lighting load of 10,000 VA.
The answer is (D) 6.
who was the first female electrical engineer in the united states? what invention is she known for?
Answers
what size copper service conductors are required for a multifamily building that has a total demand load of 260 kw for a 120/208v wye, three-phase system? the conductors are paralleled in two raceways.
Answers
Without additional information on the raceway distance, ambient temperature, and voltage drop, it is impossible to determine the size of the copper service conductors required.
To determine the size of copper service conductors required for a multifamily building with a total demand load of 260 kW for a 120/208V wye, three-phase system, additional information is needed, such as the raceway distance, ambient temperature, and voltage drop. Without this information, it is impossible to accurately calculate the conductor size.
In general, conductor sizing is determined by the National Electrical Code (NEC), which provides guidelines based on various factors, including the load, the type of conductor, the length of the run, and the ambient temperature. To determine the conductor size for this particular situation, a licensed electrician or engineer would need to perform a detailed load calculation and take into account the specific installation requirements and local code regulations.
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The best designed saw for cutting miter joints is a ______.
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A backsaw is the saw that is best suited for cutting mitre joints. For precise tasks like cutting dovetails, mitres, or tenons in cabinetry and joinery, backsaws are typically used in woodworking.
Any hand saw with a stiffening rib on the edge opposite the cutting edge known as a backsaw enables better control and more accurate cutting than other saws. For precise tasks like cutting dovetails, mitres, or tenons in cabinetry and joinery, backsaws are typically used in woodworking. Backsaws can only cut a certain amount of depth due to the stiffening rib. Backsaws typically have teeth that are closely spaced and frequently have little to no set.
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is talking about uncertainty important in science?
Answers
In many ways, uncertainty is essential to science because it motivates researchers to conduct additional studies and research.
Being free of uncertainty is a major driving force behind many actions and decisions because the desire for certainty is a strong human emotion. We never know how decisions or actions will turn out, even when we seem to put uncertainty to rest—we pick a career, our elected officials tighten laws to address pollution, the Federal Reserve Board lowers interest rates to boost economic activity. Whether we like it or not, there is always uncertainty.
But a lot of us tend to believe that science offers conclusive solutions. In the end, science explains how and why things occur. Science is a problem-solver. Future predictions are made by scientists.
However, despite our desire for scientific findings to be indisputable, they are not. Scientists can't work with absolute certainty. Probabilities are used to base conclusions. Predictions can be proved wrong by new information, and well-established theories can even be changed. In many ways, uncertainty is essential to science because it motivates researchers to conduct additional studies and research.
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A gas is compressed. The measured volume and absolute pressure before compression
are 0.30m3
and 50.7kPa, respectively. After compression the volume and the pressure
becomes 0.111m3
and 202.8kPa, respectively. What is the compressibility and bulk
modulus of elasticity of this gas?
Answers
Answer:
To determine the compressibility and bulk modulus of elasticity of a gas, we can use the following formulas:
Compressibility:
β = - (1/V) * (∆V/∆P)
where V is the initial volume of the gas, ∆V is the change in volume, and ∆P is the change in pressure.
Bulk modulus of elasticity:
B = - V * (∆P/∆V)
where V is the initial volume of the gas, ∆V is the change in volume, and ∆P is the change in pressure.
Using the given values, we can calculate the compressibility as follows:
∆V = V2 - V1 = 0.111m3 - 0.30m3 = -0.189m3
∆P = P2 - P1 = 202.8kPa - 50.7kPa = 152.1kPa
Therefore,
β = - (1/0.30m3) * (-0.189m3/152.1kPa) ≈ 0.0048 kPa^-1
Similarly, we can calculate the bulk modulus of elasticity as follows:
B = - 0.30m3 * (152.1kPa/-0.189m3) ≈ 2418 kPa
Therefore, the compressibility of the gas is approximately 0.0048 kPa^-1, and the bulk modulus of elasticity is approximately 2418 kPa.
