Answer: B. Energy
Explanation:
The Energy is the quantity that only depicts the magnitude and not the direction, hence it is a scalar quantity, so option B is correct.
What is Energy?In physics, energy is the capacity to do work. It might be potential, kinetic, thermal, electrical, chemical, radioactive, etc. Heat and work are further examples of energy being transferred from one body to another. Once it has been transmitted, energy is always allotted based on its nature. Thus, heat transmission could result in thermal energy while effort could produce mechanical energy.
The scalar quantity means they have only the magnitude and no direction. The velocity of any object tells the speed at which it is moving and its direction also, and the force applied to an object also tells the magnitude with direction, the momentum of an object is dependent on the force, so it is also a vector quantity
Therefore, Energy is the quantity that only depicts the magnitude and not the direction, hence it is a scalar quantity.
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consider a 20 kg sphere with a 10 cm radius. what weight would a scale read if the sphere was totally submerged in water?
The weight the scale would read if the sphere of mass 20 kg with a 10 cm radius was totally submerged in water is 155.1 N
Fg = m g
Fb = ρ V g
Fg = Force of gravity
Fb = Buoyant force
m = Mass
g = Acceleration due to gravity
ρ = Density of medium
V = Volume of object
m = 20 kg
g = 9.8 m / s²
ρ = 1000 kg / m³
r = 10 cm = 0.1 m
Fg = 20 * 9.81
Fg = 196.2 N
Fb = ρ ( 4 / 3 π r³ ) g
Fb = 1000 * 4 / 3 * 3.14 * 0.1³ * 9.8
Fb = 41.1 N
N = Fg - Fb
N = Scale reading
N = 196.2 - 41.1
N = 155.1 N
Therefore, the scale reading if the sphere was totally submerged in water is 155.1 N
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how do you predict that the amplitude of alpha waves recorded from a subject tested alone, in a darkened room, differ from subjects tested in a lab full of students? what might account for this?
The subject tested alone would yield better findings and higher alpha values than the subject evaluated in a lab with several pupils.
How are alpha waves recorded?Electrophysiological and closely related techniques, such as electroencephalography (EEG) or magnetoencephalography (MEG) can detect and quantify some types of brain waves, including alpha waves (qEEG).Alpha brainwaves have a higher amplitude and are slower.They oscillate between 9 and 14 cycles per second.An alpha state is frequently experienced by someone who has finished a task and is taking a break.When someone takes some time to think or meditate, they are typically in an alpha state.To learn more about Alpha brainwaves refer,
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two people are initially standing still on frictionless ice. they push on each other so that the 120 kg moves to the left at 2 m/s, while the other 80 kg person moves to the right at 3 m/s. what is the velocity of their center of mass?
A system's Center of Mass won't change if no external forces are applied to it, which means no forces from sources outside the system.
What is center of mass?In a uniform gravity field, the phrases "center of mass" and "center of gravity" are interchangeable to refer to the particular place in an item or system that can be used to describe how the system reacts to outside forces and torques. The idea of the center of mass is to calculate the average mass by dividing it by the distance from a fixed location.
Because no external force actuated on the system or any of its components, C.M. velocity is zero (0) for this problem. Although it is true that the two people exerted pressures on themselves, these forces were internal (i.e., produced by system components themselves) and as a result, the system Center of Mass was unaffected.
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a light bulb consumes energy at a rate of . how long in will it take for the light bulb to consume in energy?
It will take the lightbulb 2875 seconds to use 2.3×10⁵J of energy.
Why does power matter?Power is the amount of work completed in a given amount of time, or time spent working. The joules per second (J/s)-based SI unit of power is the Watt (W).
Given,
Power (P) = 80 J/s
Energy (E) = 2.3×10⁵ J
Time (t) = ?
The pace at which energy is utilized is a straightforward definition of power. Power can be mathematically stated as:
Energy x time equals power
P = E/t
We can calculate the time it takes for the bulb to use 2.3 105 J using the formula above. This is attainable as follows:
Power (P) = 80 J/s
Energy (E) = 2.3×10⁵ J
Time (t) = ?
