Air flows steadily through a variable sized duct in a heat transfer experiment with a speed of u = 20 – 2x, where x is the distance along the duct in meters, and u is in m/s. Because of heat transfer out of the duct, the air temperature, T, within the pipe cools as it goes downstream, according to T = 200 - 5x C. As they flow past the section at x= 3 meters, (a) determine the acceleration; (b) Determine the rate of change of temperature of air particles
Answers
Answer:
a) \(a=-28m/s^{2}\)
b) \(\frac{dT}{dx}=-5 ^{o}C/m\)
Explanation:
a)
In order to solve this problem, we need to start by remembering how the acceleration is related to the velocity of a particle. We have the following relation:
\(a=\frac{dv}{dt}\)
in other words, the acceleration is defined to be the derivative of the velocity function with respect to time. So let's take our speed function:
u=20-2x
if we take its derivative we get:
du=-2dx
this is the same as writting:
\(\frac{du}{dt}=-2\frac{dx}{dt}\)
we also know that velocity is defined to be:
\(u=\frac{dx}{dt}\)
so we get that:
a=-2u
when substituting we get that:
a=-2(20-2x)
when expanding we get:
a=-40+4x
and now we can use this equation to find our acceleration at x=3, so:
a=-40+4(3)
a=-40+12
\(a=-28 m/s^{2}\)
b)
the same applies to this problem with the difference that this will be the rate of change of the temperature per m. So we proceed and take the derivative of the temperature function:
T=200-5x
\(\frac{dT}{dx}=-5\)
so the rate of change is \( -5^{o}C/m \)
Related Questions
The trolley travels at the constant speed of 40 mi/h along a parabolic track described by y = x2/500, where x and y are measured in feet. Compute the acceleration of the trolley when it is (1) at point O; and (2) at point A.
Answers
At point O, the trolley is at the bottom of the parabolic track, where y = 0. Therefore, the position vector of the trolley is given by r = xi, where i is the unit vector in the x-direction. The velocity vector of the trolley is given by the derivative of the position vector with respect to time:
v = dr/dt = (d/dt)(xi) = (dx/dt)i
Since the trolley is traveling at a constant speed of 40 mi/h, its velocity vector has a magnitude of 40 mi/h. To find the x-component of the velocity vector, we can use the fact that the speed is constant:
40 mi/h = |v| = sqrt[(dx/dt)^2]
Solving for dx/dt, we get:
dx/dt = 40/sqrt(mi^2/h^2) = 40/5280 ft/s
Therefore, the velocity vector of the trolley at point O is given by:
v = (40/5280)i ft/s
Taking the derivative of the velocity vector with respect to time, we get the acceleration vector:
a = dv/dt = (d/dt)(40/5280)i = 0
Therefore, the acceleration of the trolley at point O is zero.
At point A, the position vector of the trolley is given by:
r = xi + (x^2/500)j
where j is the unit vector in the y-direction. To find the velocity vector of the trolley, we need to take the derivative of the position vector with respect to time:
v = dr/dt = (d/dt)(xi) + (d/dt)((x^2/500)j)
The x-component of the velocity vector is given by:
dx/dt = 40 mi/h = 40/5280 ft/s
The y-component of the velocity vector is given by:
(dy/dt)j = (d/dt)((x^2/500)j) = (2x/500)(dx/dt)j
At point A, x = 200 ft (since y = x^2/500 = 40000/500 = 80 ft at point A), so we can compute the y-component of the velocity vector:
(dy/dt)j = (2x/500)(dx/dt)j = (2*200/500)(40/5280)j = (16/1320)j ft/s
Therefore, the velocity vector of the trolley at point A is given by:
v = (40/5280)i + (16/1320)j ft/s
Taking the derivative of the velocity vector with respect to time, we get the acceleration vector:
a = dv/dt = (d/dt)((40/5280)i) + (d/dt)((16/1320)j)
The x-component of the acceleration vector is zero, since the speed of the trolley is constant:
(d/dt)((40/5280)i) = 0
The y-component of the acceleration vector is given by:
(d/dt)((16/1320)j) = (d/dt)((2x/500)(dx/dt)j) = [(2/500)(d^2x/dt^2) + (2/500)(dx/dt)^2]j
To find the second derivative of x with respect to time, we can use the fact that the speed is constant:
So, we have a list called gradebook that contains a list of dictionaries, where each dictionary contains four keys: name, homework, test, and exam. Imagine you wanted to get the entire dictionary for the first student in this list. What line of code would retrieve that dictionary?
Answers
gradebook[0], line of code would retrieve that dictionary.
What is code?
Computer code, or a set of instructions or a system of rules defined in a specific programming language, is a term used in computer programming (i.e., the source code). It is also the name given to the source code after a compiler has prepared it for computer execution (i.e., the object code). Code is heavily employed for cutting-edge ideas like artificial intelligence or machine learning, in addition to creating computer programmes and mobile applications. The next section will discuss some other uses & applications for the word code. It's critical to recognise that the word "code" has a variety of applications and meanings.
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Please help
What are saving bonds?
Answers
jennifer's job inside the company is to review resumes to identify potential candidates to itnerview. it is most likely likely that jennifer works in _______.
