Problem Description: design a digital control system for the production process of bottled water as per the following process: A motor runs the conveyor belt, which move the bottle. Then, the bottle stops for the filling process. It is filled with water in 5 seconds. After that, the bottle moves away and stops for the capping (sealing) process. It is capped in 3 seconds. Then, the process repeats again for the next empty bottle Task1:Draw the module block diagram of your design.
Answers
Here is a summarized explanation of the digital control system design for the bottled water production process:
The production processMotor/Conveyor Belt Block: This block controls the movement of the bottle along the production line. Upon detection of an empty bottle, it triggers the conveyor belt to start moving the bottle towards the filling station.
Fill Water Block: Once the empty bottle reaches the filling station, this block sends a signal to stop the conveyor belt. Concurrently, it initiates the filling process, which lasts for 5 seconds as regulated by a timer. After the filling process, it signals the conveyor belt to move the bottle to the next station, i.e., the capping station.
Capping Block: Upon the arrival of the filled bottle at the capping station, the conveyor belt is halted again via a signal from this block. This block initiates the capping process, which is managed for 3 seconds by another timer. Once the capping process concludes, it signals the conveyor belt to resume operation and transfer the bottle towards the end of the production line.
End State: The bottled water is now ready for packaging and shipment. The system resets and waits for the next empty bottle to restart the production process.
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Related Questions
When carbón and other materials are allowed with iron they forma
Answers
Answer:
steel
Explanation:
Assuming the word "allowed" was meant to be "alloyed"
a DC motor consists of a permanent magnet and an electromagnet that changes its polarity. Why does the electromagnets have to change its polarity for the motor to work?
Answers
The electromagnet in a DC motor needs to change polarity to ensure that the motor rotates continuously in one direction.
A DC motor works on the principle of electromagnetism, where the interaction between the magnetic fields generated by a permanent magnet and an electromagnet causes the motor shaft to rotate.
The electromagnet is powered by a DC current, which causes it to produce a magnetic field that interacts with the magnetic field of the permanent magnet.
To ensure that the motor shaft continues to rotate in one direction, the polarity of the electromagnet needs to change as the shaft turns, so that the interaction between the two magnetic fields remains in the same direction.
This is achieved by using a commutator, which reverses the current direction in the electromagnet every half turn of the motor shaft, thus changing its polarity and allowing for continuous rotation.
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determine the steady state temperature distribution between two concentric spheres with radii 1 and 4
Answers
Answer:
Hence, the steady state temperature distribution between concentric spheres with radii 1 and 4 is:
u = \(\frac{C1}{r }\) + C2
u = \(\frac{\frac{-320}{3} }{r}\) + \(\frac{320}{3}\)
Explanation:
Solution:
Note: This question is incomplete and lacks necessary data to solve this question. But I have found a similar question and will try to solve it.
This question has this following part missing:
"If the temperature of the outer sphere is maintained at 80 degrees and the inner sphere at 0 degrees.
Now, this question is complete.
Let's find out the steady state temperature distribution.
As, we know the spherical symmetric heat equation:
\(\frac{du}{dt}\) = \(\frac{k}{r^{2} }\) \(\frac{D}{Dr}\) (\(r^{2}\) \(\frac{Du}{Dr}\))
Where, small (d) represents the partial differentiation and Capital D represents simple derivative.
And the ordinary differential equation (ODE) for steady state temperature distribution is:
\(\frac{k}{r^{2} }\) \(\frac{D}{Dr}\)(\(r^{2}\) \(\frac{Du}{Dr}\)) = 0
So it can be said that:
\(r^{2}\) \(\frac{Du}{Dr}\)
Consequently,
\(\frac{Du}{Dr}\) = \(\frac{C1}{r^{2} }\)
Taking derivative of the above equation we get:
u = -\(\frac{C1}{r }\) + C2
Solution of the ordinary differential equation
u = \(\frac{C1}{r }\) + C2 (Consuming the negative sign into C1 constant)
As, it is given in our question that our boundary conditions are: 1 and 4
So,
Putting the boundary conditions into the variable (r) to find the constants we get:
u1 = \(\frac{C1}{1} }\) + C2 = 0 (degrees)
u1 = C1 + C2 = 0 (degrees) equation (1)
Similarly,
u4 = \(\frac{C1}{4}\) + C2 = 80 (degrees)
u4 = \(\frac{C1}{4}\) + C2 = 80 (degrees) equation (2)
Solving for C1, we get:
Equation 1 - Equation 2
(C1 - C2 = 0) - (\(\frac{C1}{4}\) + C2 = 80)
\(\frac{-3}{4}\)C1 = 80
Solving for C1
C1 = -\(\frac{320}{3}\)
With the help of value of C1, we get value of C2
Put the value of C1 in equation (1) to get value of C2
C1 + C2 = 0
-\(\frac{320}{3}\) + C2 = 0
Solving for C2
C2 = \(\frac{320}{3}\)
Hence, the steady state temperature distribution between concentric spheres with radii 1 and 4 is:
u = \(\frac{C1}{r }\) + C2
Plugging in the values of C1 and C2
u = \(\frac{\frac{-320}{3} }{r}\) + \(\frac{320}{3}\)
which of the following devices are used in networking? check all that apply?
switches, hubs,TCP or routers
Answers
Answer:
Hub , switch port , transmission media , hope I helped
Explanation:
For the following production environments, indicate whether the preferred production system is more likely to be a job shop (process layout), production line (product layout), batch process (group technology layout), or hybrid. Provide support for your answer.
a. Manufacturer of Clothes: makes many styles (shirts, pants, coats, rain jackets, etc.) and sells to small specialty stores.
b. Manufacturer of Gaskets: makes styles for 4-5 engine blocks: sells to GM and Ford (i.e., high volume).
c. Independent Automobile Service Shop: body work, general service, engine repair, serving many makes of automobiles.
d. Producer of Pharmaceutical Drugs: make approximately 50-75 drugs in tablet form: sell to pharmacies nationwide.
Answers
Answer:
A) Batch shop production
B) Batch shop production
C) Job shop production
D) production line
Explanation:
A)The preferred production system here will be Batch shop production because the manufacturer produces different styles of clothing and sells to small specialty stores hence producing in Batches can help meet up the needs
B) The preferred production system here will be Batch shop production because the manufacturer produces Gaskets and they are of different styles hence he needs to produce them in batches
C) Job shop production
D) production here is streamlined to a particular ( tablet form ) hence the production system here would be a Production line system of production
Engineer drawing:
How can i draw this? Any simple way?
Answers
Describe some three materials with nanocrystalline structures and identify each example of those material
Answers
Ultrafine crystalline grains in the nanometer range that are separated by grain boundaries or interfaces define nanocrystalline materials.
A nanocrystalline structure: what is it?A polycrystalline substance with a few nanometer-sized crystallites is referred to as a nanocrystalline (NC) substance. These materials bridge the gap between traditional coarse-grained materials and amorphous materials devoid of long-range organisation. Materials that contain clusters, crystallites, or molecules with diameters between 1 and 100 nm are said to be nanostructured materials.
What is an example of a nanostructure?The gecko's foot, iridescent butterfly wings, and hydrophobic leaves are just a few examples of nanostructures found in nature. Scientists and engineers are employing biomimicry to develop new goods with these nano-inspired qualities.
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Un mol de gas ideal realiza un trabajo de 3000 J sobre su entorno, cuando se expande de manera isotermica a una temperatura de 58°C, cuando su volumen inicial es de 25 L. Determinar el volumen final
Answers
Answer:
74,4 litros
Explanation:
Dado que
W = nRT ln (Vf / Vi)
W = 3000J
R = 8,314 JK-1mol-1
T = 58 + 273 = 331 K
Vf = desconocido
Vi = 25 L
W / nRT = ln (Vf / Vi)
W / nRT = 2.303 log (Vf / Vi)
W / nRT * 1 / 2.303 = log (Vf / Vi)
Vf / Vi = Antilog (W / nRT * 1 / 2.303)
Vf = Antilog (W / nRT * 1 / 2.303) * Vi
Vf = Antilog (3000/1 * 8,314 * 331 * 1 / 2,303) * 25
Vf = 74,4 litros
An engineer places a small sample of a material on a horizontal disk whose surface is made of another material and then rotates the disk from rest with a constant angular acceleration of 4 rad/s2. Assuming that the coefficient of static friction between the sample and disk is 0. 2, what is the angular velocity of the disk at the time instant when the sample starts slipping on the disk?.
Answers
The critical value of the angular velocity obtained just before the slipping starts is the answer to this question and it is \(\bold{\omega = \sqrt{\frac{\mu.g}{r}}}\).
Let's consider the sample to be a point object.There are 2 forces acting upon the sample when it is on the plane and rotating: the normal force from the plane and the friction force directed to the centre of the rotating axis.This friction force provides the centripetal force needed to continue the rotation on the disk keeping itself at rest on the disk relative to it.The reason for a slip is due to the lacking of this friction so that it is no longer capable of providing the required amount of centripetal force in the form of friction.The maximum friction is simply \(f_{max} = \mu_s.R\) where \(R\) is the normal force on the sample and \(\mu_s\) the coefficient of static friction. By the vertical equilibrium \(R = mg\) and that gives \(f_{max} = \mu_s. mg\)The proper condition to continue the rotation without slipping is as follows and the critical value of angular velocity can be found from it.
\(\begin{aligned}\\\\F &= ma\\\\f_{max} &\geq ma\\\\ \mu_s.mg &\geq m.r\omega^2\\\\\omega &\leq \sqrt{\frac{\mu_sg}{r}}\\\\\omega_{critical} &= \sqrt{\frac{\mu_sg}{r}}\end{aligned}\)
The critical angular velocity depends only on these parameters and for a given system it is dependent on where it is primarily placed from the centre of rotation (this question lacks this piece of data by the way).So this is the answer to this question and with the data for the constant angular acceleration, you can calculate how long it would take from the startup or how many rotations it would take until the point of slipping.For that, you can employ the formulae \(\omega = \omega_0+\alpha.\Delta t\) and \(\omega^2 = \omega^2_0+2\alpha .\Delta \theta\) respectively by putting \(\omega = \omega_{critical}\).#SPJ4
determine the components of each reaction at the ball and socket joint A and the tension in each cable necessary for equilibrium of the rod
Answers
The components of the reaction force in a ball and socket joint include the horizontal and vertical reaction forces.
What is a reaction force?A reaction force is an equal but oppositely directed force which forms a pair which the applied or action force.
Tension is a type of force which is present in a string or a rope supporting a body or object.
A ball and socket jont is a type of joint in the body which is able to rotate freely about an axis.
The components of the reaction force in a ball and socket joint include the horizontal and vertical reaction forces.
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In order to fill a tank of 1000 liter volume to a pressure of 10 atm at 298K, an 11.5Kg of the gas is required. How many moles of the gas are present in the tank? What is the molecular weight of the gas? Assuming that the gas to be a pure element can you identify it?
Answers
Answer:
The molecular weight will be "28.12 g/mol".
Explanation:
The given values are:
Pressure,
P = 10 atm
= \(10\times 101325 \ Pa\)
= \(1013250 \ Pa\)
Temperature,
T = 298 K
Mass,
m = 11.5 Kg
Volume,
V = 1000 r
= \(1 \ m^3\)
R = 8.3145 J/mol K
Now,
By using the ideal gas law, we get
⇒ \(PV=nRT\)
o,
⇒ \(n=\frac{PV}{RT}\)
By substituting the values, we get
\(=\frac{1013250\times 1}{8.3145\times 298}\)
\(=408.94 \ moles\)
As we know,
⇒ \(Moles(n)=\frac{Mass(m)}{Molecular \ weight(MW)}\)
or,
⇒ \(MW=\frac{m}{n}\)
\(=\frac{11.5}{408.94}\)
\(=0.02812 \ Kg/mol\)
\(=28.12 \ g/mol\)
for a company that wishes to reduce its carbon footprint, which of the following transportation modes is preferred?
Answers
Public transportation, cycling, and walking are the preferred modes of transportation for companies aiming to reduce their carbon footprint, as they produce fewer greenhouse gas emissions and promote sustainability.
For a company looking to reduce its carbon footprint, the preferred transportation mode would be public transportation, followed by cycling, and walking. These options produce fewer greenhouse gas emissions compared to private cars and air travel.
1. Evaluate each transportation mode in terms of carbon emissions.
2. Compare the emissions produced by each mode.
3. Choose the mode with the least environmental impact.
To reduce a company's carbon footprint, prioritize public transportation as it has lower emissions compared to private vehicles and air travel. Cycling and walking are also eco-friendly alternatives with minimal carbon emissions. These options contribute to a greener environment and help the company achieve its sustainability goals.
Public transportation, cycling, and walking are the preferred modes of transportation for companies aiming to reduce their carbon footprint, as they produce fewer greenhouse gas emissions and promote sustainability.
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why do u have to have certain limits for questions
Answers
Answer:
ok
Explanation:
What Advantage does a voltmeter have over a noncontact voltage indicator when testing for voltage
Answers
Answer:
Obviously you shouldn't rely just on the meter for your safety. You'd disconnect wall fuses or kill main switches before you start, using the meter just gives you some extra protection: with the meter you might notice for example that you've disconnected the wrong fuse and the unit is still live.
Explanation:
Hope it helps! :)
By balancing information security and access, a completely secure information system can be created.A. TrueB. False
Answers
Answer: true
Explanation:
The amusement park ride consists of a fixed support near O, the 6-m arm OA, which rotates about the pivot at O, and the compartment, which remains horizontal by means of a mechanism at A. At a certain instant, β=30ο, 2 0.75 rad/s, and 0.5 rad/s , all clockwise. Determine the horizontal and vertical forces (F and N) exerted by the bench on the 75-kg rider at P. Compare your results with the static values of these forces. (Use x-y coordinate system and vector equations
Answers
Answer:
Check the explanation
Explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
c) Three AC voltages are as follows:
e1 = 80 sin ωt volts;
e2 = 60 sin (ωt + π/2) volts;
e3 = 100 sin (ωt – π/3) volts.
Find the resultant e of these three voltages and express it in the form
Em sin (ωt ± φ). [5 MARKS]
When this resultant voltage is applied to a circuit consisting of a 10-Ω resistor and a capacitance of 17.3 Ω reactance connected in series, find an expression for the instantaneous value of the current flowing, expressed in the same form. [4 MARKS]
Answers
Answer:
E = 132.69 sin(ωt -11.56)
i(t) = 6.64 sin (ωt +48.44) A
Explanation:
given data
e1 = 80 sin ωt volts 80 < 0
e2 = 60 sin (ωt + π/2) volts 60 < 90
e3 = 100 sin (ωt – π/3) volts 100 < -60
solution
resultant will be = e2 + e2 + e3
E = 80 < 0 + 60 < 90 + 100 < -60
\(\bar E\) = 80 + j60 + 50 - j50\(\sqrt{3}\)
\(\bar E\) = 130 + (-j26.60)
\(\bar E\) = 132.69 that is less than -11.56
so
E = 132.69 sin(ωt -11.56)
and
as we have given the impedance
z = (10-j17.3)Ω
z = 19.982 < -60
and
i(t) = \(\frac{132.69}{19.982}\) sin(ωt -11.56 + 60)
i(t) = 6.64 sin (ωt +48.44) A
a 28.7 mh inductor and an 8.06 μf capacitor are placed in series to create an lc circuit. what is the resonant oscillation frequency of this circuit in hz?
Answers
The resonant frequency of the LC circuit can be calculated using the formula:
f = 1 / (2 * pi * sqrt(LC))
Plugging in the values of the inductor (L = 28.7 mH) and capacitor (C = 8.06 μF), we get:
f = 1 / (2 * pi * sqrt(28.7 mH * 8.06 μF)) = 703.8 Hz (approximately)
An LC circuit is a type of electronic circuit that consists of an inductor and a capacitor connected in series or parallel. The circuit can store energy oscillating back and forth between the capacitor and the inductor, producing a resonant frequency. The resonant frequency of an LC circuit depends on the values of the inductor and capacitor and can be calculated using the formula f = 1 / (2 * pi * sqrt(LC)). The unit of inductance is Henry (H), and the unit of capacitance is Farad (F). In this question, the inductance value is given in milliHenries (mH), and the capacitance value is given in microFarads (μF). To use the formula, we need to convert the values to Henry and Farad, respectively, before plugging them into the equation.
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1 Introduction Heat exchangers are used in many applications. They consist of two fluid streams, one hot and one cold. The cold stream is used to cool the hot stream, and vice versa. Perhaps the most common example is an automobile radiator. Coolant is circulated through the engine to keep it cool. However, this also heats up the coolant. In the radiator, the air enters and serves to cool the hot coolant before it is recirculated through the engine. In any thermodynamic system, including heat exchangers, energy must be conserved. Today's lab explores the heat and work interactions between the two fluids in a heat exchanger. 2 Assignment Consider a heat exchanger that uses hot air to heat cold water. Air enters this heat exchanger at 20psia and 200
∘
F at a rate of 100cfm and leaves at 17psia and 100
∘
F. Water enters at 20psia and 50
∘
F at a rate of 0.5lbm/s and exits at 17psia. Determine the exit temperature of the water and the fan and pump powers necessary to drive the air and water flows respectively. Figure 1: Heat exchanger with cold water running through the tubes and hot air moving across the exchanger. Plot the boundary work and heat transfer versus n in increments of 0.1, and discuss the results.
Answers
A heat exchanger is considered, that uses hot air to heat cold water. Air enters this heat exchanger at 20psia and 200 °F at a rate of 100cfm and leaves at 17psia and 100 °F. Water enters at 20psia and 50 °F at a rate of 0.5lbm/s and exits at 17psia.
The exit temperature of the water and the fan and pump powers necessary to drive the air and water flows, respectively, is to be determined. It is required to determine the exit temperature of the water and the fan and pump powers necessary to drive the air and water flows, respectively. Considering the air-side first, using the formula for enthalpy change, ∆h = C p * m * ∆T where ∆h is the enthalpy change, C p is the specific heat capacity, m is the mass flow rate, and ∆T is the temperature difference.
In this case: ∆h = C p * m * ∆T∆ h = 0.24 * 100 * (200 − 100) = 2400 BTU/h The air-side pressure drop is given by:∆P = P f − Pi = 20 − 17 = 3 psi. The air-side power required is given by the formula, Power = ∆P * V * f where V is the volumetric flow rate and f is the fluid density. Rearranging this, Power = ∆P * m / f where m is the mass flow rate. Thus, Power = (3 * 100 / 60) * 100 / 14.7 = 15.3 h p Now consider the water-side.
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A three-phase, wye-connected, 6.25 kVA, 220-V synchronous generator has a reactance of 8.4 2 per phase. Using the rated power and voltage as base values: a. Determine the per-unit reactance, and b. Refer this per-unit reactance to bases of 7.50 kVA and 230 V. a. b.
Answers
According to the data in the question, the synchronous generator's per-unit reactance with respect to bases of 7.50 kVA as well as 230 V is 1.127 pu, and its per-unit reactance with respect to bases of 1.087 pu.
What does synchronous generator mean?A synchronized generators is a machine that converts mechanical energy into alternating (AC) electricity via electromagnetic induction. Alternators or AC producers are other names for synchronous generators. It is known as a "alternator" because it produces AC electricity.
How do synchronous and asynchronous generators vary from one another?The optimum uses for synchronous motors are low speed (continuous) application with speeds under 300 RPM. High speeds, greater than 600 RPM, are suitable for asynchronous motors. By adjusting the excitation, a motor can be run at a lagging lead or unity power factor.
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at what distance r from the center of a tube of radius r0 does the average velocity occur in a laminar flow?
Answers
In a laminar flow, the average velocity of 0.707r0 occurs at a distance r from the center of a tube with radius r0.
What is the ratio of a fluid's maximum velocity to its average velocity in a pipe?The maximum velocity for a fully developed laminar viscous flow through a circular pipe is double the average velocity. The maximum velocity for fully developed laminar flow through parallel plates is equal to (3/2) times the average velocity.
What are the two average velocity formulas?Because displacement is always less than or equal to the distance traveled, average velocity is always either less than or equal to average speed.
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If a PPE doesn’t fit properly do you keep wearing them
Answers
Which of following are coding languages used in controlling a robot? *
A. Scratch
B. B/B--
C. C/C++
D. Robot Z
Answers
Answer:
C/C++
Explanation:
C/C++
Tech A says that a mechanical pressure regulator exhausts excess fluid back to the transmission pan. Tech B says that if the transmission pan is removed, the magnet must be replaced. Who is correct?
Answers
Answer:
A
Explanation:
6. You are an electrician working in an industrial plant. You are building a motor control cabinet that contains six motor starters and six pilot lamps. All control components operate on 120 volts AC. Two of the motor starters have coil currents of 0.1 amperes each and four have coil currents of 0.18 amperes each. The six pilot lamps are rated at 5 watts each. The supply room has control transformers with the following rating (in volt-amperes):
75, 100, 150, 250, 300, and 500.
Which of the available control transformers should you choose to supply the power for all the control components in the cabinet?
Answers
Answer:
It's indeed safer to suggest a 150 VA transformer. Following table however is the clarification given.
Explanation:
For 2 motors with 0.1 A, the Power will be:
P = \(2\times 120\times 0.1\)
= \(24 \ W\)
For 4 motors with 0.18 A, the Power will be:
P = \(4\times 120\times 0.18\)
= \(86.4 \ W\)
As we know, for 6 pilot lamps, the power is "5 W".
So,
The total power will be:
⇒ P = \(24+86.4+5\)
= \(115.4 \ W\)
Now,
Consider the power factor to be "0.95"
VA of transformer is:
= \(PF\times Power\)
= \(115.4\times 0.9\)
= \(109.63 \ VA\)
Technician A says polarity is simply the state of charge. Technician B says polarity does not produce current flow. Who is correct? Select one: a. Technician A b. Technician B c. Both Technician A and Technician B d. Neither Technician A nor Technician B
Answers
Polarity is the state of charge that decides the flow of electric current. Technician A is correct in stating this fact, and technician B is also correct because polarity does not produce current flow.
Polarity is a characteristic that shows the presence of an electrical charge at the ends of a conductor. Electrical current flows from an area of higher polarity to an area of lower polarity. In other words, it flows from positive to negative terminals. The polarity of a conductor is an essential consideration when designing or repairing electrical circuits. Hence, technician A is correct in stating that polarity is merely the state of charge in the circuit.Technician B is also correct in saying that polarity does not produce current flow.
Polarity is responsible for establishing the flow of electrical current. Current flows through a circuit because of the difference in polarity at the two ends of the conductor. As a result, technician B's statement is true because polarity only establishes the flow of current, and it is not responsible for producing current flow. Therefore, both technician A and technician B are correct in their statements.In conclusion, the right answer is that both technician A and technician B are correct.
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Write the equations of the forces and their dimensions which are
important in fluid mechanics
Answers
In fluid mechanics, important forces include gravitational force, pressure force, viscous force, and surface tension force. These forces play a crucial role in understanding the behavior of fluids.For example, pressure force has dimensions of force per unit area (N/m² or Pa), viscous force has dimensions of force per unit area per unit velocity gradient (N/m²·s), and surface tension force has dimensions of force per unit length (N/m).
Fluid mechanics is the study of how fluids (liquids and gases) behave under various conditions. Several forces are essential in analyzing fluid flow and understanding the forces at work.
The gravitational force is a fundamental force that acts on all objects with mass, including fluids. It causes fluids to exert pressure, which is the force per unit area exerted by a fluid. The pressure force plays a significant role in determining the direction and magnitude of fluid flow.
Viscous force is another critical force in fluid mechanics. It arises due to the internal friction between fluid layers moving at different velocities. This force opposes the relative motion of fluid layers and determines the resistance to flow.
Surface tension force is specific to liquid fluids and occurs due to the cohesive forces between molecules at the surface. It causes liquids to form droplets or rise in capillary tubes, affecting fluid behavior at the interface.
The dimensions of these forces are derived from their respective equations.
Understanding and quantifying these forces and their dimensions are crucial for analyzing fluid behavior, designing fluid systems, and solving fluid mechanics problems.
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Chisel edge pencils are used for drawing?
Answers
Answer:
Yes.
Explanation:
These pencils can be used for both. The top sharp edge can be used for finer markings, details and creating fine lines. The flat angled plane can be used for shading.
Which statement best describes how power and work are related?
O A. Power is the ability to do more work with less force.
O B. Power is a measure of how quickly work is done.
O C. Power and work have the same unit of measurement
O D. Power is the amount of work needed to overcome friction.
Pls answer quick
Answers
B
a jsdnjwevhfgruewbkuwygru
Calculate the effective value of each of the periodic voltages: (a) 6 cos 25t; (b) 6 cos 25t+ 4 sin (25t+30°); (c) 6 cos 25t+ 5 cos2(25t); (d) 6 cos 25t+ 5 sin 30t +4 V.
Answers
(a) Vrms = 4.243 V; (b) Vrms = 7.211 V; (c) Vrms = 6.481 V; (d) Vrms = 7.359 V.
What is the relationship between the peak value and the effective value of a sinusoidal waveform?To calculate the effective value (also known as the RMS or root mean square value) of each of the periodic voltages, we can use the formula:
Vrms = sqrt((1/T) * ∫[0 to T] (V(t))^2 dt),
where V(t) represents the instantaneous voltage as a function of time, T is the period of the voltage waveform, and the integral is taken over one complete period.
For V(t) = 6 cos(25t), the effective value is Vrms = 6 / sqrt(2) ≈ 4.243 V. For V(t) = 6 cos(25t) + 4 sin(25t + 30°), the effective value is Vrms = sqrt(36 + 16/2) ≈ 7.211 V. For V(t) = 6 cos(25t) + 5 cos^2(25t), the effective value is Vrms = sqrt(36 + 5/2) ≈ 6.481 V. For V(t) = 6 cos(25t) + 5 sin(30t) + 4, the effective value is Vrms = sqrt(36 + 25/2 + 4) ≈ 7.359 V.Learn more about Vrms
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