Power = Energy / time
P = E/t
80 = 2.3×10⁵ /t
80 × t = 2.3×10⁵
Divide both side by 80
t = 2.3×10⁵ / 80
t = 2875 s
As a result, it will take the lightbulb 2875 seconds to use 2.3×10⁵J of energy.
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Complete question is "A light bulb consumes energy at a rate of 80joules per second . How long in seconds will it take for the light bulb to consume 2.3×10⁵in energy?".
An object i aid to be poitively charged if it number of electron i greater than the number of proton
An object I aid to be positively charged if it has a number of electrons i greater than the number of protons. TRUE
If an object has extra protons than electrons, then the internet fee on the item is fantastic. If there are extra electrons than protons, then the net charge at the item is bad. If there are equal numbers of protons and electrons, then the object is electrically impartial.
An electrical price is created while electrons are transferred to or removed from an object. because electrons have a bad charge, while they are added to an item, it turns negatively charged. when electrons are removed from an object, it will become undoubtedly charged.
A positively charged object has misplaced electrons. A definitely charged object has won protons. A negatively charged item has lost protons. If the variety of electrons is greater than the range of protons, the particle is a negative ion, also referred to as an anion.
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Disclaimer:- your question is incomplete, please see below for the complete question.
An object I aid to be positively charged if it has a number of electrons i greater than the number of a proton. TRUE/FALSE
two resistors are connected in series across a constant voltage source without internal resistance. another resistor is added in series to the other two resistors. what happens to the power supplied by the source?
Adding a third resistor in series with two resistors connected across a constant voltage source without internal resistance will cause the power supplied by the source to decrease.
The reason is that adding the extra resistor will increase the total resistance and decrease the current through all three resistors. The new total resistance is: Rtot = R1 + R2 + R3
And as we see from Ohm's Law, V/I = R, so we can also express this as: V2/I2 + V1/I1 + V3/I3 = V4/I4.
From here, we can see that when we add a third resistor in series with two others, we have more voltage across each individual part of our circuit, but less current flowing through each part of it. That means our total power supplied by the source decreases because there is less current flowing through all three resistors combined.
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fixing the brakes on your bicycle, you have the bicycle turned upside down. to test the brakes, you spin the wheel to a high speed in a counter-clockwise direction from your perspective. what is the direction of the angular displacement of the wheel?
The direction of the angular displacement of the wheel is -Toward you.
What does angular displacement refer to?The definition of angular displacement is "the angle, expressed in radians (degrees, revolutions), through which a point or line has been rotated in a particular sense about a certain axis." It is the angle at which a body travels around in a circle.
A vector quantity, angular velocity has both a magnitude and a direction. The direction matches the direction of the angular displacement, which is where we derived the angular velocity.
The rate at which angular velocity changes over time is referred to as angular acceleration. Typically, it is stated in radians per second per second. As a result, d = d t. The term "rotational acceleration" also applies to the angular acceleration.
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The two prisms shown in the diagram below are made of glass. A ray of red light enters each prism from the air, as shown. The critical angle for red light at the glass-air boundary is 42°.
On the diagram, complete the paths of the rays passing through each prism and out into the air again.
Answer:
That's all i know
Anyway welcome
what is the compressive stress exerted on the soles of your feet by your body weight? assume that each foot has a contact area of 200 cm2, the stress spreads out evenly over that area and that your mass is 72 kg.
The stress that spreads over the soles of the feet by the body is 18000 N/m².
The compressive stress exerted on a body is given by the force applied to the body divided by the area,
So, we can write,
Stress = force/area
In this case, the force will be equal to the weight of the body.
F = Mg
M is the mass of the person,
g is the acceleration due to gravity.