Answers
Jennifer's job of reviewing resumes to identify potential candidates for interviews suggests that she works in the Human Resources (HR) department or the Recruitment department of the company. These departments are responsible for screening and selecting candidates for job positions within the organization.
Jennifer's role of reviewing resumes and identifying potential candidates for interviews is typically associated with the Human Resources (HR) department or the Recruitment department of a company. Here's an explanation of why:
Human Resources (HR) Department: The HR department is responsible for managing the overall human capital of the organization. This includes tasks such as recruitment, selection, and hiring of employees. Reviewing resumes and identifying suitable candidates aligns with the HR department's responsibilities in sourcing and evaluating potential candidates for job positions.
Recruitment Department: Some larger organizations may have a dedicated Recruitment department. This department focuses specifically on the process of attracting, sourcing, and selecting candidates for job openings. Reviewing resumes is a crucial step in the recruitment process to assess the qualifications, skills, and experience of applicants.
In both cases, Jennifer's role involves carefully reviewing resumes to screen applicants and identify those who meet the desired qualifications and criteria set by the company. She plays a vital role in shortlisting candidates for further evaluation and potential interviews.
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What is constructor and it's example in C++?
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In C++, a constructor is a special "MEMBER FUNCTION" with the same moniker as the class it belongs to and is used to establish some data points to an object's data members.
What does the term "constructor" mean?Constructor: In object-oriented programming, a constructor is a particular method of a form or structure that initializes a newly formed object of that kind. The constructor is always invoked when an object is created.
How does the constructor operate?The name of the constructor frequently matches that of the declaring class. They must initialize the data members of the object and establish the class invariant, failing if the equilibrium point is incorrect.
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Maintenance Management is part of the scope of work for Property Manager
Answers
Maintenance Management is an essential aspect of the scope of work for Property Managers. It involves the process of overseeing, planning, and implementing the upkeep and repair of a property to ensure its optimal condition.
Property Managers are responsible for coordinating routine maintenance tasks, addressing emergency repairs, and organizing preventative measures to maintain the property's value and safety. Their duties include scheduling inspections, working with contractors, and managing budgets. By effectively handling Maintenance Management, Property Managers play a crucial role in preserving the property's overall functionality and appearance, contributing to tenant satisfaction and long-term success.
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A runner ran a 600 m race in 2 min 17 seconds. Calculate his average speed in m/sec.
Answers
The Rule That Packets Not Originating From Inside Your LAN Should Not Be Forwarded Relates To ___________. Question 31 Options: 1) Servers 2) Workstations 3)
Answers
The Rule That Packets Not Originating From Inside Your LAN Should Not Be Forwarded Relates to routers
What is meant by routers ?In order to transfer data between two or more packet-switched computer networks, a router—either real or virtual—is used.. The Internet Protocol address (IP address) of the destination is examined by a router, which then determines the optimal path for the data packet to take to get there.
According to the various application categories, there are five different types of routers available. They include VPN routers, core routers, edge routers, wireless routers, and wired routers. The aforementioned fundamental details can be used to aid in making the best router selection possible.
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The student came up with a model that shows a loop of wire being rotated by some external force between two strong, permanent magnets. This causes the charges in the loop to flow. Pole piece Armature Slip ring What did the student make - a model of --
A. a motor B. both a motor and a generator C. neither a motor nor a generator D. a generator
Answers
The model that the student made is a motor. So, the answer is option A.
Key elements in the motor modelThe following are the key elements that the student has used to make a model of a motor:
Pole pieceArmatureSlip ringThe pole pieces are placed on the edges of the strong, permanent magnets.
The Armature is a loop of wire that the student is rotating.
Finally, the slip rings are used to transfer electrical power from the armature to the external source.
With the flow of current in the loop, a magnetic field is established that interacts with the poles of the magnet, causing the armature to spin. The model is similar to a motor as it uses the basic principle of a motor - electromagnetic induction to convert electrical energy into mechanical energy.
Therefore, the student has made a model of a motor..
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What does efficiency measure?
Answers
Answer:
Efficiency is defined as any performance that uses the fewest number of inputs to produce the greatest number of outputs. Simply put, you're efficient if you get more out of less.
Explanation:
what development methodology repeatedly revisits the design phase?
Answers
There are several development methodologies that repeatedly revisit the design phase, including Agile, Scrum, and Rapid Application Development (RAD).
These methodologies prioritize flexibility and adaptability, and therefore require frequent design revisions to ensure that the end product meets the evolving needs of stakeholders. In Agile, for example, design is an ongoing process that occurs throughout the development cycle in short, iterative sprints. Similarly, Scrum emphasizes collaboration and frequent communication between team members to ensure that the design remains aligned with the project goals. Ultimately, the choice of development methodology depends on the specific project requirements and the team's preferred approach to design and development.
