Mutual inductance is the property by which one coil affects the current and voltage of the other coil.
Magnetic flux us the total magnetic field around both the coils.
EMF are invisible energy around the coils, which are mainly referred to as radiation.
How to find mutual inductance, magnetic flux and EMF around two coils?
We know
N = 30 turns
N¹= 310 turns
Inner solenoid length L¹= 20 CM= 0.2m long
Diameter d¹= 2.5 CM= 0.025m
Current i¹= 0.150 A
Rate of increase in current = di¹/dt= 1700A/s
Part A : magnetic flux = ∅¹= B¹A¹
B¹= ûⁿ × n¹ × i¹ = 2.92× 10↑-4T
Thus, ∅= 2.92×10↑-4× π/4×0.025²
= 1.432×10↑-7 Wb
Part B
Magnetic flux in one coil× number of turns in second coil = mutual inductance× current in the first coil
∅¹ × N² = Mi¹
= 1.432×10^-7 ×30
M × 0.150=1.432×10^-7×30
M=2.86×10^-5H
Part C
E = M di¹/dt
= 2.86×10^-5×1700 V
= 0.048 V
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In view of both the given query The inner solenoid's mean flux density per rotation is 1.43 * 10⁻⁷ Wb, or the two solenoids' mutual coupling is 2.86 x 10⁻⁴ H. The induced emf in the exterior loop is 4.86 * 10⁻¹ V.
How do solenoids function?A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core. The electromagnetic field causes the armature to move, and when it does, it opens and closing valves or switches, converting mechanical energy into electrical movements and force.
Briefing:Given:
N1 = 310 revolutions in the inner solenoid.
N2 = 30 is the number of revolutions in the outer solenoid.
The inner solenoid's length is 20 cm, or 0.2 meters.
Inner solenoid radius = r = diameter/2 = 2.50/2 = 1.25 cm = 0.0125 m
The inner solenoid's current I is equal to 0.150 A.
1700 A/s is the current growth rate, di/dt.
A). Average magnetic flux across the inner solenoid's turns is equal to BA.
Include the values:
Average magnetic flux via the inner solenoid's turns:
= [4π x 10⁻⁷][310/0.2][0.150]π(0.0125)²
= 1.43 * 10⁻⁷ Wb
B). The two solenoids' mutual inductance is given by M = N2 x (average flux) / current.
= (30 x 1.43 * 10⁻⁷) / 0.150
= 2.86 x 10⁻⁴ H
C). The change in current there in inner solenoid causes an induced emf in the outer magnet that is equal to M*di/dt.
= 2.86 x 10⁻⁴ * 1700
= 4.86 * 10⁻¹ V
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Who has a greater weight to mass ratio, a person weighing 400 n or a person weighing 600 n?.
A greater weight to mass ratio, a person weighing 400 N or a person weighing 600 N is never possible .
What is gravity?
The force of attraction felt by a person which is directed at the center of a planet or Earth is called as the gravity.
The force of attraction is directly proportional to the product of masses of the object and inversely proportional to the square of distance between them.
Weight = Mass x Acceleration due to gravity (g)
W₁/m₁ =g = W₂/m₂
400 N/m₁ = 600N/m₂ = 9.81 m/s²
So, weight to mass ratio for a person weighing 400 N and person weighing 600 N will be same.
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the clock on the big ben tower in london reads 12 noon. if you travel away from the clock at a very high speed and view it with a telescope, you would see group of answer choices run faster than a clock in your vehicle. run slower than a clock in your vehicle. be frozen at 12 noon.
"The clock on the big ben tower in London reads 12 noon. If you travel away from the clock at a very high speed and view it with a telescope, you would see it run slower than a clock in your vehicle" (Option A) This phenomenon is known as Time Dilation.
What is time dilation?
Time dilation is defined in physics and relativity as the difference in elapsed time as measured by two clocks. It is either owing to a difference in relative velocity or a difference in gravitational potential between their places.
When left undefined, "time dilation" generally refers to the impact of velocity.
