Determine the streamline, pathline and streakline that pass through the origin (0, 0) at t=t' for v=(u,v) with u=cos(wt)
Answers
The streamline passing through the origin occurs at times t' = nπ/w, where n is an integer.
The pathline passing through the origin occurs at times t' = nπ/w, where n is an integer.
The streakline passing through the origin is x = (1/w) * sin(wt'), where t' ≤ t.
To determine the streamline, pathline, and streakline that pass through the origin (0, 0) at time t = t' for the velocity field v = (u, v) with u = cos(wt), we need to analyze the given velocity field and understand the definitions of each of these concepts.
1. Streamline:
A streamline is a curve that is tangent to the velocity vector at every point along the curve. In other words, the velocity field is always tangent to the streamline.
To find the streamline passing through the origin, we need to integrate the differential equations for the velocity components:
dx/dt = u = cos(wt)
dy/dt = v
Integrating the first equation, we get:
x = (1/w) * sin(wt) + C1
Integrating the second equation, we have:
y = ∫v dt = ∫(0) dt = C2
Since the streamline passes through the origin (0, 0), we substitute these values into the equations:
0 = (1/w) * sin(wt') + C1 (Equation 1)
0 = C2 (Equation 2)
From Equation 2, we get C2 = 0, meaning the streamline passes through the y-axis.
Substituting C2 = 0 into Equation 1, we have:
0 = (1/w) * sin(wt') + C1
To satisfy this equation for all t', the term sin(wt') must be zero. This happens when wt' = nπ, where n is an integer.
Therefore, the streamline passing through the origin occurs at times t' = nπ/w, where n is an integer.
2. Pathline:
A pathline is the actual trajectory of a fluid particle as it moves through space. It traces the path of a specific fluid particle over time.
To find the pathline passing through the origin, we need to solve the differential equations for the velocity components:
dx/dt = u = cos(wt)
dy/dt = v
Integrating the first equation, we get:
x = ∫u dt = ∫cos(wt) dt = (1/w) * sin(wt) + C3
Integrating the second equation, we have:
y = ∫v dt = ∫(0) dt = C4
Since the pathline passes through the origin (0, 0), we substitute these values into the equations:
0 = (1/w) * sin(wt') + C3 (Equation 3)
0 = C4 (Equation 4)
From Equation 4, we get C4 = 0, meaning the pathline passes through the y-axis.
Substituting C4 = 0 into Equation 3, we have:
0 = (1/w) * sin(wt') + C3
This equation holds true for all t' if sin(wt') = 0. This occurs when wt' = nπ, where n is an integer.
Therefore, the pathline passing through the origin occurs at times t' = nπ/w, where n is an integer.
3. Streakline:
A streakline is formed by fluid particles that have passed through a particular point in space at different times. It represents the history of fluid particles that have traveled through the point.
To find the streakline passing through the origin, we consider all fluid particles that have passed through (0, 0) at different times.
The streakline passing through the origin is given by the set of points (x(t'), y(t')) for all t' ≤ t, where t is the current time.
Using the equations for x and y derived earlier, we can express the streakline passing through the origin as:
x(t') = (1/w) * sin(wt')
y(t') = 0
Therefore, the streakline passing through the origin is x = (1/w) * sin(wt'), where t' ≤ t.
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Related Questions
A car drives 40 miles at an angle of 35 degrees north of east then drives for 50 miles due north and finally 10 miles at an angle of 20 degrees north of west what is the cars resultant magnitude and direction
Answers
Answer:
Below
Explanation:
FIND TOTAL NORTH DISPLACEMENT
40 sin 35 + 50 + 10 sin 20 = 76.363 mi
FIND TOTAL E-W DISPLACEMENT
40 cos 35 - 10 cos 20 = 23.369 mi
Total resultant displacement ( using pythag theorem)
sqrt ( 76.363^2 + 23.369^2 ) = 79.86 mi
angle = arctan ( 79.23 / 23.37) = 73 ° North of East
You drop a lead fishing weight and a filled water balloon. Which do you expect to fall faster?
Answers
I believe they should fall at the same pace.
Please help me!! Time = 98 seconds speed=7.5 meters/second what is the distsnce in meters
Answers
Answer:
735 mExplanation:
The distance covered by an object given it's speed and time taken can be found by using the formula
distance = speed × time
From the question we have
distance = 7.5 × 98 = 735 m
We have the final answer as
735 mHope this helps you
Two uncharged spheres are separated by 2.00 m. If 3.50 3 1012 electrons are removed from one sphere and placed on the other, determine the magnitude of the Coulomb force on one of the spheres, treating the spheres as point charges.