F = 72×10
F = 720N
The area of the soles is given to be 200 cm²
Converting into meter square,
Area = 0.02 m²
As there are two soles,
Area = 0.04
Putting values to find stress,
Stress = 720/0.04
Stress = 18000N/m²
So, the stress on the soles is 18000 N/m².
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What is the potential difference measured if the following voltmeter (refer to picture) is used and connected to the circuit via the 3V terminal?
Since the meter's 3V terminals are connected to the circuit, we have to read the "zero-to-3" scale on the meter to get our measurement. That's the scale under the marks.
On that scale, the needle points to 1.4 DC Volts. That's the potential difference between the two points the meter probes are touching.
for a slinky, the unstretched length is much shorter than the stretched length. suppose that the fundamental standing wave is oscillating on a slinky. how does the period of the standing wave change as the length of the slinky is altered?
Using the concepts of simple harmonic progression, we got that period of the standing wave changes directly proportional as the length of the slinky is altered.
We know very well that a standing wave traverse alternatively from crest to trough.
Crest is defined as that point when amplitude is maximum in positive y-direction and trough is defined as that point when amplitude is maximum in negative y-direction.
To traverse from crest to trough, a standing wave requires some time.
When the length of standing wave changes the time required by the standing wave also changes.
It means if we increase the length of slinky then the time required by the standing wave also increases and if we decrease the length of slinky then the time required by the standing wave also decreases.
Hence, when the fundamental standing wave is oscillating on a slinky, the period of the standing wave change directly proportional as the length of the slinky is altered.
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a long solenoid that has 950 turns uniformly distributed over a length of 0.390 m produces a magnetic field of magnitude 1.00 10-4 t at its center. what current is required in the windings for that to occur? ma
current is required in the windings for that to occur is 32.67mA
N=950
L=0.390m
B=1.0×10⁻⁴
B=μ₀ni
n=N/L(number of turns per unit length)
i=current
μ₀=permeability of free space =4π×10⁻⁷mkgs⁻²A⁻²or4π×10⁻⁷Tesla-m/A
i=B/μ₀n
i=1.0×10⁻⁴×0.390/4π×10⁻⁷×950
i=32.67mA
Electric current is a flow of charged particles—such as electrons or ions—that moves through a conductor for electricity or into void space. It is measured by the net rate of electric charge passing through a surface or into a control volume. Moving particles, or charge carriers, can be any number of distinct kinds of particles depending on the conductor. The charge carriers in electrical circuits are frequently electrons moving down a wire. In semiconductors, they could be electrons or holes. Ions are the charge carriers in an electrolyte, and plasma, an ionized gas, is composed of both electrons and ions.
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A source vibrating at constant frequency generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is quadrupled, by what factor does the amplitude change?.
As the tension of the spring is held constant as well as the frequency of the resulted sinusoidal wave, if the power delivered to the string is quadrupled, the amplitude will increase by factor 2.
If the frequency is held constant, the energy delivered to a wave is directly proportional to the square of its amplitude, or:
E ∝ A²
Where:
E = energy
A = amplitude
Power is energy per unit time, therefore power is also directly proportional to the square of amplitude.
P₂ : P₁ = A₂² : A₁²
From the problem, we know that P₂ = 4P₁
Hence,
4P₁ : P₁ = A₂² : A₁²
A₂² = 4 A₁²
A₂ = 2 A₁
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Ryan scores during his Waterpolo match by throwing the water polo ball hard. If the water polo bairs mass is 0.45 kg, the ball’s weight is ___N
The ball accelerates at a rate of 5.0 m/a^2 after Ryan throws it The net force on the ball is ___N.
The friction between the ball and the air is 2.65 N. To throw the ball at 5.0 m/a^2. Ryan has to apply a force of ___N
Ball’s weight is 4.4129925 N , net force on the ball is 2.25 N , Ryan has to apply a force of 4.9 N.
What is force ?
Whenever there is an interaction between two objects, there is a force acting on each object. When the interaction stops, the two objects no longer receive forces. Forces arise only through interactions , describes the technique of rocks converting their bodily houses with out converting their simple composition.