Time dilation is the "slowing down" of a clock as determined by an observer in relative motion with regard to that clock under the theory of special relativity.
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[NOTE: THIS IS AN INCOMPLETE QUESTIO. THE COMPLETE QUESTION IS:
Suppose you look at the huge clock on the Big Ben Tower in London and it reads 12 noon. If you could travel away from the clock at the speed of light and view it with a telescope, it would:
a) run slower than usual
b) run faster than usual
c) be frozen at 12 noon]
. the latent heat for the water/steam transition is 2256 kj/kg, i.e., to convert 1 kg of water into steam requires 2256 kj. what is the latent heat per molecule of h2o? express your answer in joules and in ev.
Latent heat per molecule of H2O expressed in joules is 124976.7 J/mol.
Latent heat is the amount of heat energy required to change the state of a substance without changing its temperature. To calculate the latent heat per molecule of H2O, we need to use the following equation:
Latent heat per molecule = (Latent heat / Mass of 1 molecule of H2O)
The mass of one molecule of H2O is approximately 18 x 10-3 kg.
Therefore, the latent heat per molecule of H2O is:
Latent heat per molecule = (2256 kJ / 18 x 10-3 kg) = 125333.33 kJ/mol
This is equivalent to 125333.33 kJ/mol = 124976.7 J/mol
In terms of electron volts, this is equivalent to 124976.7 J/mol = 7.2 x 1020 eV.
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(1) the electrons in a certain material have a full band of possible energies separated from a completely empty energy and by energy gap of 2.8 ev. this material is a
When the electrons in a certain material have a full band of possible energies, the material is a semiconductor.
What is a semiconductor?A semiconductor is a material with specific electrical properties that allow it to be used as the foundation for computers and other electronic devices. It is typically a solid chemical element or compound that conducts electricity only under certain conditions.
If the valence band is completely full and the conduction band is completely empty, electrons cannot move within the solid because there are no available states, and no current generation occurs because there is no net charge carrier mobility. The semiconducting material is represented by an energy gap of 1.1 eV.
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certain stars, like betelgeuse, have a lower surface temperature than the sun and yet are more luminous. how do these stars produce so much more energy than the sun?
Some stars, like Betelgeuse, are more bright and produce a lot more energy than the Sun despite having a lower surface temperature. This is as a result of their expansion into massive stars. Because of their considerably larger size (each portion of the star's surface is cool, but there are so many bits that, collectively, the stars send out more energy), they generate more total energy.
The mass of a star is always drawn toward its core by gravity. There is a mechanism that can prevent a star from collapsing due to gravity, and there is a "balance" between them at different times in a star's life.
When a star is in equilibrium, the gamma rays produced by fusion in the center of the star fight against the inward gravitational collapse. In general, balances are reached when a "fuel" (element) hot enough to fuse is present in the core, as is the case during the main-sequence stage when hydrogen fusion takes place and during helium core fusion following the helium flash
Astronomers who desire to study the evolution of stars can benefit greatly from stellar clusters. It is plausible to believe that each star in a cluster emerged from the same cloud of gas and dust at roughly the same time. The only first distinction between the stars is hence their mass (and not their composition or the time that they began). Additionally, by monitoring where a cluster of stars' stars are now departing the main sequence, we can infer the age of the cluster because high-mass stars evolve considerably more swiftly than low-mass stars do.
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What would be the final speed of a 40g car released from an initial height of 25cm?
What would be the final speed of a 600g car released from an initial height of 115cm?
Answer:
Below
Explanation:
Potential Energy of the cars is turned into Kinetic Energy (ignoring friction)
mgh = 1/2 mv^2 divide both sides by 'm'
gh = 1/2 v^2 solve for v
v = sqrt (2gh) Note that the mass of the cars is irrelevent
For the first car : 25 cm = .25 m
v = sqrt (2 * 9.81* .25) = 2.2 m/s
Similarly , for car 2 v = 4.8 m/s (115 cm = 1.15 m)
unpolarized sunlight with intensity 1000 w m2 is incident on two polarizers, whose transmission axes make an angle of 30◦ . calculate the intensity of the transmitted light from the second polarizer. select one of
The intensity of the transmitted light from the second polarizer is 375 W/m².