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Water is the working fluid in an ideal Rankine cycle. Superheatedvapor enters the turbine at 10MPa, 480°C, and the condenser pressure is6 kPa. Isentropic efficiencies of the turbine and pump are 80% and 75%,respectively. Determine for the cyclea.the actual heat transfer to the working fluid passing through thesteam generator, in kJ per kg of steam flowing.b.the thermal efficiency.c.the actual heat transfer from the working fluid passing through thecondenser to the cooling water, in kJ per kg of steam flowing
Answers
Answer:
Explanation:
Given that:
Superheated vapor enters the turbine at 10 MPa, 480°C,
From the tables of superheated steam tables; the following values are obtained
\(h_1 = 3322.02 \ kJ/kg\\\\ s_1 = 6.52846 \ kJ/kg.K\)
Also; from the system, the isentropic line is 1-2 in which s_2 is in wet state
\(s_2 = s_{f \ 6 kpa} +xs_{fg \ 6 kpa}\)
\(s_2 =0.51624 + x(7.82)\)
\(s_2 =0.51624 + 7.82x\)
From the values obtained;
\(s_1 =s_2= 6.52846 \ kJ/kg.K\)
Therefore;
6.52846 = 0.51624+7.82x
6.52846 - 0.51624 = 7.82 x
6.01222 = 7.82 x
x = 6.01222/7.82
x = 0.7688
The enthalpy for this process at state (s_2) can be determined as follows:
\(h_2 = h _f +xh_{fg} \\ \\ h_2 = 150.15 +(0.77 \times 2415.92) \\ \\ h_2 =150.15 +( 1629.2584 ) \\ \\ h_2 =2010.4084 \ kJ/kg\)
The actual enthalpy at s_2 by using the isentropic efficiency of the turbine can determined by using the expression:
\(n_T = \dfrac{h_1-h_{2a}}{h_1-h_2}\)
\(0.8 = \dfrac{3322.02-h_{2a}}{3322.02-2010.4084}\)
\(0.8 = \dfrac{3322.02-h_{2a}}{1311.6116}\)
\(0.8 * {1311.6116}= {3322.02-h_{2a}\)
\(1049.28928= {3322.02-h_{2a}\)
\(h_{2a}= {3322.02- 1049.28928\)
\(h_{2a}= 2272.73072\) kJ/kg
The work pump is calculated by applying the formula:
\(w_p = v_{f \ 6 kpa} (p_4-p_3)\)
\(w_p = 0.0010062 * (10000-6)\)
\(w_p = 0.0010062 *9994\)
\(w_p = 10.0559628 \ kJ/kg\)
However;
\(w_p = h_4 -h_3\)
From the process;
\(h_3 = h_{f(6 kpa)} = 150.15 \ kJ/kg\)
\(10.0559628 = h_4 - 150.15\)
\(10.0559628+ 150.15 = h_4\)
\(160.2059628= h_4\)
\(h_4= 160.2059628 \ kJ/kg\)
The actual enthalpy at s_4 by using the isentropic efficiency of the turbine can determined by using the expression:
\(n_P = \dfrac{h_4-h_{3}}{h_{4a}-h_3}\)
37. In ______ combination of drugs, the effects of one drug cancel or diminish
the effects of another.
A.additive
B.antagonistic
C.synergistic
D.energetic
(For drivers ed btw)
Answers
Answer:
In antagonistic combination of drugs, the effects of ine drug cancel or diminish the effects of another
The entire population of a given community is examined, and all who are judged to be free from bowel cancer are questioned extensively about their diets. These people then are followed for several years to see whether their eating habits will predict their risk of developing bowel cancer. Which of the following study designs most appropriately characterizes this situation?
A. Cross-sectional study.
B. Case-control study.
C. Prospective cohort study.
D. Historical prospective cohort study.
E. Clinical trial.
F. Community trial.
Answers
Answer:
C) Prospective Cohort study
Explanation:
prospective cohort study can be regarded as longitudinal cohort study that comes up with periods of time when group of individuals that are different in terms of some factors that are undergoing some study, so that how theses factors influence rates of some particular outcomes can be known.
An Otto cycle with air as the working fluid has a compression ratio of 8.2. Under cold air standard conditions, what is the thermal efficiency of this cycle?
Answers
Answer:
Under cold air standard conditions, the thermal efficiency of this cycle is 56.9 percent.
Explanation:
From Thermodynamics we remember that thermal efficiency of the ideal Otto cycle (\(\eta_{th}\)), dimensionless, is defined by the following formula:
\(\eta_{th} = 1-\frac{1}{r^{\gamma-1}}\) (Eq. 1)
Where:
\(r\) - Compression ratio, dimensionless.
\(\gamma\) - Specific heat ratio, dimensionless.
Please notice that specific heat ratio under cold air standard conditions is \(\gamma = 1.4\).
If we know that \(r = 8.2\) and \(\gamma = 1.4\), then thermal efficiency of the ideal Otto cycle is:
\(\eta_{th} = 1-\frac{1}{8.2^{1.4-1}}\)
\(\eta_{th} = 0.569\)
Under cold air standard conditions, the thermal efficiency of this cycle is 56.9 percent.
Consider a fuel cell vehicle. The vehicle draws 30 kW of power at 60 mph and is 40% efficient at rated power. (It converts 40% of the energy stored in the hydrogen fuel to electric power.) You are asked to size the fuel cell system so that a driver can go at least 300 miles at 60 mph before refueling. Specify the minimum volume and weight requirements for the fuel cell system (fuel cell + fuel tank) given the following information:
• Fuel cell power density: 1 kW/L
• Fuel tank energy density (compressed hydrogen): 4 MJ/L
Answers
Answer:
minimum volume = 367.5 lit
minimum weight = 228.75 kg
Summarize the general due process of how an if statement with an else clause executes.