Explanation:
an industrial load consists of the following individual loads: a. a 50hp motor with a efficiency of 86% and a 70% lagging power factor (fully loaded). b. a 100hp motor with a efficiency of 89% and a 80% lagging power factor (82% loaded). c. two 20hp motors with a efficiency of 92% and a 85% lagging power factor(fully loaded). d. a 300hp motor with a efficiency of 92% and a 84% lagging power factor(75% loaded). e. 50kw of incandescent lighting. find the total power factor and the real, reactive, and apparent power used by the facility.
Answers
Answer: To find the total real, reactive, and apparent power used by the facility, we need to calculate the power consumption of each individual load first.
Explanation:
a. The power consumed by the 50hp motor is given by:
P = (50 hp) / (0.86 × 0.70) = 83.63 kW
The reactive power consumed by the motor is given by:
Q = P × tan(cos⁻¹(0.70)) = 57.63 kVAR
b. The power consumed by the 100hp motor is given by:
P = (100 hp × 0.82) / 0.89 = 91.01 kW
The reactive power consumed by the motor is given by:
Q = P × tan(cos⁻¹(0.80)) = 54.72 kVAR
c. The power consumed by each of the two 20hp motors is given by:
P = (20 hp) / (0.92 × 0.85) = 25.08 kW
The reactive power consumed by each motor is given by:
Q = P × tan(cos⁻¹(0.85)) = 14.07 kVAR
d. The power consumed by the 300hp motor is given by:
P = (300 hp × 0.75) / 0.92 = 245.11 kW
The reactive power consumed by the motor is given by:
Q = P × tan(cos⁻¹(0.84)) = 160.89 kVAR
e. The power consumed by the incandescent lighting is given by:
P = 50 kW
The reactive power consumed by the lighting is zero, since it is a resistive load.
Now we can find the total real, reactive, and apparent power used by the facility:
Total real power = 83.63 kW + 91.01 kW + 2 × 25.08 kW + 245.11 kW + 50 kW = 529.91 kW
Total reactive power = 57.63 kVAR + 54.72 kVAR + 2 × 14.07 kVAR + 160.89 kVAR + 0 kVAR = 301.98 kVAR
Total apparent power = √(529.91² + 301.98²) = 609.57 kVA
The total power factor is given by:
cos(θ) = 529.91 kW / 609.57 kVA = 0.8691
θ = cos⁻¹(0.8691) = 29.59 degrees
Therefore, the total power factor is 0.869 lagging. The real power used by the facility is 529.91 kW, the reactive power used is 301.98 kVAR, and the apparent power is 609.57 kVA.
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the beam is subjected to a moment of 15 kip-ft. determine the percentage of this moment that is resisted by the web d of the beam.
Answers
To determine the percentage of the moment that is resisted by the web of the beam, we need to find the moment of inertia of the entire cross-section of the beam, as well as the moment of inertia of just the web. The moment of inertia of the web represents the portion of the total moment that is resisted by the web.
Assuming a rectangular beam with dimensions b (width), h (height), and t (thickness of the web), the moment of inertia of the entire cross-section can be calculated as:
I_total = (1/12) * b * h^3
The moment of inertia of just the web can be calculated as:
I_web = (1/12) * t * h^3
The moment of the applied load is 15 kip-ft. To determine the percentage of this moment that is resisted by the web, we can use the formula:
% resisted by web = (I_web / I_total) * 100%
Substituting the expressions for I_web and I_total, we get:
% resisted by web = [(1/12) * t * h^3 / (1/12) * b * h^3] * 100%
Simplifying the expression, we get:
% resisted by web = (t/b) * 100%
Therefore, the percentage of the moment that is resisted by the web of the beam is equal to the ratio of the thickness of the web to the width of the beam, multiplied by 100%.
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a signal is to be sampled at 1 khz. to prevent aliasing, the signal should first be passed through an anti-aliasing filter with a cutoff frequency of:
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To prevent aliasing, the anti-aliasing filter's cutoff frequency should be less than half of the sampling frequency (Nyquist frequency). Therefore, for a signal to be sampled at 1 kHz, the cutoff frequency of the anti-aliasing filter should be less than 500 Hz.
When sampling an analog signal, it is important to ensure that the resulting digital signal accurately represents the original signal. Aliasing can occur when the signal is not properly sampled, resulting in distortion or errors in the digital signal.