Let the two polarized sunlight be P₁ and P₂
Given,
Angle between P₁ and P₂ = 30⁰
Intensity of the unpolarized sunlight = 1000 W/m²
Now,
Angle between P₁ and P₂ = 90⁰ - 30⁰ = 60⁰
The intensity of light transmitted by P₁ is
I₁ = I₀/2 = 1000/2 = 500 W/m²
According to Malus law the intensity of light transmitted by P₂ is
I₂ = I₁ cos²30⁰ = 500[(√3)/2]² = 375 W/m²
Therefore, The intensity of the transmitted light from the second polarizer is 375 W/m².
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at what temperature is the reading on a fahrenheit scale twice the reading on a celsius scale? express your answers, separated by a comma, to three significant figures.
The reading on the Fahrenheit scale is twice the temperature on the Celsius scale at 160 degrees Celsius.
Relationship between Fahrenheit scale and Celsius scale
F=9C/5+32
Applying the given condition
2C=F (given)
Replace F in the first formula with 2C from the second,
Then 2C = 9C/5+32
Subtract 9/5C from both sides,
2C-9C/5=32
1C/5=32
C= 160 degrees
Therefore 160 degrees Celsius scale is twice as long as the Fahrenheit scale
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1. we assumed that no mechanical energy is transferred to thermal energy, but saw that at least a little mechanical energy is lost. Can this explain the difference between the spring constants you found in part 1 and part 2? Please explain ?2. The mass of the puck is difficult to measure because it sublimates and looses mass over time. Can this explain the difference between the spring constants you found in part 1 and part 2.
No mechanical energy is transferred to thermal energy, but saw that at least a little mechanical energy is lost as heat.
1. Due to the vertical oscillation of the pluck connected with the spring, the spring is getting compressed and elongated. There are inter atomic bonds of the material with which the spring is made of. When the spring is getting compressed or elongated atoms connected with inter atomic bonds also gets compressed for elongated. This causes some of the bonds to break.
We know each bond is having some internal energy stored in it. So when the bond breaks that internal energy is emits in the form of thermal energy. Hence we see that some of the energy of oscillation is getting used in breaking the bond. This mechanical energy is getting lost. So with each period of oscillation the energy associated with the oscillating spring mass system decays with time.
Hence the amplitude of oscillation also decrease with time. Since by applying a certain amount of force to the pluck we are getting little small displacement compared to the actual displacement hence the corresponding spring constant will also be different compared to the actual one.
2. We know the spring constant is here define as the the ratio of applied force with the displacement of the mass. Here the force is the resultant of the weight of the mass and the the buoyancy force on the mass by the liquid. But when we sublimate the mass inside the liquid it loses mass with time. Hence the force on the spring also decays with time. Hence the the displacement of the mass also decays with time. Which implies the spring constant also changes.
Thermal power refers back to the energy contained inside a device this is liable for its temperature. warmness is the go with the flow of thermal electricity. an entire branch of physics, thermodynamics, offers with how heat is transferred among specific systems and how paintings is accomplished within the method (see the 1ˢᵗ law of thermodynamics).
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the plates of a parallel plate capacitor are separated by 0.1mm of bakelite dielectric. if the bakelite has a dielectric constant of 4.9 and the plates have an area of 0.0049 m2 , what is the capacitance in nf?
if the plates of a parallel plate capacitor are separated by 0.1mm of bakelite dielectric, and the bakelite has a dielectric constant of 4.9 and the plates area 0.0049m^2, the capacitance is 2.126nF
What is capacitance?
It is the ability of a component or circuit to collect and store energy in the form of an electrical charge. Capacitors are energy-storing devices available in many sizes and shapes.