What is acceleration ?
Acceleration is a vector quantity defined as the rate at which an object's velocity changes. An object accelerates when its velocity changes.
What is friction ?
Friction is the resistance to movement of 1 item transferring relative to another. According to the International Journal of Parallel, Emergent and Distributed Systems(opens in new tab), it isn't always handled as a essential force, like gravity or electromagnetism. Instead, scientists accept as true with it's miles the end result of the electromagnetic appeal among charged debris in touching surfaces.
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describe the rotation curve of the milky way galaxy and contrast its shape with that of the solar sysstem
Compared to the orbital speeds of the planets in our solar system, the Milky Way Galaxy's rotation curve is far more flat and steady. While there is less mass as we get farther from the sun in our solar system.
The orbital speed of an astronomical body or object (such as a planet, moon, artificial satellite, spacecraft, or star) in gravitational bound systems is its speed relative to the most massive body's centre of mass, or the barycenter, if one body is significantly more massive than the other bodies in the system put together.
The phrase can be used to describe either the mean orbital speed (i.e., the speed throughout the course of an orbit) or its instantaneous speed at a specific location in the orbit. For objects in closed orbits, the maximum (instantaneous) speed occurs at periapsis (perigee, perihelion, etc.), whereas the smallest speed occurs at apoapsis (apogee, aphelion, etc.). When two-body systems are perfect, things An astronomical body or object (such as a planet, moon, man-made satellite, spacecraft, or star) moves through space at a certain speed called its orbital speed in gravitational bound systems.
When a system closely resembles a two-body system, the object's specific orbital energy, also known as "total energy," and its distance from the central body can be used to calculate the object's instantaneous orbital speed at a specific point in the orbit. Independent of position, the specific orbital energy is constant.
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a uniform meter stick is suspended from the ceiling by a string attached to the 60. cm mark. a 0.050 kg mass placed at 90. cm mark causes the meter stick to balance in the horizontal position. find the mass of the meter stick.
The mass of the meter stick is 0.15 kg.
The parameter
Meter Stick length = 100 cmA string attached to the 60 cmMass = m = 0.05 kgA mass placed at 90 cmAcceleration due to gravity = 10 m/s²Calculate the weight of the mass.
w = mg
w = [tex]0.05 \times 10[/tex]
w = 0,5 N
Look at the picture. The weight of the stick is in the middle of its length at 50 cm. The meter stick is balanced in the horizontal position. At point A
Distance between mass and string = 90-60 = 30 cmDistance between weight of the stick and string = 60-50 = 10 cmΣ τ = 0
(ws × 10) - (w × 30) = 0
ws × 10 = w × 30
ws × 10 = 0.5 × 30
ws × 10 = 15
[tex]w_s = \frac{15}{10}[/tex]
ws = 1.5 N
ms × 10 = 1.5
[tex]m_s = \frac{1.5}{10}[/tex]
ms = 0.15 kg
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what is one major difference between federal and unitary governments
Explanation:
While the unitarios fought for a centralized government, located in the city of Buenos Aires, the federales sought political decentralization so that the autonomy of the provinces within the nation would be respected.
Stan argues that momentum cannot be conserved when a collision is not a head-on collision. Rachel insists it is conserved because each body receives an impulse of equal magnitude. Rachel is correct because.
Rachel is correct because she said that is body receive equal magnitude of impulse which completely satisfy the law of conservation of linear momentum.
According to law Conservation of Linear Momentum, if there is no external force working on the system, then the linear momentum remains conserved before and after the collision.
We know that,
Momentum is nothing but the product of force and the time taken for the contact period of the colliding bodies.
We assume that during the head on collision of the body, the body is remain in contact for such a short period of time that there is no external force all the impulse created due to the external force is neglected.
So, because the impulse imparted on both the bodies are equal to each other.
We know that impulse is nothing but the change in momentum.
So, from here we conclude that bodies received equal magnitude of impulse.