To prevent aliasing, an anti-aliasing filter is used to remove any frequency components above the Nyquist frequency, which is half the sampling rate. In this case, the signal is to be sampled at 1 kHz, so the Nyquist frequency is 500 Hz.
Therefore, the cutoff frequency of the anti-aliasing filter should be set at or below 500 Hz to prevent any frequency components above the Nyquist frequency from being sampled and causing aliasing. A good rule of thumb is to set the cutoff frequency at about 70% of the Nyquist frequency, so a cutoff frequency of around 350 Hz would be appropriate in this case.
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The acceleration function of an object doing curvilinear motion is a = {(-0.2)i+2j+1.5k) m/s², where t is in s. If its initial velocity vo 8i m/s, and initial position is at the origin, determine the magnitude of its velocity when t = 3 s.
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To solve this problem, we need to integrate the acceleration function to obtain the velocity function, and then evaluate the magnitude of the velocity at t = 3 s.
The velocity function can be obtained by integrating the acceleration function as follows:
v(t) = ∫a(t)dt
v(t) = ∫((-0.2)i+2j+1.5k)dt
v(t) = (-0.2t)i+(2t)j+(1.5t)k + C
where C is a constant of integration. To determine the value of C, we can use the initial velocity, which is given as vo = 8i m/s when t = 0 s:
v(0) = (-0.2(0))i+(2(0))j+(1.5(0))k + C = 8i
C = 8i
Therefore, the velocity function is:
v(t) = (-0.2t)i+(2t)j+(1.5t)k + 8i
Now, to determine the magnitude of the velocity at t = 3 s, we can simply evaluate the velocity function at t = 3 s and compute its magnitude:
v(3) = (-0.2(3))i+(2(3))j+(1.5(3))k + 8i
v(3) = (-0.6)i+6j+4.5k + 8i
v(3) = 7.4i+6j+4.5k
|v(3)| = sqrt((7.4)^2 + 6^2 + (4.5)^2)
|v(3)| = sqrt(102.41 + 36 + 20.25)
|v(3)| = sqrt(158.66)
|v(3)| ≈ 12.6 m/s (rounded to one decimal place)
Therefore, the magnitude of the velocity when t = 3 s is approximately 12.6 m/s.
Answer:
the magnitude of the velocity when t = 3 s is 10.54 m/s.
Explanation:
To solve this problem, we can use the following kinematic equation that relates velocity, acceleration, and time:
v = vo + at
where:
v = final velocity
vo = initial velocity
a = acceleration
t = time
First, we need to find the velocity of the object at time t = 3 s. To do this, we can substitute the given values into the kinematic equation and solve for v:
v = vo + at
v = 8i + (-0.2i+2j+1.5k) x 3
v = 8i - 0.6i + 6j + 4.5k
v = 7.4i + 6j + 4.5k
The magnitude of the velocity is given by:
|v| = sqrt(vx^2 + vy^2 + vz^2)
where:
vx, vy, vz = the x, y, and z components of the velocity vector
Substituting the values from above, we get:
|v| = sqrt((7.4)^2 + 6^2 + (4.5)^2)
|v| = sqrt(54.81 + 36 + 20.25)
|v| = sqrt(111.06)
|v| = 10.54 m/s (approx)
the american wire gage numbers specify the size of round wire in terms of its diameter and cross-sectional area. true or false
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The following statement is true. The American wire gage numbers specify the size of round wire in terms of its diameter and cross-sectional area.
The American Wire Gauge (AWG) is a standardized system used in the United States to specify the diameter of electrical conductors such as wires and cables. The AWG number assigned to a wire indicates its cross-sectional area, which in turn determines the wire's current-carrying capacity and other electrical properties.
As the AWG number increases, the diameter of the wire decreases, and vice versa. For example, a wire with a higher AWG number (such as 24) has a smaller diameter and lower current-carrying capacity than a wire with a lower AWG number (such as 12).
In summary, the AWG number of a wire specifies its diameter and cross-sectional area, which are important factors in determining its electrical properties.
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generally, uncontrolled intersections are found in
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Hope this helps!
in the aim content planning process, you develop your information and ideas by
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The aim of the content planning process is to create a content strategy that aligns with your organization's goals and objectives. This process involves developing information and ideas through research, analysis, and creative thinking.