How to calculate the capacitance in nF?The formula of capacitance of the capacitors is with dielectric constant as follows :
C = Kε₀A / D
where
C = Capacitance
k = dielectric constant
ε₀ = permittivity free space
d = distance between the plate
A = area between the plate
we are using this formula because it said parallel plate capacitor.
from the question given as follows :
k = 4.9 (dielectric constant)
d = 0.1mm = 1 * 10^-8 m^2
A = 0.0049m^2
ε₀ = 8.854 * 10^-12 F/m (from literature, permittivity of the free space)
C = 4.9 * 8.854*10^-12 * 0.0049 / 1 * 10^-8
C = 0.000021258454
C = 2,125.845 * 10^-12 F
C = 2.125845 * 10^-9 F
C = 2.126nF (rounded)
Therefore, the capacitance is 2.126nF for the plates.
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what happens to the gravitational force between two objects if the distance between them triples? (1 point)
Gravitational force between two objects if the distance between them triples reduces by 9.
What is gravitational force ?
The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation. The force constantly tries to pull different masses towards each rather than pushing them apart from each other we tend to refer to this force of attraction as gravity.
Gravitational force [tex]F[/tex] = [tex]G\frac{m_{1} m_{2} }{r^{2} }[/tex]
where m1 = mass of object 1
m2 = mass of object 2
G gravitational constant
r = distance between the two object
If the distance between the two object is triples i.e. r = 3r
Then Gravitational force [tex]F^{'} = \frac{F}{(3r)^{2} }[/tex] =
[tex]F^{'} = \frac{F}{9r}[/tex]
Thus gravitational force between the object will reduce by a factor of 9.
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a battery is several electrochemical cells stacked together. please select the best answer from the choices provided t f
True; A battery is several electrochemical cells stacked together.
A source of electricity made up of one or more electrochemical cells with connections on the outside that can be used to run electrical appliances is known as an electric battery.
The cathode and anode of a battery are represented by their positive and negative terminals, respectively, when it is supplying electricity.
Electrons will come from the terminal labeled "negative" and travel to the terminal labeled "positive" via an external electric circuit. When a battery is connected to an external electrical load, a redox reaction changes high-energy reactants into lower-energy products, and the free-energy difference is sent to the external circuit as electrical energy. Historically, a "battery" was a device made up of numerous cells; however, the phrase has come to be used to describe a single cell as well.
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during an isothermal compression of an ideal gas, 200 j of heat must be removed from the gas to maintain constant temperature. how much work is done by the gas during the process?
The overall work done for isothermal compression is 200 Joules.
Theory :
Thermal and ISO stand for temperature and constant, respectively. The processes in which the temperature is constant are known as isothermal processes. When a system's volume is reduced or its pressure is raised, this is referred to as compression. The compression process known as isothermal compression occurs at a constant temperature. A closed system is where the thermodynamic process takes place. Thermal equilibrium is maintained by the process.Integration of dW, where dW is the displacement work or PdV, constitutes the work produced by an isothermal process.Boyle's law, which applies to an ideal gas in this process, governs the behavior of the gas and the work it does.The system's molar heat capacity in this process is infinite because there is no temperature difference.Mathematics & Calculations:
[tex]dQ=dU + w\\\\\\dq=heat \\dU=energy\\\\dU=nCdT=0 \\\\dQ=w\\\\dQ =200J\\\\Work=w=200J[/tex]
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the cosmic microwave background tells us a lot about our universe, including what shape it is, geometrically! what shape do we believe the universe is, and based on which property of the cmb?
We believe that the shape of the universe is geometrically flat based on critical density of the CMB.
New measurements of the cosmic microwave background by the Atacama Cosmology Telescope find that the universe is flat, with a density matching the critical density. There is no evidence of deviation from flatness. According to ACT scientists, the interpretation that the deviation seen by Planck is a statistical fluctuation.”
The CMB is useful to scientists because it helps us learn how the early universe was formed. It is at a uniform temperature with only small fluctuations visible with precise telescopes. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large-scale structures of galaxies and they can measure the basic parameters of the Big Bang theory.
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a ceiling fan at rest is turned on and reaches a speed of 12.5 rad/sec in 2.4 sec. how many revolutions does it rotate during this time?