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What is the initial speed of a shopping cart if it ends up going 20 m/s in 4 seconds, and has an acceleration of 2 m/s^2?
The initial speed of a shopping cart is 36 m/s.
What is acceleration?
Acceleration is the term used to describe how quickly a velocity's speed and direction change over time. It is said to have been accelerated when something changes its direction and moves faster or slower. Motion on a circle accelerates even when the speed is constant because the direction is constantly changing.
What is kinematic equation?
The set of equations known as the kinematic equations describes how an object moves with constant acceleration. Integrals, rates of change, and derivatives must be understood in order to solve kinematic equations.
List the known and unknown values.
u = initial velocity = 20 m/s
v = final velocity = ? m/s
a = acceleration = 4 m/s²
t = time interval = 4 s
s = displacement = ? m
The following kinematic equation should be used to determine the final velocity.
v = u + at
v = 20 m/s + (4 m/s² × 4 s) = 36 m/s
Now calculate the displacement using the following kinematic equation.
s = ut + ½at²
s = (20 m/s × 4 s) + (0.5 × 4 m/s² × (4 s)²)
s = 80 m + 32 m = 112 m
Therefore, the initial speed of a shopping cart is 36 m/s.
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The graph shows the displacement of a mouse
What is the farthest position the mouse reaches inside the tunnel?
7 meters into the tunnel
4 meters into the tunnel
3 meters into the tunnel
It cannot be determined from the information given
The farthest position the mouse reaches inside the tunnel is 4 meters into the tunnel.
From the graph,
The positions reached after,
5 s = 4 m
10 s = 2 m
20 s = 2 m
35 s = 3 m
40 s = 0 m
So the farthest position here is 4 m into the tunnel.
The rate of change of positions is displacement. So displacement will be change in initial and final positions divided by change in time.
s = Δx / Δt
Therefore, the farthest position the mouse reaches inside the tunnel is 4 meters into the tunnel.
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Thousands of small rocky objects are located in the solar system between mars and jupiter. These objects are.
Thousands of small rocky objects known as asteroids can be found in the solar system between Mars and Jupiter.
What exactly is a solar system?The Solar System is composed of the Sun and the objects that orbit it. It was created by the gravitational collapse of a massive interstellar molecular cloud 4.6 billion years ago. The Sun contains the vast majority of the system's mass, with Jupiter holding the majority of the remaining mass.
Asteroids are rocky bodies that orbit the Sun. Although asteroids orbit the Sun in the same way that planets do, they are much smaller. In our solar system, there are numerous asteroids. The majority of them are found in the main asteroid belt, which lies between the orbits of Mars and Jupiter.
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what did the herschels find when they counted stars in 683 regions around the milky way? about the same number of stars in each direction. many more stars are in the direction of the constellation sagittarius than in any other direction in the milky way. the doppler shifts in stellar spectra are about half redshifted and half blueshifted. the mass-luminosity relationship for main sequence stars. that the sun is moving toward the constellation cygnus.
The sun is moving toward the constellation Cygnus, as discovered by Herschel when they counted stars in 683 regions around the Milky Way.
One of the significant discoveries made by Galileo in his Sidereus Nuncius in 1610 was that, when viewed through a telescope, some of the Milky Way resolved into a cluster of numerous stars.
The Sun is the darker star towards the image's center. Herschel has indicated its location in the image above. Herschel's research leads to the conclusion that the Sun is situated at or close to the Milky Way's center.
The Milky Way galaxy is the home of the Sun. About 100,000,000,000 stars are thought to be present in the Milky Way alone, according to astronomers.
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How large a net force is required to accelerate a 2000-kg suv from rest with an acceleration of 0. 14 m/s2?.
Answer:
280 N
Explanation:
Remember F = ma
F = 2000 * .14 = 280 N
compared to the flow of water in streams, most ground water moves relatively slowly. group of answer choices true false
Most ground water will move rather slowly when compared to how fast water moves in streams.