Answers
Two uncharged spheres separated by 2.00 m. If 3.50 × 10¹² electrons are removed from one sphere and placed on the other, determine the magnitude of the Coulomb force on one of the spheres, treating the spheres as point charges.
The Coulomb force between two point charges separated by a distance r is represented by the Coulomb's law given as: \[F=k\frac{q_1q_2}{r^2}\]Where F represents force, q1 and q2 are the charges of the two bodies, k is the Coulomb constant, and r is the distance between the two point charges.
The Coulomb constant k is given as: \[k = \frac{1}{4\pi \varepsilon_0}\]Where ε0 is the permittivity of free space and is defined as: \[\varepsilon_0 = 8.854 × 10^{−12} \frac{C^2}{N⋅m^2}\]From the question;Charge on the 1st sphere = q1 = -3.50 × 10¹²Charge on the 2nd sphere = q2 = +3.50 × 10¹²Distance between the two spheres = r = 2.00 mUsing the Coulomb's law,\[F=k\frac{q_1q_2}{r^2}\]Substituting the given values,\[F= 9\times 10^9 \times \frac{\left( -3.50\times 10^{12} \right) \left( 3.50\times 10^{12} \right)}{\left( 2.00 \right)^2}\]Simplifying,\[F= -6.12 \times 10^{-2} N\]Therefore, the magnitude of the Coulomb force on one of the spheres is 6.12 × 10^-2 N.
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a photo taken by an american spy plane pilot at 60,000 feet was just released. what does it show?
Answers
Historically, photographs taken by American spy planes at high altitudes have been used for various purposes such as reconnaissance and intelligence gathering.
Depending on the specific photograph in question, it could potentially show a wide range of information such as military installations, troop movements, or other sensitive information. The altitudes at which a photo is taken can affect the level of detail that can be seen in the image. However, it is important to note that the use of such technology can also raise privacy and security concerns, particularly if it is used to gather information on individuals or groups without their consent or knowledge.
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George rides his bike to his friend’s house that is 5 kilometers from his house. If he rides his bike at an average speed of 15 km/h, how long will it take him to get to his friend’s house?
Answers
Answer:
The answer is 0.33 H!
Explanation:
a ball on the end of a string is whirled with constant speed in counterclockwise horizontal circle. at point a in the circle, the string breaks. which of the curves sketched below most accurately represents the path that the ball will take after the string breaks?
Answers
When the string breaks at point a, the ball will continue to move in a straight line tangent to the point on the circle where it broke free. The third curve most accurately represents the path the ball will take after the string breaks.
This means that the ball will continue moving in the direction it was moving at the moment the string broke. In the first curve, the ball appears to continue moving in a circle, which is not possible as it has lost its centripetal force.
The second curve shows the ball moving in a straight line in the direction of its velocity at point a, which is the correct direction. However, the curve appears to be too steep as the ball should continue moving in a straight line with constant velocity. The third curve shows the ball moving in a straight line with constant velocity, which is the correct behavior.
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how has evidence changed our views on the universe
Answers
Answer:
We found out more about how the universe had started (Big Bang theory), how the planets were created and how stars are born.
3. 500ml of 60oC water at is added to a beaker. Water’s specific heat is 4.186 J/g °C. You have 40ml of and unknown substance that you add to the same beaker. The unknown substance’s specific heat is 14.3/goC The final temperature of the beaker is 45oC. What was the initial temperature of the unknown substance?
Answers
which of the following is a force contributing the to advancement of ai that is producing vast amounts of data for ai applications?
Answers
Rapid increases in network connected smart devices is a force contributing the to advancement of AI that is producing vast amounts of data for AI applications.So option B is correct.
AI applications require vast amounts of data to train and improve their performance. This data can come from a variety of sources, such as sensors, social media, and customer transactions. However, one of the biggest sources of data for AI applications is network connected smart devices.
Smart devices are everywhere, from our homes to our cars to our workplaces. They collect data about our activities, our environment, and our interactions with the world around us. This data can be used to train AI applications to do things like recognize objects, predict behavior, and make decisions.
The rapid increase in the number of network connected smart devices is one of the key forces driving the advancement of AI. As more and more devices collect data, AI applications will become more powerful and capable.