5.20rad/sec revolutions does it rotate during this time.
What is average velocity?Average velocity is a sign of a vector. Average velocity is defined as the difference between a change in position or displacement (x) and the intervals of time (t) during which it occurs. The average velocity may be positive or negative depending on how the displacement is dispersed.
According to the equation v = s/t, velocity (v) is a vector quantity that measures displacement (or change in position, s), over change in time (t).
velocity = number of revolutions / time
12.5 rad/sec = number of revolutions/time
number of revolutions = 12.5/ 2.4
number of revolutions = 5.20rad/sec.
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Why do astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system?.
Astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system because it generated telltale patterns of unstable, short-lived radioactive isotopes.
Did a supernova cause the solar system to form?Our solar system may have formed when a cataclysmic supernova explosion's shockwave collided with a gas cloud.Samples of early meteorites still contain traces of the material ejected from the ancient blast.The supernova explosion that gave birth to our sun may have also contributed to the rotation of our solar system, enabling the construction of the planets, including Earth, according to scientists researching this process.The shock wave from a supernova may have had enough energy to crush the dust cloud before it, according to earlier research. And investigators have looked for signs of that explosion: Radioactive isotopes that are unstable and short-lived form distinctive patterns after supernovae.The identification of these anomalies' telltale signs in prehistoric rocks would support the theory that a supernova sparked the formation of the solar system.What Is a Supernova?The largest explosion that humans have ever witnessed is a supernova. Each blast is the extremely bright, super-powerful explosion of a star.Can learn more about supernova from https://brainly.com/question/24811835
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Three identical train cars, coupled together, are rolling east at speed . A fourth car traveling east at catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?
There are two collisions occurring in this question, finally after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity, by the conservation of momentum principle.
What is Conservation of Momentum?
According to the Principle of Conservation of Momentum, when two objects meet, their total momentum is the same before and after the collision (provided that no external forces - for example, friction - act on the system). This is incredibly helpful since it means you can predict what will happen following a collision before it occurs.
What are the Calculations?
First collision (between three-car trains and a fourth car moving with 2[tex]V_{0}[/tex] in the same direction)
We will apply conservation of momentum to calculate the velocity of the train after the first collision
M1V1 + M2V2 = (M1 + M2)V 3M([tex]V_{0}[/tex]) + M2[tex]V_{o}[/tex] = (3 M + M)V .(5M)V. V (4M.V) V = [tex]\frac{5}{4} Vo[/tex]
Now the mass of the four-car train is 4M and is moving with a velocity of [tex]\frac{5}{4} Vo[/tex]
Second collision (between four-car trains and fifth car at rest)
Again we will apply conservation of momentum to calculate the velocity of the train after the second collision
M1V1 + M2V2 = (M1 + M2)V (4M × [tex]\frac{5}{4} V_{o}[/tex]) + (M × 0) = (4 M + M)V (5M)[tex]V_{o}[/tex] = (5M)V. V = [tex]V_{o}[/tex]
Finally, after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity.
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a majorette in a parade is performing some acrobatic twirlings of her baton. assume that the baton is a uniform rod of mass 0.120 kgkg and length 80.0 cmcm . figure1 of 1 part a initially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/srad/s . (figure 1)what is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton? express your answer in kilogram meters squared per second.
The magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton is 1.92*10^-2 kg*m^2/s and angular momentum of rod 7.68*10^-2 kg*m^2/s.
The axis of rotation intersects the center of the baton is 1.92*10^-2 kg*m^2/s
A)
Moment of inertia of rod = 1/12*m*L^2
= 1/12*0.12*0.8^2 = 0.0064
Angular momentum = I*ω
= 0.0064*3
= 0.0192 = 1.92*10^-2 kg*m^2/s
B)
Moment of inertia of rod = 1/3*m*L^2
= 1/3*0.12*0.8^2 = 0.0256
Angular momentum = 0.0256*3 =
00768 = 7.68*10^-2 kg*m^2/s
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if the distance between two charges is doubled, what will happen to the force between the charges? (4 points)
The force between them is reduced to 1/4 when the distance between the two charges is doubled. The force between them is inversely proportional to the distance.