Answers
The due process of an if statement with an else clause involves evaluating the condition, executing the if block if the condition is true, skipping the if block if the condition is false and there is no else clause, and executing the else block if the condition is false and there is an else clause.
Firstly, when an if statement is encountered in a program, the condition specified within the parentheses is evaluated. If the condition evaluates to true, the statements within the if block are executed.
If the condition evaluates to false, the statements within the if block are skipped and the program moves on to the next line of code. However, if an else clause is present, the statements within the else block are executed instead.
It is important to note that only one of the two blocks (if or else) will be executed, depending on the evaluation of the condition. Additionally, the else clause is not mandatory and can be omitted if not needed.
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What is the most common impediment to communication in cross functional team
Answers
Answer:
Conflicting goals. Specialised jargon. Unequal responsibilities
In an international film festival, a penal of 11 judges is formed to judge the best film. At
last two films FA and FB were considered to be the best where the opinion of judges got
divided. Six judges where in favor of FA whereas five in favor of FB. A random sample
of five judges was drawn from the panel. Find the probability that out of five judges,
three are in favor of film FA.Enunciate demerits of classical probability.
Answers
Answer:
International Film Festival
Judging the best best film:
a. The probability that out of five judges (random sample), three are in favor of film FA is:
= 33%.
b. The demerits of classical probability are:
1. Classical probability can only be used with events that have definite numbers of possible outcomes.
2. Classical probability can only handle events where each outcome is equally likely.
3. Classical probability is based on the assumption of linear relationship (which is not always true in real life) between the latent variable and observed scores.
Explanation:
a) Number of judges = 11
Number of judges in favor of FA film = 6
Number of judges in favor of FB film = 5
Probability of judges in favor of FA film = 6/11
Probability of judges in favor of FB film = 5/11
Random sample of judges = 5
Probability that out of five judges, three are in favor of film FA = 3/5 * 6/11
= 18/55
= 33%
b) Classical probability is the simple probability showing that each event has equal chance of happening. It can be contrasted with empirical probability that is obtained from experiments.
A bomb thrown from a plane flying at a height of 400m moves along the path vector r
= (50 t)i + (4t
2
)j m. where t in sec. The origin is taken as the point from where, the bomb is
released and the +ve Y axis is taken as pointing downwards. Find,
i) Equation of path followed by bomb
ii) Time taken to reach the ground
iii) Horizontal distance traversed by the bomb.
iv) Displacement, velocity and acceleration at t=5sec.
v) Tangential and normal component of acceleration at t=5 sec.
Answers
Answer:
Explanation:
This problem involves projectile motion, and we can use the equations of motion to find the various quantities asked for:
i) Equation of path followed by bomb:
The path of the bomb is given by the vector equation r = (50t)i + (4t^2)j, where i and j are unit vectors in the x and y directions, respectively. We can rewrite this equation in terms of x and y coordinates by substituting i = (1, 0) and j = (0, 1), which gives:
x = 50t
y = 4t^2
Therefore, the equation of the path followed by the bomb is y = (1/100)x^2.
ii) Time taken to reach the ground:
The bomb will reach the ground when its height above the ground (y-coordinate) becomes zero. So we can set y = 0 and solve for t:
0 = 4t^2
t = 0 or t = sqrt(0) = 0
This means the bomb will hit the ground at t = 0 and stay on the ground afterwards.
iii) Horizontal distance traversed by the bomb:
The horizontal distance traversed by the bomb is equal to the displacement in the x-direction, which is given by:
Δx = x(final) - x(initial) = 50t - 50(0) = 50t
At t = 0 (when the bomb hits the ground), Δx = 0. Therefore, the bomb travels a horizontal distance of 50t before hitting the ground.
iv) Displacement, velocity and acceleration at t=5sec:
At t=5sec, we can find the displacement of the bomb by substituting t=5 into the vector equation of the path:
r(5) = (50(5))i + (4(5^2))j = 250i + 100j
Therefore, the displacement of the bomb at t=5sec is 250i + 100j.
To find the velocity and acceleration at t=5sec, we can differentiate the vector equation of the path with respect to time:
v = dr/dt = (50)i + (8t)j
a = d^2r/dt^2 = 0i + 8j
Substituting t=5 into these equations, we get:
v(5) = (50)i + (8(5))j = 50i + 40j
a(5) = 0i + 8j
Therefore, the velocity of the bomb at t=5sec is 50i + 40j, and the acceleration is 8j.
v) Tangential and normal component of acceleration at t=5 sec:
The acceleration at t=5sec is 8j. The tangential component of acceleration is zero, since the velocity vector is purely horizontal at this time. The normal component of acceleration is equal to the magnitude of the acceleration vector, since it is perpendicular to the velocity vector. Therefore, the tangential component of acceleration is zero, and the normal component of acceleration is 8 m/s^2.
Once you have chosen a topic, what should you do before beginning the research process? a. Find as many possible facts and details on your topic c. Discuss your idea with others b. Choose a position d. None of these Please select the best answer from the choices provided A B C D
Answers
Answer:
The answer is C
Explanation:
Once you have chosen a topic, the next thing you should do before beginning the research process is: C. discuss your idea with others.