The process typically includes the following steps:
1. Define your audience: In this step, you need to identify the audience you want to target with your content. This can be done by analyzing your existing customer base or by conducting market research to understand the needs and interests of your target audience.
2. Set goals and objectives: You need to establish clear goals and objectives for your content marketing efforts. These goals should be specific, measurable, achievable, relevant, and time-bound (SMART). For instance, your goal may be to increase brand awareness, generate leads, or boost sales.
3. Develop a content strategy: Once you have identified your audience and set your goals, you need to develop a content strategy that will help you achieve these objectives. This involves identifying the types of content you will create, the channels you will use to distribute it, and the key messages you want to communicate.
4. Create a content calendar: A content calendar is a schedule that outlines the topics, formats, and channels you will use to distribute your content over a specified period. This helps ensure that your content is timely, relevant, and consistent.
5. Execute your plan: Once you have developed your content plan, you need to execute it by creating and publishing your content. You should also track your progress and adjust your strategy as needed to ensure that you are meeting your goals.
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Select the correct definition for the word: Decimal.
A shortened version of the term "decimal fraction."
The top number in a fraction.
The shape made by two straight lines meeting in a point.
The bottom number in a fraction.
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The correct definition for the word Decimal is a shortened version of the term "decimal fraction.A decimal is a fraction that has a denominator of ten, hundred, thousand, or any other power of ten.
Decimals are a way of expressing parts of a whole, especially when dealing with fractional values. They are often used in money calculations, measurement, and science to give precise values.The decimal system is a method of organizing numbers that employs the digits 0 through 9. It is based on the powers of ten and place values. Decimal fractions can subtracted, added, multiplied, and divided like whole numbers, making them simple to work with.
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A piston -cylinder device as in figure, with a set of stops on the top. initially contains 1 kg of air at 200 kPa and 27 degree C. Heat is now transferred to the air. and the piston rises until it hits the stops, at which point the volume is 1.5 times the initial volume. More heat is transferred until the pressure inside the cylinder also 1.5 times the initial pressure. Determine I A) the total work done (in kJ). (B) the heat transfer amount (in kJ). and (C) show the process on a P-v diagram.
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To determine the total work done, heat transfer amount, and the process on a P-v diagram for the given scenario, we need to use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the amount of heat added minus the amount of work done.
A) To find the total work done, we need to calculate the area under the curve of the pressure-volume diagram. This area can be divided into two parts: the work done in expanding the gas from initial volume to final volume, and the work done in increasing the pressure from an initial pressure to final pressure. Using the ideal gas law, we can find the initial and final states of the gas and then use the formula for work done: W = PΔV. The total work done can be found by adding the work done in expansion and compression.
B) The heat transfer amount can be found using the formula Q = ΔU + W, where ΔU is the change in the internal energy of the system. We can find the change in internal energy using the First Law of Thermodynamics and then add the work done to find the heat transfer amount.
C) To show the process on a P-v diagram, we need to plot the initial and final states of the gas and connect them with a curve. The curve will represent the process that the gas undergoes. The process can be either adiabatic, isothermal, or isobaric, depending on the amount of heat transfer and the type of work done.
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True/False? a three-bend saddle is a saddle consisting of a center bend and two side bends with the center bend having twice the angle of the side bends.
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What does a filter drier do?
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Answer:
they trap coarse particulate contamination and copper shavings
Water flows through a horizontal bend and discharges into the atmosphere as shown. When the pressure gauge reads 10 psi, the resultant x-direction anchoring force, FAX in the horizontal plane required to hold the bend in p lace is shown in the figure. Determine the flow rate through the bend and the y-direction anchoring force, FAY required to hold the bend in place. The flow is not frictionless. Ans: 7.01 ft^3/s and 674 lbs.
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FAY = 62.4 lb/ft^3 * 7.01 ft^3/s * 11.67 ft/s * sin(30 degrees) ≈ 674 lbs
Thus, the flow rate through the bend is approximately 7.01 ft^3/s, and the y-direction anchoring force required to hold the bend in place is approximately 674 lbs.