The other options are also important forces contributing to the advancement of AI, but they do not produce vast amounts of data for AI applications. Increased computing power allows AI applications to process more data and make more complex decisions. Cloud computing makes it easier to store and share data, which is essential for AI applications. Breakthroughs in AI techniques allow AI applications to learn and improve more effectively.
However, without the vast amounts of data collected by network connected smart devices, AI applications would not be able to achieve their full potential. Therefore, option B is correct.
The question should be:
Which of the following is a force contributing the to advancement of AI that is producing vast amounts of data for AI applications?
(a)Increased computing power
(b)Rapid increases in network connected smart devices
(c)Cloud computing
(d)Breakthroughs in AI techniques
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The length, breadth and height of a box is 2m, 3m and 1m respectively. What is its volume?
Answers
Answer:
6m^3
Explanation:
volume of box= length×breadth×height
= 2×3×1
=6m^3
Answer:
i n k ok
Explanation:
What is the velocity?
Answers
Answer:
B. 0.98 m/s
Explanation:
This is because we use the simple formula of dividing the distance by the time. In which case would be 13.69m (distance) divided by 13.92s (time) and we will get 0.983477011 or 0.98m/s (your answer)
I hope this made sense and hoped it helped. Good luck with your test luv :)
The circulatory system:
a. transports oxygen to the body's cells
b. absorbs oxygen from the lungs
c. carries oxygen in the bloodstream
d. all answers are correct
Answers
Brian Berg of lowa built a house of cards 4.88 m tall. Suppose Berg throws a ball from ground level
with a velocity of 9.98 m/s straight up. What is the velocity of the ball as it first passes the top of
the card house?
Answers
Answer:
Vf = final velocity = 1.96 [m/s]
Explanation:
To solve this problem we must use the following equation of kinematics.
\(v_{f}^{2}=v_{o}^{2}-2*g*x\)
where:
Vf = final velocity [m/s]
Vo = initial velocity = 9.98 [m/s]
g = gravity acceleration = 9.81 [m/s²]
x = vertical distance [m]
\(v_{f}^{2}=(9.98)^{2}-2*9.81*4.88\\v_{f}^{2} = 99.6-95.74\\v_{f}=\sqrt{3.8544}\\v_{f}=1.96[m/s]\)
Note: The negative sign of the gravity acceleration means that the gravity acceleration is pointing in the opposite direction of the movement.
From which evidence can a forensic expert extract DNA?
Answers
Answer:
The biological material used to determine a DNA profile include blood, semen, saliva, urine, feces, hair, teeth, bone, tissue and cells.
Explanation:
Answer:
bone
Explanation:
What are the two ways a nose cone will affect the flight of a rocket?
Answers
The nose cone of a rocket can affect its flight in two primary ways: aerodynamic efficiency and stability.
Aerodynamic Efficiency: The shape of the nose cone plays a crucial role in reducing aerodynamic drag, which is the resistance that a rocket experiences as it moves through the atmosphere. A well-designed nose cone is streamlined and tapered, allowing the rocket to move through the air with minimal drag. By reducing drag, the rocket can achieve higher speeds and improve its overall efficiency. The nose cone's shape is typically designed to minimize shockwaves and pressure build-up, ensuring smooth airflow over the rocket's surface.
Stability: The nose cone also contributes to the rocket's stability during flight. Stability is essential to maintain control and prevent the rocket from veering off course or experiencing undesirable oscillations. The nose cone's position and shape affect the distribution of the rocket's center of gravity (CG) and center of pressure (CP). The CG represents the average location of the rocket's mass, while the CP is the point where the aerodynamic forces acting on the rocket are considered to be concentrated. For stable flight, the CP must be located behind the CG. The nose cone can be designed to provide stability by contributing mass towards the front of the rocket, shifting the CG forward, or by incorporating fins or other stabilizing features.
In summary, the nose cone of a rocket influences its flight by reducing aerodynamic drag and improving efficiency, as well as contributing to stability by affecting the rocket's center of gravity and center of pressure.
What is Velocity?*
O The measurement of an object's speed and direction
The measurement of an object's tendency to remain at rest
How fast an object travels
O Where an object travels
Answers
Answer:
The rate of change of displacement is called velocity.
Explanation:
How fast an object travels
Answer:
O The measurement of an object's speed and direction
Explanation:
A ray of light strikes a plane mirror at an angle of incidence of 60°, is reflected from the mirror and then strikes a second plane mirror placed so that the angle beftween the mirrors is 45°. The angle of reflection at the second mirror, in degrees, is
A 15
B 25
C 45
D 65
E 75
plz help me guys ASAP!
Answers
Answer:
60 - 45 = A. 15
Explanation:
Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
What is Plane mirror?A flat or highly polished surface called a plane mirror reflects light or waves to create an image. It is a polished, smooth surface that creates a virtual representation of the actual object.
A plane mirror is a surface on which an image can only be produced by at least two light beams. The intersection of these two beams can occur inside the mirror or appear to occur somewhere behind the mirror.
The image that follows illustrates how an object appears when viewed via a plane mirror.
Therefore, 60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
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a .5 kg steel ball is suspended from teh ceiling by a 2.5 m long string. the ball is pulled to the side until it is 1 m above its lowest point and then released from rest. the tension in the string when the ball passes through its lowest position is
Answers
The tension in the string when the ball passes through its lowest position is 5N (rounded).
The pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements.
How to calculate the tension in the string when the ball passes through its lowest position?
Tension = m*g
T = 0.5 * 9.8
= 4.9N
Approximately the tension would be equal to 5N (rounded)
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What does the word vector mean?
Answers
Answer:
Vector, in physics, a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude. Although a vector has magnitude and direction, it does not have position
In a particular diffraction pattern, the violet component
(λ = 440 nm) in the third-order spectrum is deviated at an angle of
50°. How many lines per millimeter does the grating have?
Answers
The grating has approximately 495 lines per millimeter.
To determine the number of lines per millimeter in the grating, we can use the grating equation:
nλ = d sin θWhere:
n = order of the spectrum (in this case, n = 3 for third-order spectrums)λ = wavelength of light (in this case, λ = 440 nm or 440 x \(10^{-9}\) m for violet component)d = distance between adjacent lines in the grating (unknown)θ = angle of deviation (in this case, θ = 50°)We need to find d and then convert it to lines per millimeter. Rearranging the grating equation to solve for d:
d = nλ / sin θ
Substitute the given values:
d = (3)(440 x \(10^{-9}\) m) / sin(50°)Now, calculate the value of d:
d ≈ 2.020 x 10^-6 mTo convert d to lines per millimeter, we can take the reciprocal of d and then convert meters to millimeters:
lines per millimeter = 1 / d = 1 / (2.020 x 10^-6 m) = 495,049 lines/mSince 1 m = 1000 mm, we can divide the number of lines by 1000 to get the number of lines per millimeter:
lines per millimeter = 495,049 lines/m ÷ 1000 = 495 lines/mmSo, the grating has approximately 495 lines per millimeter.
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TRUE/FALSE. the greater the amount of methylene blue dye leached into the heavy metal solution from the lichen means that the metal has low electronegativity.
Answers
The statement is FALSE.
The amount of methylene blue dye leached into the heavy metal solution from the lichen does not directly indicate the metal's electronegativity. Electronegativity refers to an atom's ability to attract electrons towards itself in a chemical bond. It is a property of individual atoms, not the amount of dye leached from a lichen.
To determine the electronegativity of a metal, we need to consider its position in the periodic table. Generally, metals have lower electronegativity values compared to nonmetals. The greater the electronegativity difference between two atoms, the more polar the bond between them. However, this is not related to the leaching of methylene blue dye.
The leaching of methylene blue dye into a heavy metal solution from the lichen may be influenced by other factors such as the concentration of the dye, the solubility of the metal ions in the solution, and the interaction between the metal ions and the dye molecules. These factors are independent of electronegativity.
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you know that for some sample of 9 scores, that the est.σ² =20. what is the variance of the sample?
Answers
The estimated sample variance is approximately 17.78 using a relation formula
If the estimated population variance is known to be 20 for a sample of 9 scores, we can use this information to estimate the variance of the sample, s², using a formula that relates both things:
\(s² = ((n-1)/n) * σ²\)
where n : sample size. Put values:
\(s^2\) = ((9-1)/9) * 20
\(s^2\) = (8/9) * 20
\(s^2\) = 160/9
\(s^{2}\) = 17.78
Therefore, the estimated sample variance is approximately 17.78. This tells us how much the individual scores in the sample vary from the sample mean. It is an important statistic for describing the distribution of the data, and can be used to calculate other measures of variability, such as the standard deviation.
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a positively charged insulated rod is brought near two neutral conducting spheres, a and b, which are touching each other and held in place and insulated from the rest of the environment. once the rod is close to (but not touching) sphere a, the spheres are separated from each other. sphere a is then suspended from a string, and the rod is brought near it again while sphere b is moved far away. sphere a is attracted to the rod. the investigation is repeated with a negatively charged rod, and the observed results are the same. which of the following best explains why the results are the same for a positively charged rod and a negatively charged rod?
Answers
The best explanation for why the results are the same for a positively charged rod and a negatively charged rod is that the charge on the spheres is redistributed to create opposite charges on the spheres.
The charge on the spheres is redistributed to create opposite charges on the spheres, which is why the results are the same for a positively charged rod and a negatively charged rod. This redistribution happens as a result of induction. As a result of the charge redistribution, the spheres develop an attraction to the rod. When a negatively charged rod is brought close to the spheres, the charge on the spheres is redistributed, causing one of the spheres to have a net positive charge and the other to have a net negative charge.
The sphere with the opposite charge (in this case, the one with a net positive charge) is attracted to the negatively charged rod, while the sphere with the same charge (in this case, the one with a net negative charge) is repelled. This redistribution results in the spheres separating from one other.When a positively charged rod is brought near the spheres, the same charge redistribution occurs, resulting in the same attraction between the oppositely charged sphere and the rod. Sphere B is far away, hence it does not undergo any charge redistribution as a result of the presence of the charged rod.
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why should a building have better thermal insulation placed in its ceiling than in its walls
Answers
Answer:
In a building, heat rises. By putting the insulation in the ceiling heat will rise and get trapped at the top and fill up the entire room. The purpose of insulation is to minimize the transmission of heat within the walls, floors, and ceilings. By minimizing the transmission of heat, you not only keep the room warm but you also lower your electricity and heat bill.
A block has two forces on it. One force is 15 N going north and the other is 22 N going east. What is the overall force pushing on the block with magnitude and direction?
Answers
Answer:
The overall force pushing on the block is 26.63 N in the direction of N 34° E
Explanation:
Given;
force going north, F₁ = 15 N
force going east, F₂ = 22 N
The resultant of the two forces is the hypotenuse side of the right angled triangle formed by the two forces.
Let the magnitude of the resultant force = F
F² = F₁² + F₂²
F = √(F₁² + F₂²)
F = √(15² + 22²)
F = 26.63 N
The direction of the force is the angle between the resultant force and the horizontal force.
tan θ = 15 / 22
tan θ = 0.6818
θ = tan⁻¹ ( 0.6818)
θ = 34°
Therefore, the overall force pushing on the block is 26.63 N in the direction of N 34° E
The outer circle illustrates the moon as it looks from Earth. Which of the following BEST explains why we see different phases of the moon each night from our position on Earth? The amount of sunlight reflected from the moon's surface changes each night.
Answers
We see different phases of the moon each night from our position on Earth because the amount of sunlight reflected from the moon's surface changes each night.
As the moon orbits Earth, its position relative to the Sun changes, causing the illuminated portion of its surface that is visible from Earth to change.
This results in the various moon phases we observe, such as the new moon, crescent, half, gibbous, and full moon.
In summary, the changing phases of the moon are caused by the changing amount of sunlight reflected from the moon's surface as it orbits Earth and its position relative to the Sun changes.
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A 1200N load is to be lifted with 200N effort using a first class lever. At what distance
from the fulcrum must the effort be applied when the load is 15 cm away from the
fulcrum?
[Ans: 90 cm]
Answers
Explanation:
Hey there!!
Let's simply work with it.
Here,
load = 1200N
Effort = 200N
Load distance = 15cm
We have,
According to the principle of lever.
L×LD = E×ED.
1200×15 = 200× ED.
18000 = 200ED.
\(ed = \frac{18000}{200} \)
Therefore, Effort Distance = 90cm.
Hope it helps....
how to sketch the following:Sketch a ray diagram for a spherical convex lens with an object at Do = 2f. (Submit a file with a maximum size of 1 MB.)
Answers
Do = 2f means that object distance is 2 x focal length.
2 x focal length = radius of curvature
When an object is placed at the radius of curvature, a real, inverted image is formed at the other radius of curvature. The sizes of the image and the object are the same. The sketch is shown below
Calculate the frequency (v) in Hertz (Hz) of a wave that has a wavelength of 4.71 meters.
Answers
Answer:
6.37 x 10⁷Hz
Explanation:
Given parameters:
Wavelength = 4.71m
Unknown:
Frequency = ?
Solution:
To solve this problem, we use the expression below:
V = F∧
V is the velocity = 3 x 10⁸m/s
F is the frequency
∧ is the wavelength
3 x 10⁸ = F x 4.71
F = 63694267.52Hz = 6.37 x 10⁷Hz