What is coulomb's law?
Charged bodies experience a force of attraction or repulsion on approach.
From Coulomb's Law, it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.
From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:
[tex]F=k\frac{Qq}{d^{2}}[/tex]
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).
Q and q are the values of the two-point charges. They are measured in Coulombs (C).
d is the value of the distance that separates them. It is measured in meters (m).
K is a constant of proportionality called Coulomb's law constant. It depends on the medium in which the charges are located.
Thus, force is reduced to 1/4.
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. how does the energy of photons change as they travel from the core to the surface of the sun? explain the methods of energy transfer that occur and why they change as the photons travel from the core.
As the photons travel from the center to the surface, their energy decreases; they cool to a temperature of about 6000 K, which is similar to the sunlight we observe.
Conduction is quite ineffective in this situation, but convection does contribute—it begins at the outer core. The outer core provides energy to the inner convection cells, which then interact with the outer convection cells.
However, radiation is the main cause. It takes a photon a long time to reach the surface because after it emits, hits something, and is excited by that something, the photon is then released once more in an arbitrary direction.
What does radiation signify from a physics perspective?
Radiation is the name for energy that comes from a source and travels through space at the speed of light.
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The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals:a) x(t) = 1 + cos(2,000πt) + sin(4,000πt)b) x(t)= sin(4000 π t) / π tc) x(t)= 2 [sin(4000 π t) / πt]2
Nyquist rate = 2*(maximum signal frequency)
Sampling rate must exceed Nyquist rate in order to be able to fully reconstruct the signal.
a) x(t) = 1 + cos (2000πt) + sin(4000πt)
Frequency for each term:-
Term 1 is DC -> w₁ = 0
Term 2 -> w₂ = 2000π
Term 3 -> w₃ = 4000π
Maximum signal frequency (wm) = 4000π
Another way of saying this is that X(jw) = 0 for |w| > 4000π
Acc to Sampling theorem ws > 2wm, ws>8000π
So, the Nyquist rate is 8000π
b) x(t) = sin(4000πt) / πt
Using Fourier Transport table, we have X(jw) = 1 for |w| < 4000π
.0 for |w| > 4000π
Therefore, maximum signal frequency (wm) = 4000π
Acc to the sampling theorem ws > 2wm, ws > 8000π
c) x(t) = {sin(4000πt) / πt}²
We can rewrite the above function as x(t) = x₁(t) x₁(t), where,
x₁(t) = sin(4000πt) / πt
Using the convolution property X(jw) = (1/2π)X₁(jw) * X₁(jw)
We know that convolving a signal with itself will double the maximum frequency therefore:
Therefore, maximum signal frequency (wm) = 8000π
Acc to the sampling theorem ws > 2wm, ws > 16000π
Therefore, the frequency to determine the Nyquist rate is 16000π.
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What is the minimum diameter at section (1) in the pipe below to avoid cavitation at that location? Take D2= 15 cm. Neglect friction head loss in the pipe. (3) Water 5 m (1) (2)
The minimum diameter at section (1) in the pipe below to avoid cavitation at the location is 16.6 cm.
Look at the picture
In section (1) according to Torricelli's law the speed of waterAccording to Bernoulli's equation in sections (1) and (2)
p₁ + 0.5 ρv₁² = p₂ + 0.5 ρv₂²
1.5 × 10⁵ + (0.5 × 1,000 × 14²) = 1.01 × 10⁵ + (0.5 × 1,000 × v₂²)
1.5 × 10⁵ - 1.01 × 10⁵ + 98,000 = 500 × v₂²
49,000 + 98,000 = 500 × v₂²
147,000 = 500 × v₂²
v₂² = 147,000 ÷ 500
v₂² = 294
[tex]v_2 = \sqrt{294}[/tex]
v₂ = 17.15 m/s
According to the continuity equation for fluids
A₁ v₁ = A₂ v₂
[tex]\frac{1}{4} D_1^2 v_1 = \frac{1}{4} D_2^2 v_2[/tex]
D₁² v₁ = D₂² v₂
D₁² × 14 = 15² × 17.15
D₁² = 3,858.75 ÷ 14
D₁² = 275.625
[tex]D_1 = \sqrt{275.625}[/tex]
D₁ = 16.6 cm
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a child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25°. what is the maximum speed of the child as she swings?