What is a research topic?A research topic refers to an event, issue, or subject that a researcher is keenly and deeply motivated or interested in, especially when conducting a study or research.
Based on scientific information and records, it is very important you discuss your idea with others once you have chosen a topic, before beginning the research process.
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Discuss electric vehicles (EV) and their impacts on supply
chains from manufacturing to consumption.
Answers
Electric vehicles (EVs) have significant impacts on supply chains, influencing various stages from manufacturing to consumption. The introduction and increasing adoption of electric vehicles have profound implications for supply chains.
In terms of manufacturing, the production of electric vehicles requires different components and technologies compared to traditional internal combustion engine vehicles. This necessitates adjustments in the supply chain to procure and distribute the necessary parts, such as batteries and electric drivetrain components. Additionally, the establishment of charging infrastructure becomes a crucial aspect of the supply chain, ensuring convenient access to charging stations for EV owners. Furthermore, the shift to electric vehicles affects the distribution network, as the charging requirements and driving range of EVs influence logistics and delivery routes. Lastly, the consumption of electric vehicles impacts the service and maintenance sector, as EVs have different maintenance needs compared to conventional vehicles. Overall, the transition to electric vehicles necessitates adjustments throughout the supply chain to accommodate the unique requirements and demands of EV manufacturing, distribution, and consumption.
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A uniform plane electromagnetic wave propagates in a lossless dielectric medium of infinite extent. The electric field in the wave has the instantaneous expression
E(r,t) = (ix √3 - iz) 2 sin(2π.10^8t + 2πx/3 + 2nz/√3 + 30 ), V/m.
Find:
a. iE, the unit vector in the direction of the wave electric field
b. the amplitude Eo of the wave
c. the wavelength of the wave
d. ik, the unit vector in the direction of propagation
Answers
Answer:
Explanation:
From the information given:
The instantaneous expression of the electric field in the wave is:
\(E(r,t)= (i_x \sqrt{3} -i_z) 2 \ sin (2 \pi*10^8t + 2 \pi x/3+2 \pi z /\sqrt{3} + 30 ^0) , \ V/m\)
To determine the unit vector in line with the wave electric field, we take the first term in E(r,t) for \(I_E^\to\) as:
\(I_E^\to = i_x \sqrt{3}-i_z \\ \\ I_E^\to = \dfrac{i_x \sqrt{3}-i_z}{\sqrt{3 +1}} \\ \\ \mathbf{ I_E = \dfrac{i_x\sqrt{3} -i_z}{2}}\)
The amplitude is denoted by the numerical value after the first term, which is:
\(\mathbf{E_o = 2}\)
The wavelength can be determined by using the expression:
\(\beta =\dfrac{2 \pi}{\lambda }\)
from the given instantaneous expression:
\(\beta = \dfrac{2 \pi}{3}x+\dfrac{2 \pi}{\sqrt{3}}z\)
\(\beta = \sqrt{\dfrac{2 \pi}{(3)^2}+\dfrac{(2 \pi}{(\sqrt{3})^2}}\)
\(\beta = \sqrt{\dfrac{2 \pi}{9}+\dfrac{2 \pi}{{3}}}\)
Factorizing 2π
\(\beta =2 \pi \sqrt{\dfrac{1}{9}+\dfrac{1}{{3}}}\)
\(\beta =2 \pi \sqrt{\dfrac{9+3}{9*3}}}\)
\(\beta =2 \pi \sqrt{\dfrac{12}{27}}}\)
\(\beta =2 \pi \sqrt{\dfrac{4*3}{9*3}}}\)
\(\beta =2 \pi \sqrt{\dfrac{4}{9}}}\)
\(\beta =2 \pi\times {\dfrac{2}{3}}}\)
recall from the expression using in calculating wavelength:
\(\beta =\dfrac{2 \pi}{\lambda }\)
∴
equating both together, we have:
\(\dfrac{2 \pi}{\lambda }= 2 \pi\times {\dfrac{2}{3}}}\)
\(\lambda = \dfrac{3}{2}\)
λ = 1.5 m
In line with the wave direction; unit vector \(i_k\) can be computed as follows:
\(i_k = - [ \beta_1x +\beta_2z]/\beta\)
where;
\(\beta_1 = \dfrac{2 \pi }{3} \ ; \ \beta_2 = \dfrac{2 \pi }{\sqrt{3}} \ ; \ \beta = \dfrac{2 \pi \times 2}{3} ;\)
∴
\(i_k = - \Big[\dfrac{2 \pi}{3}x + \dfrac{2 \pi}{\sqrt{3}} z\Big]\times \dfrac{1}{\dfrac{2 \pi *2}{3}}\)
\(i_k = - \Big[\dfrac{x}{2} + \sqrt\dfrac{{3}}{4}} z\Big]\)
\(i_k = - \Big[\dfrac{1}{2}x + \sqrt{\dfrac{3}{4} }z\Big]\)
\(\mathbf{i_k = - \Big[0.5x +0.86 z\Big]}\)
A rear wheel drive car has an engine running at 3296 revolutions/minute. It is known that at this engine speed the engine produces 80 hp. The car has an overall gear reduction ratio of 10, a wheel radius of 16 inches, and a 95% drivetrain mechanical efficiency. The weight of the car is 2600 lb, the wheelbase is 95 inches, and the center of gravity is 22 inches above the roadway surface. What is the closest distance the center of gravity can be behind the front axle to have the vehicle achieve its maximum acceleration from rest on good, wet pavement?