The statement is true
Why does water movement matter?Water quantity both affect flow. It is significant because it affects the habitats of living things in the stream as well as the water quality. Small streams are less able to dilute and degrade contaminants than large, fast running rivers, which can receive pollution releases with little impact.
How do we define flow?To "flow" is to move in a stream, just like water. As air circulates, the word "flow" also signifies to move. Flow is a noun that refers to motion that resembles a stream. The noun and verb 'flow' can be used in a variety of various contexts. Something flows when it moves like a stream of water.
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in a simple electric circuit, ohm's law states that , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms. assume that, as the battery wears out, the voltage decreases at 0.01 volts per second and, as the resistor heats up, the resistance is increasing at 0.04 ohms per second. when the resistance is 400 ohms and the current is 0.04 amperes, at what rate is the current changing?
The rate is the current changing is = - 1.3 x 10⁻⁴ A/s
Solution:
We take the derivative of Ohm's law with respect to time
V = IR
Using the product rule:
dV/dt = I(dR/dt) + R(dI/dt)
We are given that voltage is decreasing at 0.01 V/s
resistance is increasing at 0.04 ohm/s
resistance itself is 400 ohms,
and current is 0.04 A
Substituting:
-0.01 V/s = (0.04 A)(0.04 ohm/s) + (400 ohms)(dI/dt)
dI/dt = -1.3 x 10⁻⁴ A/s.
The relationship between current, voltage, and resistance. The amount of continuous current flowing through many materials is directly proportional to the potential difference or voltage between them.
Law of Electricity The strength of a direct current is directly proportional to the potential difference and inversely proportional to the resistance of the circuit. Ohm's Law is a formula for calculating the relationship between voltage, current, and resistance in a circuit. Ohm's law describes the relationship between current, voltage, and resistance. This shows that at a constant temperature, the current through the circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit.
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an atwood's machine (see the figure below) consists of two masses: one of mass 4.93 kg and the other of mass 11.9 kg. when released from rest, what is the acceleration of the system? (enter the magnitude in m/s2.)
Using the concepts of atwood machine, we got 4.05m[tex]s^{-2}[/tex]. is the acceleration of system when released from rest.
We know very well that in atwood`s two bodies having different mass are hanged around the pulley.
The accceleration of the atwood is given by :
a=((m2-m1)/(m2+m1))×g, where m2 is the mass of heavier body,m1 is the mass of lighter body and g is the acceleration due to gravity.
So, according to question m2=11.9,m1=4.93 and g=9.8
So, on putting the value in above formula, we got
a=[(11.9-4.93)/(11.9+4.93)]×9.8
=>a=[(6.97)/(16.83)]×9.8
=>a=4.05m[tex]s^{-2}[/tex].
Hence, an atwood machine in which two masses: one of mass 4.93 kg and the other of mass 11.9 kg. when released from rest, the acceleration of the system is 4.05m[tex]s^{-2}[/tex].
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A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. if the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30 cm deep?
Answer:
Approximately [tex]0.033\; {\rm m\cdot min^{-1}}[/tex] (meters per minute.)
Explanation:
Let [tex]A[/tex] and [tex]B[/tex] denote the bottom and top width of the trough, respectively. It is given that [tex]A = 30\; {\rm cm} = 0.30\; {\rm m}[/tex] and [tex]B = 80\; {\rm cm} = 0.80\; {\rm m}[/tex]. Let [tex]H[/tex] denote the height of this trough; [tex]H = 50\; {\rm cm} = 0.50\; {\rm m}[/tex].
Let [tex]h[/tex] denote the current depth of the water in this trough.
Let [tex]b[/tex] denote the current width of the surface of the water. As water fills the trough, this width increases from [tex]A = 0.30\; {\rm m}[/tex] (width of bottom of trough) to [tex]B = 0.80\; {\rm m}[/tex] (width of top of trough.)