A child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25° the maximum speed of the child as she swings is approximately 0.829 m/s.
To find the maximum speed of the child as she swings, we can use the formula for the velocity of an object in simple harmonic motion:
v = Aωcos(ωt)
where A is the amplitude of the motion, ω is the angular frequency (ω = 2π/T, where T is the period of the motion), and t is the time.
Given:
- T = 3.3 s (period of the motion)
- A = 25° (amplitude of the motion)
To use the formula, we need to convert the amplitude from degrees to radians:
- A = 25° * (π/180)
= 0.4363 radians
Now we can calculate the angular frequency:
- ω = 2π/T
= 2π/3.3
= 1.90 rad/s
At the maximum displacement (when the child is at the bottom of the swing), the velocity is at its maximum.
At this point, cos(ωt) = 1, so we can simplify the formula to:
v = Aω
Substituting the values, we get:
- v = 0.4363 radians * 1.90 rad/s = 0.829 m/s
Thus, the maximum speed of the child as she swings is approximately 0.829 m/s.
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in an electric motor, a commutator a. is made out of dozens of wire loops wrapped around a ferromagnetic core. b. repeatedly reverses the flow of current through the armature. c. is a magnet. d. is directly connected to the current source. please select the best answer from the choices provided a b c d
Commutators are used in DC machinery, such as universal motors and DC generators. A motor's windings get an electric current from a commutator. By reversing the direction of the current in the spinning windings every half turn, a constant rotational torque is generated.
According to this option b) is correct.
Describe a DC machine.
An electro-mechanical energy conversion system is known as a DC machine. There are two different kinds of DC machines: a DC motor and a DC generator. A DC motor transforms D.C. electrical power into mechanical power (ωT), whereas a DC generator converts mechanical power (T) into DC electrical power (EI).
What does a DC machine do?
An electrical device called a DC generator's principal job is to turn mechanical energy into electricity. Based on the electromagnetic induction theory of Faraday's Laws, an emf will be produced when the conductor cuts the magnetic flux.
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In a study conducted by a University of Illinois researcher, the football team at Unity High School in Tolono, IL was equipped for an entire season with helmets containing accelerometers. Information about every impact in practice and in games was sent to a computer present on the sidelines. The study found that the average force on a top of the head impact was 1770 N. If the initial velocity of the head was 2.09 m/s and the collision brings the head to a stop, and assuming the head has a mass of 4.12 kg, determine the duration of the impact.
(Note: we are treating the head as a free body which is a bit of an approximation).
The duration of the impact, given that the head has a mass of 4.12 Kg is 0.005 s
How do I determine the duration (i.e time)?We'll begin by obtaing the impulse. This can be obtained as follow:
Initial velocity = 2.09 m/sMass (m) = 4.12 KgFinal velocity = 0 m/sImpulse =?Impulse = m(v + u)
Impulse = 4.12 × (0 + 2.09)
Impulse = 4.12 × 2.09
Impulse = 8.61 Ns
Finally, we can obtain the duration of the impact. This can be obtained as follow:
Force (F) = 1770 NImpulse = 8.61 NsDuration (t) =?Impulse = force × time
8.61 = 1770 × t
Divide both sides by 1770
t = 8.61 / 1770
t = 0.005 s
Thus, we can conclude that the duration is 0.005 s
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the interaction between two waves that meet is called a. reflection. b. refraction. c. diffraction. d. interference. please select the best answer from the choices provided a b c d
The interaction between two waves that meet is called interference.
Interference is a phenomenon of wave interactions. When two waves meet at a point, they cancel each other out.
There are two types of interference, constructive and destructive.When the crests or troughs of two interfering waves meet, their amplitudes add up. This principle is known as constructive interference. When the opposite happens and it's called destructive interference. When the crest and trough of two interfering waves meet, one amplitude is subtracted from the other.Wave interference is a phenomenon that occurs when two waves meet while traveling through the same medium.Interference of waves causes the medium to take on a shape that results from the net effect of two individual waves on the particles of the medium.Answer d. interference is the correct answer
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assuming that the wave’s frequency ω remains constant, create a plot of the wavelength λ as a function of the current speed u. as u increases, what do you expect to happen to i) the wave’s length? ii) the wave’s amplitude? iii) the wave’s steepness? (5p)
A wave is a propagating dynamic disturbance of one or more quantities. Waves can be periodic, in which these quantities repeatedly oscillate around their equilibrium values at specific frequencies.
Whether vibrations or waves, they can all be characterized by four characteristics: Amplitude, Wavelength, Frequency, Velocity.
u = ωλ
Where, u = velocity of the wave
ω = frequency of wave
λ = wavelength of wave
For the first case:
If the wave’s frequency ω remains constant, then the velocity of wave will be proportional to wavelength:
u ∝ λ
So, if the velocity increases then there will be an increase in wavelength.
For the second case:
The amplitude of the wave is completely independent of the speed of propagation u and depends only on the amount of energy in the wave.
So, there will be no change of amplitude.
For the third case:
Wave steepness is the ratio of wave height(H) to wave length(λ).
Wave steepness = H/λ
This indicates that wave steepness is inversely proportional to wavelength.
Wave steepness ∝ 1/λ
But we know,
u ∝ λ
Then,
Wave steepness ∝ 1/λ ∝ 1/u
So, according to above application wave steepness in inversely proportional to velocity. This means that steepness will decrease with increasing velocity.
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If the sun mysteriously gets twice as massive as it is right now, what effect will it have on its pull on mars?.
Answer:
well, it would start burning it slowly. but it wouldn't just melt it immediately. then, if it got any bigger it would definitely melt it
Explanation:
a particle of charge q and mass m is moving with a velocity v along the x-axis in a magnetic field b which is along the z-axis. how much time will it take for the particle to return to its original location
The time required for the particle to return to its original location is (2πm/Bq) s.
We have to see the direction of magnetic force works on a particle. Using right-hand rule
Point your pointer finger according to the direction particle is moving. To the x-axis.Point your middle finger in the direction of the magnetic field. To the z-axisYour thumb points to the direction of the magnetic force pushing on the particle. To -y-axis.The magnetic force will deflect the direction of the particles so that the particles will move in a circle. The magnetic force becomes the centripetal force because it always points to the center of the circle.
Fc = Fm
[tex]m \frac{v^2}{R} \:=\: Bqv[/tex]
mv² = BqvR
mv = BqR
[tex]R \:=\: \frac{mv}{Bq}[/tex]
R = mv ÷ Bq
If the particle return to its original location, it means the particle travel one full circle. According to uniform motion
t = d ÷ v
t = perimeter of the circle ÷ v
t = 2πR ÷ v
t = (2πmv ÷ Bq) ÷ v
t = (2πm ÷ Bq) s
t = [tex]\frac{2 \pi m}{Bq}[/tex]
t = (2πm/Bq) s
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An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz.
Find:
(a) the period
(b) the angular frequency
(c) the mass of this object.
An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz: =0.0845 kg.
(a) Time period, T = 1/f = 1/6.0 = 0.167 s
(b) Angular frequency, ω = 2πf = 6.28x6 =37.7 rad/s
(c) For the mass, use the formula. ω2 =k/m
So, mass, m =k/ ω2
= 120/37.68x37.68
=0.0845 kg.
In physics, a force is a power that may change the movement of an object. A force can purpose an object with mass to trade its velocity, i.e., to accelerate. pressure can also be defined intuitively as a push or a pull. A force has both significance and path, making it a vector amount.
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