Answers
Answer:
the closest distance the center of gravity can be behind the front axle to have the vehicle achieve its maximum acceleration from rest on good, wet pavement is 47.8 in
Explanation:
Given that;
Weight of car W = 2600 lb
power = 80 hp = 44000 lb ft/s
Engine rpm = 3296
gear reduction ratio e = 10
drivetrain efficiency n = 95% = 0.95
wheel radius R = 16 in = 1.3333 ft
Length of wheel base L = 95 in =
coefficient of road adhesion u = 0.60
height of center of gravity above pavement h = 22 in
we know that;
Coefficient of rolling resistance frl = 0.01 for good wet pavement
distance of center of gravity behind the front axle lf = ?
Maximum tractive effort (Fmax) = (uW / L) (lf - frl h) / (1 - uh / L)
First we calculate our Fmax to help us find lf
Power = Torque × 2π × Engine rpm / 60 )
44000 = Torque ( 2π×3296 / 60)
Torque = 127.5 lb ft
so
Fmax = Torque × e × n / R
so we substitute in our values
Fmax = 127.5 × 10 × 0.95 / 1.333
Fmax = 908.66 lb
Now we input all our values into the initial formula
(Fmax) = (uW / L) (lf - frl h) / (1 - uh / L)
908.66 = [(0.6×2600/95) (lf - 0.01×22)] / [1 - 0.6×22) / 95]
908.66 = (16.42( lf - 0.22)) / 0.86
781.4476 = (16.42( lf - 0.22))
47.59 = lf - 0.22
lf = 47.59 + 0.22
lf = 47.8 in
Therefore the closest distance the center of gravity can be behind the front axle to have the vehicle achieve its maximum acceleration from rest on good, wet pavement is 47.8 in
Each of the two sequences x1 [n] and x2[n] has a period n = 4, and the corresponding fourier series coefficients are specified asx1[n] ⇿ ak, x2 [n] ⇿ bkwherea0 =a3 = 1/2a1 = 1/2 a2 = 1 and b0 = b1 = b2 = b3 =using the multiplication property in table 3. 1 determine the fourier series coefficients ck
Answers
The Fourier series coefficients of the product sequence ck are:
c₀ = 1/2c₁ = -1/4 + j/4c₂ = -1/2c₃ = -1/4 - j/4How to determine Fourier series coefficients?Use the multiplication property of Fourier series to find the Fourier coefficients of the product of two sequences, which is given by:
c_k = (1/N) × sum_{n=0}^{N-1} x_1[n] × x_2[(n-k) mod N]
Here, N = 4 and x1[n] and x2[n] are given by their Fourier series coefficients:
x1[n] ⇿ ak, where a0 =a3 = 1/2, a1 = 1/2, a2 = 1
x2[n] ⇿ bk, where b0 = b1 = b2 = b3 = 1/4
Substituting the Fourier series coefficients into the equation for ck:
c_k = (1/4) × [a0bk + a1b(k-1 mod 4) + a2b(k-2 mod 4) + a3b(k-3 mod 4)]
Simplifying the expression by substituting the values of a and b:
c_k = (1/4) × [(1/2) × (1/4) + (1/2) × (1/4) × e^(-jk2pi/4) + 1 × (1/4) × e^(-jk4pi/4) + (1/2) × (1/4) × e^(-jk6*pi/4)]
c_k = (1/8) × [1 + e^(-jkpi/2) + e^(-jkpi) + e^(-jk3 × π/2)]
c_k = (1/8) × [1 + j^k + (-1)^k + (-j)^k]
Therefore, the Fourier series coefficients of the product sequence ck are:
c0 = 1/2
c1 = -1/4 + j/4
c2 = -1/2
c3 = -1/4 - j/4
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The transfer function of a typical tape-drive system is given by
KG(s) = K(s + 4)/ s(s + 0.5)(s + 1)(s2 = 0.4s + 4)
where time is measured in milliseconds. Using Routh's stability criterion, determine the range of K for which this system is stable when the characteristic equation is 1 + KG(s) = 0.