The relationship between [tex]b[/tex] and [tex]h[/tex] is linear:
[tex]\displaystyle b = \frac{h}{H}\, (B - A) + A[/tex].
Cross-section area of water in this trough:
[tex]\begin{aligned}(\text{area}) &= \frac{1}{2}\, (A + b) \, h \\ &= \frac{1}{2}\, \left(A + \frac{h}{H}\, (B - A) + A\right)\, h \\ &= A\, h + \frac{1}{2\, H} (B - A)\, h^{2}\end{aligned}[/tex].
Let [tex]L[/tex] denote the length of this trough; [tex]L = 10\; {\rm m}[/tex].
Let [tex]v[/tex] denote the volume of water in this trough:
[tex]\begin{aligned}v &= (\text{area})\, L \\ &= \frac{1}{2}\, (A + b) \, h\, L \\ &= \frac{1}{2}\, \left(A + \frac{h}{H}\, (B - A) + A\right)\, h\, L \\ &= A\, L\, h + \frac{L}{2\, H} (B - A)\, h^{2}\end{aligned}[/tex].
Differentiate both sides implicitly with respect to [tex]v[/tex]:
[tex]\displaystyle \frac{d}{dv}[v] = \frac{d}{dv}\left[A\, L\, h + \frac{L}{2\, H}\, (B - A)\, h^{2}\right][/tex].
[tex]\displaystyle \frac{d}{dv}[v] = \frac{d}{dv}[A\, L\, h] + \frac{d}{dv}\left[\frac{L}{2\, H}\, (B - A)\, h^{2}\right][/tex].
[tex]\displaystyle 1 = A\, L\, \frac{dh}{dv} + \frac{L}{2\, H}\, (B - A)\, 2\, h\, \frac{dh}{dv}[/tex].
(Note that [tex]A[/tex], [tex]B[/tex], [tex]L[/tex], and [tex]H[/tex] are constants.)
Rearrange this equation to obtain:
[tex]\displaystyle 1 = A\, L\, \frac{dh}{dv} + \frac{L}{H}\, (B - A)\, h\, \frac{dh}{dv}[/tex].
[tex]\displaystyle 1 = \left(A\, L + \frac{L}{H}\, (B - A)\, h \right)\, \frac{dh}{dv}[/tex].
[tex]\displaystyle \frac{dh}{dv} = \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}[/tex].
Let [tex]t[/tex] denote time. It is given that the trough is being filled at a rate of [tex]0.2\; {\rm m^{3}\cdot min^{-1}}[/tex]. In other words:
[tex]\displaystyle \frac{dv}{dt} = 0.2\; {\rm m^{3}\cdot min^{-1}}[/tex].
Apply the chain rule to find the rate at which [tex]h[/tex] is changing with respect to time [tex]t[/tex]:
[tex]\begin{aligned} \frac{dh}{dt} &= \frac{dh}{dv}\cdot \frac{dv}{dt} \\ &= \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}\cdot \frac{dv}{dt} \end{aligned}[/tex].
Substitute in [tex]A = 0.30\; {\rm m}[/tex], [tex]L = 10\; {\rm m}[/tex], [tex]H = 0.50\; {\rm m}[/tex], [tex]B = 0.80\; {\rm m}[/tex], [tex]h = 0.30\; {\rm m}[/tex] (converted from [tex]30\; {\rm cm}[/tex]), and that the rate of change in [tex]v[/tex] is [tex]0.2\; {\rm m^{3}\cdot min^{-1}}[/tex]:
[tex]\begin{aligned} \frac{dh}{dt} &= \frac{dh}{dv}\cdot \frac{dv}{dt} \\ &= \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}\cdot \frac{dv}{dt} \\ &= \frac{0.2\; {\rm m^{3}\cdot min^{-1}}}{\displaystyle 0.30\; {\rm m} \times 10\; {\rm m} + \frac{10\; {\rm m}}{0.60\; {\rm m}}\, (0.80\; {\rm m} - 0.30\; {\rm m}) \, 0.30\; {\rm m}} \\ &=0.033\; {\rm m\cdot min^{-1}} \end{aligned}[/tex].
In other words, the depth of the water in this trough increases at a rate of approximately [tex]0.033\; {\rm m \cdot min^{-1}}[/tex] (meters per minute.)
what is re, the reynolds number re, for water flows at 10 m/s speed through a typical household water pipe of 30 mm diameter? viscosity of water is 8.90 x 10-4 pa.s.
To learn the viscosity and speed and resistance to calculate the diameter.
What is viscosity?
Viscosity is a fluid's (liquid or gas) resistance to a change in shape or motion of adjacent parts concerning one another. Viscosity indicates resistance to flow.
What constitutes speed?
The speed of a change in an object's position in any direction Speed is defined as the ratio of distance to the amount of time it takes to cover that distance. Since speed has only a direction and no magnitude, it is a scalar quantity.
Resistance AC circuit
in resistance AC circuit the voltage and current are related as,
Emf; E= EoSinωt
where, I_O=E_O/R
In purely resistive circuit, there is no phase change occurs. the phase angle between voltage and current is zero.
the maximum value of current is I_0 =v_0\R
if tha maximum volatge v_0 is increase with decrease of resistance R then current in the circuit will maximum and denoted asI_0
capacitive AC circuit
In capacitive AC circuit the voltage and current are related as,
Emf: E=E_Osinωt
and current I =I_Osinωt
⇒ I =I _0sin(ωt+π/2)
where,I_0 =E_0/X_C
in purely capacitive circuit, current leads the end by phase of π/2. the phase angle between volatge and current is π\2
The maximum value of current is,I_0 =E_0\X_C
if the maximum voltage E_0 is increases with decreases of capacitive X_c then current in the circuit will maxmium and denoted as I_0
when the emf is zero then current is maximum magnitude.so the current is maxmium before it leads or lag in the circuit.
inductive AC circuit:
Inductive AC circuit the voltage and current are related as
Emf: E= E_0sinωt
And current : I= (-)I_0cosωt
⇒ I= I_0sin(ωt -π/2)
where, Iπ_0 =E_0/X_L and x=∈L
In purely inductive circuit, the current lags behind the voltage (emf) by phase of π/2. The phase angle between volatge and current is π/2
The maximum value of current is, I_0 = E_0/X_L
if the maximum voltage E_0 is increase with decrease of inductive resistance X_L then current in the circuit will maximum and denoted is I_0.
Therefore, the emf is zero then current is maximum magnitude. so the current is maximum before it leads or lag in the circuit.
Learn more about Viscosity from the given link.
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at a location in europe, it is necessary to supply 1000 kw of 60-hz power. the only power sources available operate at 50 hz. it is decided to generate the power by means of a motor- generator set consisting of a synchronous motor driving a synchronous generator. how many poles should each of the two machines have in order to convert a 50-hz power to 60 hz?
The number of poles that the two machines should have in order to convert a 50-hz power to 60-hz is a 10 pole synchronous motor must be coupled to a 12-pole synchronous generator.
n = 120 f / P
n = Speed of synchronous machine
f = Frequency
P = Number of poles
For motor,
f = 50 Hz
n = 120 * 50 / Pm
For generator,
f = 60 Hz
n = 120 * 60 / Pg
To accomplish the frequency conversion, the speed of the motor and generator must be equal. So,
120 * 50 / Pm = 120 * 60 / Pg
Pg / Pm = 6 / 5
Pg / Pm = 12 / 10
Therefore, to accomplish the frequency conversion, a 10 pole synchronous motor must be coupled to a 12 pole synchronous generator.
To know more about frequency conversion
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9. Determine the total capacitance between points A and B. D н А- В с E с C C с с с c
Answer:
Determine the total capacitance between points A and B in the figure below. C =104F C = 5uF C=20uF MAE ce Select the best answer: 2.84uF 2.80uF O 2.90pF 2.86F
Explanation:
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