Answers
Answer:
the range of K can be said to be : -3.59 < K< 0.35
Explanation:
The transfer function of a typical tape-drive system is given by;
\(KG(s) = \dfrac{K(s+4)}{s[s+0.5)(s+1)(s^2+0.4s+4)]}\)
calculating the characteristics equation; we have:
1 + KG(s) = 0
\(1+ \dfrac{K(s+4)}{s[s+0.5)(s+1)(s^2+0.4s+4)]} = 0\)
\({s[s+0.5)(s+1)(s^2+0.4s+4)]} +{K(s+4)}= 0\)
\(s^5 + 1.9 s^4+ 5.1s^3+6.2s^2+ 2s+K(s+4) = 0\)
\(s^5 + 1.9 s^4+ 5.1s^3+6.2s^2+ (2+K)s+ 4K = 0\)
We can compute a Simulation Table for the Routh–Hurwitz stability criterion Table as follows:
\(S^5\) 1 5.1 2+ K
\(S^4\) 1.9 6.2 4K
\(S^3\) 1.83 \(\dfrac{1.9 (2+K)-4K}{1.9}\) 0
\(S^2\) \(\dfrac{11.34-1.9(X)}{1.83}\) 4K 0
S \(\dfrac{XY-7.32 \ K}{Y}\) 0 0
\(\dfrac{1.9 (2+K)-4K}{1.9} = X\)
\(\dfrac{11.34-1.9(X)}{1.83}= Y\)
We need to understand that in a given stable system; all the elements in the first column is usually greater than zero
So;
11.34 - 1.9(X) > 0
\(11.34 - 1.9(\dfrac{3.8+1.9K-4K}{1.9}) > 0\)
\(11.34 - (3.8 - 2.1K)>0\)
7.54 +2.1 K > 0
2.1 K > - 7.54
K > - 7.54/2.1
K > - 3.59
Also
4K >0
K > 0/4
K > 0
Similarly;
XY - 7.32 K > 0
\((\dfrac{3.8+1.9K-4K}{1.9})[11.34 - 1.9(\dfrac{3.8+1.9K-4K}{1.83}) > 7.32 \ K]\)
0.54(2.1K+7.54)>7.32 K
11.45 K < 4.07
K < 4.07/11.45
K < 0.35
Thus the range of K can be said to be : -3.59 < K< 0.35
What may be defined as the components required to identify, analyze, and contain an incident?
Answers
The components required to identify, analyze, and contain an incident may be defined as the incident response plan. An incident response plan specifies the actions to be taken by an organization's incident response team in the event of a security breach, cyber attack, or other disruptive event.
The plan typically includes procedures for detecting and reporting incidents, assessing their severity and impact, containing the incident to prevent further damage, and restoring normal operations as quickly as possible. It may also include communication protocols for keeping stakeholders informed and coordinating with external resources such as law enforcement or third-party service providers.
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Tidal turbines convert the energy of a flowing tide to generate electricity. Early designs of these machines commonly had their rotor attached to a supporting tower mounted on the seabed – see for example Figure QC2.1. A representation of a tide-driven flow of water past a tidal turbine is sketched in Figure QC2.2. An expansion of the flow from d1 to d2 is imagined to occur over the rotor, with half of the expansion (in area) happening upstream of the rotor, and half downstream.
(a) Explain why the active part of the inflow (the streamtube shown in Figure
QC2.2) expands its cross-section as it passes the turbine. (2)
Analysis for the analogous situation of a wind turbine with uniform inflow, attributed to Albert Betz and others in the 1920s, demonstrated that for optimum efficiency of energy extraction from the inflow, the far upstream flow speed should be reduced by the turbine such that the far downstream speed is 1/3rd of the far upstream speed.
(b) Suggest three reasons why this theoretical maximum efficiency will in general
not be achieved in a practical tidal turbine deployment. (3)
(c) The Alstom 1.4 MW OceadeTM turbine has a rotor diameter of 18 m. The
supporting tower has a height of 15 m and a diameter of 3 m. In a 3 ms-1 tidal
flow, estimate the total fluid loading experienced by the whole machine. State
and justify the assumptions that you make in arriving at this estimate. (12)
(d) How would you expect to use these estimates of forces when designing the
turbine and tower structure?
Answers
(a) The active part of the inflow expands its cross-section as it passes the tidal turbine due to conservation of mass and energy.
(b) Several reasons contribute to the theoretical maximum efficiency not being achieved in practical tidal turbine deployments, including turbulence, non-uniform flow, and mechanical losses.
(c) Estimating the total fluid loading on the Alstom 1.4 MW OceadeTM turbine requires considering the flow velocity, rotor and tower dimensions, and making assumptions about the flow characteristics and structural properties.
(d) The estimates of forces obtained from the fluid loading calculations are essential for designing the turbine and tower structure by ensuring that they can withstand the anticipated loads and stresses.
(a) The active part of the inflow expands its cross-section as it passes the tidal turbine due to the principle of conservation of mass and energy. As the tidal flow encounters the turbine rotor, some of the kinetic energy of the flow is converted into mechanical energy to drive the turbine. To satisfy the conservation of mass, the cross-sectional area of the flow must increase to compensate for the reduction in flow velocity caused by energy extraction.
(b) Achieving the theoretical maximum efficiency in practical tidal turbine deployments is challenging due to several reasons. First, tidal flows are often characterized by turbulence, which disrupts the uniformity of the flow and reduces overall efficiency. Second, tidal flow itself is not uniformly distributed, and the flow characteristics vary with tidal cycles, further impacting efficiency. Lastly, mechanical losses in the turbine's components, such as friction and resistance, reduce the efficiency of energy conversion.
(c) Estimating the total fluid loading on the Alstom 1.4 MW OceadeTM turbine involves considering the flow velocity, rotor diameter, and tower dimensions. Assuming a tidal flow velocity of 3 m/s, the fluid loading can be estimated by considering the momentum change and forces acting on the rotor and tower surfaces. Assumptions may include a simplified flow model, neglecting factors such as turbulence and non-uniform flow, and assuming a stationary tower. These assumptions simplify the calculation while providing a reasonable estimate of the fluid loading.
(d) The estimates of forces obtained from the fluid loading calculations are crucial for designing the turbine and tower structure. These estimates help engineers determine the required structural strength, material selection, and design considerations to ensure that the turbine and tower can withstand the anticipated fluid forces and mechanical stresses. By considering the estimated forces, designers can optimize the structural integrity, stability, and reliability of the turbine and tower, ensuring safe and efficient operation in tidal environments.
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1. Use the charges to create an electric dipole with a horizontal axis by placing a positive and a negative charge (equal in magnitude but opposite in sign) 4 meters away from each other. (Axis of a dipole is a line passing through both charges.) Place positive charge on the left and negative on the right.
2. Describe the field at the following locations, and explain these results using the superposition principle:
on the horizontal axis to the right of the dipole;
on the horizontal axis between charges;
on the horizontal axis to the left of the charges;
on the vertical line bisecting the line segment connecting the charges, above the dipole;
on the vertical line bisecting the line segment connecting the charges, below the dipole;
is there a location where the electric field is exactly zero?
Remove the negative charge and replace it with equal in magnitude positive charge.
3. Observe the change in electric field, and again describe the field at the following locations, explaining these results using the superposition principle:
on the horizontal axis to the right of the charges;
on the horizontal axis between charges;
on the horizontal axis to the left of the charges;
on the vertical line bisecting the line segment connecting the charges, above the charges;
on the vertical line bisecting the line segment connecting the charges, below the charges;
is there a location where the electric field is exactly zero?
Answers
Answer:
2)
a) to the right of the dipole E_total = kq [1 / (r + a)² - 1 / r²]
b)To the left of the dipole E_total = - k q [1 / r² - 1 / (r + a)²]
c) at a point between the dipole, that is -a <x <a
E_total = kq [1 / x² + 1 / (2a-x)²]
d) on the vertical line at the midpoint of the dipole (x = 0)
E_toal = 2 kq 1 / (a + y)² cos θ
Explanation:
2) they ask us for the electric field in different positions between the dipole and a point of interest. Using the principle of superposition.
This principle states that we can analyze the field created by each charge separately and add its value and this will be the field at that point
Let's analyze each point separately.
The test charge is a positive charge and in the reference frame it is at the midpoint between the two charges.
a) to the right of the dipole
The electric charge creates an outgoing field, to the right, but as it is further away the field is of less intensity
E₊ = k q / (r + a)²
where 2a is the distance between the charges of the dipole and the field is to the right
the negative charge creates an incoming field of magnitude
E₋ = -k q / r²
The field is to the left
therefore the total field is the sum of these two fields
E_total = E₊ + E₋
E_total = kq [1 / (r + a)² - 1 / r²]
we can see that the field to the right of the dipole is incoming and of magnitude more similar to the field of the negative charge as the distance increases.
b) To the left of the dipole
The result is similar to the previous one by the opposite sign, since the closest charge is the positive one
E₊ is to the left and E₋ is to the right
E_total = - k q [1 / r² - 1 / (r + a)²]
We see that this field is also directed to the left
c) at a point between the dipole, that is -a <x <a
In this case the E₊ field points to the right and the E₋ field points to the right
E₊ = k q 1 / x²
E₋ = k q 1 / (2a-x)²
E_total = kq [1 / x² + 1 / (2a-x)²]
in this case the field points to the right
d) on the vertical line at the midpoint of the dipole (x = 0)
In this case the E₊ field points in the direction of the positive charge and the test charge
in E₋ field the ni is between the test charge and the negative charge,
the resultant of a horizontal field in zirconium on the x axis (where the negative charge is)
E₊ = kq 1 / (a + y) 2
E₋ = kp 1 / (a + y) 2
E_total = E₊ₓ + E_{-x}
E_toal = 2 kq 1 / (a + y)² cos θ
e) same as the previous part, but on the negative side
E_toal = 2 kq 1 / (a + y)² cos θ
When analyzing the previous answer there is no point where the field is zero
The different configurations are outlined in the attached
3) We are asked to repeat part 2 changing the negative charge for a positive one, so in this case the two charges are positive
a) to the right
in this case the two field goes to the right
E_total = kq [1 / (r + a)² + 1 / r²]
b) to the left
E_total = - kq [1 / (r + a)² + 1 / r²]
c) between the two charges
E₊ goes to the right
E₋ goes to the left
E_total = kq [1 / x² - 1 / (2a-x)²]
d) between vertical line at x = 0
E₊ salient between test charge and positive charge
E_total = 2 kq 1 / (a + y)² sin θ
In this configuration at the point between the two charges the field is zero
Who is he where is he from
Answers
Answer:
Levi Ackerman is the tritagonist of the anime/manga series Attack on Titan. He is a Captain in the Survey Corps , known to be the strongest soldier alive. He has a harsh and unsocial personality, but is well-regarded by his subordinates and he cares about their lives. Levi Ackerman spent his childhood in the Underground City. It was the slums of the Attack on Titan’s entire world
Explanation: