The work done by the force field f! (x, y) = x sin(y)i + yj on a particle that moves along the parabola y = x2 from (−1, 1) to (2, 4) will be 15/2 + 1/2 cos1 -1/2 cos4
Work done on a body is equal to the increase in the energy of the body, for work transfers energy to the body. If, however, the applied force is opposite to the motion of the object, the work is considered to be negative, implying that energy is taken from the object.
The units in which work is expressed are the same as those for energy, for example, in SI (International System of Units) and the metre-kilogram-second system, joule (newton-metre)
Equation of parabola : y = [tex]x^{2}[/tex]
dy = 2x dx
f(x , y) = x sin (y) i + y j
= [tex]\int\limits^2__{} \, -1[/tex] [tex]\ {x sin (x^{2} )} \, dx[/tex] + [tex]\int\limits^2__{} \, -1[/tex] 2x . [tex]x^{2}[/tex] dx
= [tex]\int\limits^2__{} \, -1[/tex] [tex]\ {x sin (x^{2} )} \, dx[/tex] + [tex]\int\limits^2__{} \, -1[/tex] 2 [tex]x^{3}[/tex] dx
= 1/2[tex]x^{4}[/tex] * ( - 1/2 cos [tex]x^{2}[/tex] ) + [tex]x^{4}[/tex] / 2
= 8 - 1/2 + (-1/2 cos 4 + 1/2 cos 1)
= 15/2 + 1/2 cos1 -1/2 cos4
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A child has an ear canal that is 1. 3 cm long. at what sound frequencies in the audible range will the child have increased hearing sensitivity?
A child has an ear canal that is 1. 3 cm long. Sound frequencies in the audible range for the child to have increased hearing sensitivity is 6600 Hz to 19,800 Hz
The shape of the human ear is similar to a pipe that has a closed end and other end is open. Hence,
λ = 4L where L is the length of child's ear
Wavelength, λ = 4 × Length of the ear of the child
λ = 4 × 0.013m
λ = 0.052m
Frequency is the no. of oscillations per unit time.
The frequency of the sound, ν = c/λ
where c is the speed of sound i.e. 343 m/s
λ is the wavelength of sound
The child's audible range is equal to
ν = 343/0.052
ν = 6600Hz
We can also say that, ν is 13200 Hz or 19,800 Hz.
In general, the audible range of frequency for human ear is 20Hz to 20,000Hz.
Hence, sound frequencies in the audible range will the child have increased hearing sensitivity is 6600Hz to 19800 Hz.
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Why doesn’t the total pressure increase when more gas is added to the chamber? (hint: what would you see if the volume of the chamber was fixed?)
Answer:
It won't increase according to Boyle's law
Explanation:
Volume of a gas varies inversely as the pressure so as more fixed volume of gas is added to the chamber the pressure reduces
In a ruby laser, an electron jumps from a higher energy level to a lower one. if the energy difference between the two levels is 1. 8 ev, what is the wavelength of the emitted photon?
The wavelength of the emitted photon is([tex]\lambda[/tex])= 690nm
How can we calculate the wavelength of the emitted photon?To calculate the wavelength of the photon we are using the formula,
[tex]\triangle E= \frac{h\times c}{\lambda}[/tex]
Or,[tex]\lambda= \frac{h\times c}{\triangle E}[/tex]
We are given here,
[tex]\triangle E[/tex]= The energy difference between the two levels = 1. 8 ev= [tex]1.8\times 1.6 \times 10^{-19}[/tex] C.
h= Planck constant = [tex]6.626\times 10^{-34}[/tex] Js.
c= speed of light = [tex]3\times10^8[/tex] m/s.
We have to find the wavelength of the emitted photon =[tex]\lambda[/tex] m.
Therefore, we substitute the known parameters in the above equation, we can find that,
[tex]\lambda= \frac{h\times c}{\triangle E}[/tex]
Or,[tex]\lambda= \frac{6.626\times 10^{-34}\times 3\times 10^8}{1.8\times 1.6 \times 10^{-19}}[/tex]
Or,[tex]\lambda= 690\times 10^{-9}[/tex] m
Or,[tex]\lambda[/tex]=690 nm.
From the above calculation we can conclude that the wavelength of the emitted photon is 690nm.
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You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?
A Final statement or concluding statement
As, Pressure(P)=(Force(F))/(Area(A)) . So, By Lying down flat on the ice and crawl towards shore will help to get off the ice safely.
What is the relationship between Area and Pressure?Pressure and area of contact are related in such a way that they are inversely proportional to each other.
As the area shrinks, so does the pressure.
Consider the difference between the pressure exerted by a finger pressing on the skin and the pressure exerted by a needle attached to a syringe.
When pressed, the finger may cause a slight depression on the skin but may not cause any pain.
When the same force is applied to a needle, however, the pressure produced is sufficient to puncture the skin.
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Gold’s natural state has a shape and a define volume that is gold’s natural state
Answer:
Gold's natural state has a definite shape and a definite volume. Gold's natural state is solid.In nature, gold most often occurs in metallic form, alloyed with silver.Heat is transferred from the sun-warmed surface of earth to the cooler overlying troposphere via _______
Heat is transferred from the sun-warmed surface of the earth to the cooler overlying troposphere via conduction.
Heat transfer from earth to atmosphere:Conduction, convection, latent heating, and water phase transitions all help to carry heat from the Earth's surface, which has been warmed by the Sun, to the cooler troposphere above.
Latent heat flux is the worldwide transfer of latent heat energy via water and air currents. Here, we demonstrate how air circulation transports latent heat energy horizontally to cooler regions, where it condenses into rain or is deposited as snow, releasing the heat energy that was previously trapped there.
When air is heated from below by sunshine or by coming into contact with a warmer land or sea surface, convection occurs and the air below becomes less dense than the air above.
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A carnival ride accelerates upwards at 2.5 m/s. what is the apparent weight of a 35 kg child on the ride
The apparent weight of the child is 437.5 N.
Calculation:The weight of a person/object moving up with an acceleration "a" is given by
W = m (g + a)
where,
W = apparent weight
m = mass of the person/object
g = acceleration due to gravity = 10 m/s²
a = acceleration of the object/person
Given,
m = 35 kg
a = 2.5 m/s²
To find,
W =?
Put the value sin the formula,
W = m (g + a)
W = 35 (10 + 2.5)
= 35 (12.5)
= 437.5 N
Therefore, the apparent weight of the child is 437.5 N.
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A research team designed a new personality test to measure how extroverted or introverted someone is. what should they do to test the validity of their questionnaire?
The research team should compare all their test results along with other kinds of similar personality tests to know if they will have similar type of results.
What is the personality test known as?It is known to be Myers-Briggs Personality Type Indicator and this is said to be a kind of a self-report inventory that is made to know a person's personality type, along with their strengths, and preferences.
Note that the questionnaire was made or created by Isabel Myers along with her mother Katherine Briggs and it is one that is based on their work with the use of Carl Jung's theory of personality types.
Hence, The research team should compare all their test results along with other kinds of similar personality tests to know if they will have similar type of results.
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What is the inductance of a coil if the coil produces an emf of 2.50 v when the current in it changes from -28.0 ma to 25.0 ma in 12.0 ms?
The inductance of a coil if the coil produces an emf of 2.50 v when the current in it changes from -28.0 ma to 25.0 ma in 12.0 ms is L = 0.566 H
An inductor is a passive electronic component that stores energy in the form of a magnetic field. In its simplest form, an inductor consists of a wire loop or coil. The inductance is directly proportional to the number of turns in the coil.
The SI unit of inductance is Henry abbreviated as 'H'. It is defined as the measure of electric current changes at one ampere per second resulting in an electromotive force of one volt across the inductor.
The expression for induced emf
E=−L (di /dt)
L= E (dt / di )
di = 25 - ( -28) = 53 mA = 53 * [tex]10^{-3}[/tex] A
dt = 12 ms = 12 * [tex]10^{-3}[/tex] sec
E = 2.5 V
L = 2.5 ( 12 * [tex]10^{-3}[/tex] / 53 * [tex]10^{-3}[/tex] )
L = 0.566 H
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Which components are a possible representation of vector w if the magnitude of vector -3w is ?
The components that are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15 are:
<-3,4><0,-5>What are the vector about?From the question, we were given:
|-3w| = 15
3|-w| = 3|w| = 15
Hence:
|w| = 15/3
|w| = 5
If vector w is represented by <-3,4>, then:
[tex]\sqrt{(-3)^2 + (4)^2} \\\\\\\sqrt{25} = 5[/tex]
If vector w is represented by <0,-5>
[tex]\sqrt{(0)^2 + (-5)^2} \\\\\\\sqrt{25} = 5[/tex]
Therefore, The components that are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15 are:
<-3,4><0,-5>See full question below
Which components are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15?
<1,-9>
<-3,4>
<4,5>
<-5,-3>
<0,-5>
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450n 360n 710n 1400n 230n a block is placed in oscillation on a frictionless horizontal surface attached to a spring that is also attached to a wall. If, when stretched away from equilibrium by 15cm and released, it oscillates with a period of 0. 25s, and if the mass of the block is 15kg, what force was required to stretch the spring by the initial 15cm?.
F = 1420 N
Force was required to stretch the spring by the initial 15cm is 1420 N.
m = 15, P = 0.25, x = 0.15
F = -K x for spring
where,
F = force
K = constant
ω = (K/m)^1/2
where,
ω = angular frequency
m = mass of the block
ω^2 = K / m
K = m ω^2 = m (2 π f)^2 = m 4 π^2 / P^2
K = 4 π^2 m / P^2
F = K x = x * 4 π^2 m / P^2
F = 0.15 * 4 * π^2 * 15 / 0.25^2
F = 1420 N
What is oscillation?The movement between two locations back and forth, or to swing back and forth like a pendulum is known as oscillation.
What is equilibrium?A condition where competing forces or actions are in balance is called equilibrium.
What is the stretching force?Tensional force is the force exerted by a stretched item. It could be a rope, string, elastic band, or wire that is being stretched. The object's tensional force is applied to the objects stretching it. The stretched object is subject to tensile force.Exactly why does a spring stretch?A typical spring is a tightly wrapped metal coil or spiral that stretches when pulled (by applying force) and returns to its original shape when released (remove the force). A spring is elastic, in other words.To learn more about forced for stretching visit:
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A circuit has an impedance of 5 ohms and a voltage of 100 volts. What is the current flow?
A circuit with an impedance of 5 ohms and a voltage of 100 volts has a current flow of 20 A.
The expression of an electronic component, circuit, or system's resistance to alternating and/or direct electric current is called impedance, indicated by the letter Z. Resistance and reactance are two distinct scalar (one-dimensional) phenomena that combine to form impedance, a vector (two-dimensional) variable.
[tex]Z^{}[/tex] = [tex]\frac{V}{I}[/tex]
(for a pure resistor where Z=R,preserving the form of the DC Ohm's law).
[tex]I=\frac{V}{Z}[/tex]
[tex]I = \frac{100}{5}[/tex]
I = 20 A
Therefore, A circuit with an impedance of 5 ohms and a voltage of 100 volts has a current flow of 20 A.
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What happens to the visible radiation produced by new stars within a molecular cloud?
The visible radiation produced by new stars within a molecular cloud get absorbed by dust grains and heats up the cloud
A molecular cloud is an interstellar cloud of gas and dust in which molecules can form, the most common of which is hydrogen .
The formation of stars occurs exclusively within molecular clouds because of their low temperatures and high densities, because the gravitational force acting to collapse the cloud must exceed the internal pressures that are acting "outward" to prevent a collapse.
Visible radiation are absorbed by dust grains and heats up the cloud as it cannot penetrate through the cloud instead get absorbed by the cloud . Newly formed stars are visible nearby, their images reddened by blue light which got scattered by the pervasive dust.
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What must you do at a flashing red light? * 1 point slow down and proceed with caution be ready for a traffic light ahead stop and wait until the light stops flashing stop and proceed only when clear
Stop and wait until the light stops flashing stop and proceed only when clear.
Flashing Red - A flashing red traffic signal light means "STOP." After stopping, you may proceed when it is safe.
How must you react to a flashing red traffic light?
Flashing Red: If the traffic signal is flashing red, treat it as a stop sign and come to a complete stop at the intersection. Look carefully in all directions before proceeding. Other directions may have a different type of signal indication.What must a driver do at a flashing yellow light ?
A flashing yellow light warns drivers to slow down and proceed with caution. Drivers may turn left on a green light. However, drivers must yield the right-of-way if other traffic is approaching from the opposite direction.Learn more about traffic lights
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When 6a of ac current at 114 v flows in the primary coil of an ideal transformer, how many amps at 29 v wul flow in the secondary?
The current that will flow in the secondary coil will be 23.5 Amperes
Power is the rate per unit time, at which electrical energy is transferred by an electrical circuit.
The SI unit of power is the watt and is given by Voltage * Current
Let's solve the question:
Given:
Voltage ( Primary ) = Vp = 114 V
Current ( Primary ) = Ip = 6 A
Voltage ( Secondary ) = Vs = 29 V
Current ( Secondary ) = Is = ?
In Ideal Transformer Primary Power = Secondary Power
Therefore, Vp * Ip = Vs * Is
114 * 6 = 29 * Is
684 = 29 Is
Is = 23.5 Amperes
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An organization is located in an area that experiences frequent and lengthy power blackouts. what will the effect of an electric generator be in this circumstance?
Electric utility power blackouts will result in short electric power outages for the organization.
Power blackouts :When the electrical power network, often known as the electrical grid, is down, there are power outages. Power outages can have a variety of causes, but they always tend to affect entire regions or cities rather than simply a single residence. For example, the Northeast blackout of 2003 left 50 million people without power from New York to Canada’s capital Ottawa.
A place experiences a blackout when all power is lost. Power outages of this kind generally affect a sizable population over perhaps extraordinarily broad areas. Blackouts are particularly difficult to quickly fix because they typically result from significant damage to electrical generation facilities (such as structural damage from violent wind storms or lightning strikes). As a result, these types of outages can, in the worst-case scenarios, last for several weeks.
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What must the amplitude of a traveling wave of frequency 72.0 hz be in order for the average power carried by the wave to be 0.363 w ? express your answer with the appropriate units.
The tension in the wire, the wave's speed, its frequency, and its average power are used to calculate the wave's amplitude.
To find the answer, we have to know about the simple harmonic motion.
How to find the amplitude of a traveling wave?We have the expression for average power carried by the wave as,P = (¹/₂)(T/v²)(ω²)(A²)(v)
P = (¹/₂)(T/v)(ω²)(A²)
P = (¹/₂)(T/v)(2πf)²(A²)
where; U is the average power of the wave, T is the tension e wire, ω angular frequency of the wave, A is amplitude of the wave, v is the speed of the wave and f is frequency of the wave.
Thus, the tension in the wire, the wave's speed, its frequency, and its average power are used to calculate the wave's amplitude.
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Suppose that we repeat the experiment, except that we place the sodium flame in a strong, localized electric field. The field changes the energy levels of the sodium atom, but it does not affect the sodium in the lamp or the photons it produces. The shadow cast by the sodium flame when illuminated by the sodium lamp should?.
The shadow cast by the sodium flame when illuminated by the sodium lamp should become lighter.
What is Zero current point ?The interruption phenomenon in high power circuit breakers is referred to as current zero (CZ). Today, it is unlikely that high voltage circuits could be inexpensively disrupted using anything other than an electric arc.
electric field -
The electric force per unit charge is referred to as the electric field. It is assumed that the field's direction corresponds to the force it would apply on a positive test charge. From a positive point charge, the electric field radiates outward, and from a negative point charge, it radiates in.
In order to provide the lamp with a virtually constant current rather than a constant voltage in order to ensure reliable operation, the lamp is often supplied by an AC voltage source connected in series with an inductive ballast. To minimise resistive losses, the ballast is often inductive rather than just resistive. Because the sodium flame's shadow is growing lighter and this lamp's current is going toward its zero-current point.
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what is the best estimate for the product 2,704.241 X 165.9
The best estimate for the product of 2,704.241 and 165.9 is determined as 448,633.58.
What is product of numbers?The product of numbers is the multiplication of two or more integers together.
Product of the given numberThe product of the given numbers is calculated as shown blow.
The best estimate for the product of 2,704.241 and 165.9.
= 2,704.241 X 165.9
= 448,633.58
Thus, the best estimate for the product of 2,704.241 and 165.9 is determined as 448,633.58.
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1. Consider the potential energy diagram shown below. This graph shows the chemical potential energy in a reaction system over time. The y-axis is potential energy in kilojoules. The x-axis is the reaction progress or time.
Does this graph represent an endothermic or an exothermic reaction? Explain your answer.
What is the enthalpy change, ΔH, for this reaction? Show your work.
What is the activation energy, Ea, for this reaction? Show your work.
THE GRAPH IS BELOW
150 kJ of energy was given out over the course of the reaction and 200kJ is required for the reactants to be converted into products.
What is the potential energy graph?We know that the combination of the reactants is what leads to the formation of products. The interaction of the reactants and the products is what is shown on the potential energy curve. The hump at the highest point of the graph is the activation energy while the difference between the energy of the reactant and the products is the enthalpy of the reaction.
Now; the enthalpy change is given as;
ΔH = 200 kJ - 50 kJ = 150 kJ
Ea = 250 kJ - 50 kJ = 200kJ
We can see that 150 kJ of energy was given out over the course of the reaction and 200kJ is required for the reactants to be converted into products.
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(b) A ball is thrown vertically upwards with
velocity of 20 m/s from the top of a tower of
height 25 m from ground. How long does it
remain in air? (g = 10 m/s²)
Answer:
5 seconds
Explanation:
The vertical position of the ball will be given by the equation
df = do + vo t + 1/2 a t^2 df = final position = 0 ( on the ground
do = original position ( 25 m )
vo = original velocity (+ 20 m/s)
a = - 10 m/s^2
So this becomes
0 = 25 + 20 t - 1/2 (10)t^2
= - 5 t^2 +20 t + 25 Use Quadratic Formula a = -5 b=20 c = 25
to find the positive value of t = 5 seconds
The energy of a photon of red light is ____ the energy of a photon of blue light
A photon's energy and wavelength are inversely related. Since the wavelength of photons of blue light is less than photons of red light, it contains more energy than red photons.
Wavelengths of blue light are shorter, ranging from 450 to 495 nanometers. Red light has wavelengths that range from 620 to 750 nm and longer waves. Compared to red light, blue light has a greater frequency and more energy.
A photon's energy varies with its wavelength; those with longer wavelengths have less energy than those with shorter ones. For instance, red photons are less energetic than blue ones.
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An electric motor has an effective resistance of 29. 4 ω and an inductive reactance of 42. 6 ω. When working under load. the rms voltage across the alternating source is 442 v. Calculate the rms current
An electric motor has an effective resistance of 29. 4 ω and an inductive reactance of 42. 6 ω. When working under load. the rms voltage across the alternating source is 442 v. The rms current will be 8.54 A
AC stands for “Alternating Current,” meaning voltage or current that changes polarity or direction, respectively, over time. AC electromechanical generators, known as alternators, are of simpler construction than DC electromechanical generators.
RMS or root mean square current/voltage of the alternating current/voltage represents the D.C current/voltage that dissipates the same amount of power as the average power dissipated by the alternating current/voltage. For sinusoidal oscillations, the RMS value equals peak value divided by the square root of 2.
I (RMS) = RMS voltage / [tex]\sqrt{R^{2}+ X_{L} { ^{2} }[/tex]
= 442 / [tex]\sqrt{29.4^{2} + 42.6^{2} }[/tex]
= 442 / [tex]\sqrt{864.36 + 1814.76}[/tex]
= 442 / [tex]\sqrt{2679.12}[/tex]
= 8.54 A
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Katie rolls a toy car off the end of a table.
Answer:
The toy car will fall off Katie's hands and onto the ground .
Explanation:
This happens due to gravity.
If the ambulance siren was emitting a crest at time = 0, what is the siren doing at time = 0. 02 s? is it emitting a crest or trough, or is it somewhere else in the cycle? how do you know?
while the siren produces waves of constant frequency, as it approaches us the observed frequency increases and our ear hears a higher pitch. After it has passed us and is moving away, the observed frequency and pitch drop this effect is known as Doppler effect.
The characteristic sound of a motorcycle buzzing by is an example of the Doppler effect. Specifically, if you are standing on a street corner and observe an ambulance with a siren sounding passing at a constant speed, you notice two characteristic changes in the sound of the siren. First, the sound increases in loudness as the ambulance approaches and decreases in loudness as it moves away, which is expected. But in addition, the high-pitched siren shifts dramatically to a lower-pitched sound.
what is Doppler effect?
The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer. Although less familiar, this effect is easily noticed for a stationary source and moving observer.
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When a proton slows from 0. 8c up to 0. 6c, it’s kinetic energy decreases by what factor?
When a proton slows from 0. 8c up to 0. 6c, it’s kinetic energy decreases by what factor of 1/4.
Kinetic energy of a proton having a charge Q and Voltage V is given by:
Kinetic energy = Q×V
Where, Q is the charge
V is the Voltage
Kinetic energy is directly proportional to the charge on a proton.
Let the kinetic energy of proton having charge 0.8C be KE₁ and kinetic energy of proton having charge 0.6C be KE₂
Hence KE₁ = 0.8 × V
KE₂ = 0.6 × V
Now, KE₁ / KE₂ = 0.8 V / 0.6 V
⇒ KE₁ / KE₂ = 4 / 3
⇒ KE₂ / KE₁ = 3/4
⇒ KE₂ = 3/4 times KE₁
Hence, the final kinetic energy becomes 3/4 times the initial kinetic energy.
The kinetic energy decreases by a factor of:
Change = KE₁ - KE₂
Change = KE₁ - 3/4KE₁
Change = 1/4 KE₁
Hence, the kinetic energy decreases by a factor of 1/4
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What is the mathematical relationship between wavelength and energy transmission?.
The mathematical relationship between wavelength and energy transmission E = hv.
What is Wavelength and Energy transmission?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is most frequently described in nanometers (nm), which are units of 10⁻⁹ m, or angstroms (Å), which are units of 10⁻¹⁰ m, for infrared (IR), visible light (UV), and gamma radiation (γ).
The most fundamental aspect of global energy integration is energy transmission. With the flow of electricity produced from coal as well as from hydro, nuclear, wind, and solar energy all being transported through power networks, electric energy transmission is a significant source of energy transport.
Wavelength and frequency are connected to energy in the same way as they are to light. Greater energy is correlated with shorter wavelengths and higher frequencies. Therefore, lower energy is produced by longer wavelengths and lower frequencies. E = hv is the energy equation.
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A film of soapy water (n = 1. 33) on top of a plastic cutting board (n > 1. 33) has a thickness of 147 nm. what color is most strongly reflected if it is illuminated perpendicular to its surface?
A film of soapy water (n = 1. 33) on top of a plastic cutting board (n > 1. 33) has a thickness of 147 nm. The color that is most strongly reflected if it is illuminated perpendicular to its surface is 294nm.
When the light is reflected it experiences a half of phase change. Then, the ray will be refracted by travelling through the soapy water down due to the refractive index. It will hit the second boundary which is plastic but light does not pass through the plastic. This will again reflect with again half of a phase change.
So, the formula used is:
2t = λ / 2 + λ / 2
Given,
refractive index of soap = 1.33
refractive index of air = 1
The relation between the thickness of the board and the wavelength used is as follows:
2t = λ / 2 + λ / 2
where, t is the thickness
λ is wavelength
On solving,
2t = λ
On substituting in above equation,
2(147) = λ
λ = 294nm
The color that is most strongly reflected if it is illuminated perpendicular to its surface is 294nm.
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What average emf (in volts) is induced, given the plane of the coil is originally perpendicular to the earth’s field and is rotated to be parallel to the field in 11 ms?
The average emf induced is "ωBA volts".if we know the value of ω, B & A we can easily calculate the value. Faraday's law of induction determines the typical emf produced by spinning a coil's turn in the earth's magnetic field.
Discussion:
According to this equation, the magnetic flux through a closed loop changes at a time rate equal to the negative of the induced emf in the loop.
When a coil is exposed to a magnetic field, it encounters a flux that is equal to the magnetic field's intensity times the area that the loop encloses times the Sine of the angle that exists between the standard to the region and the magnetic field.Calculation:
This flux value is constant and no electromagnetic field (EMF) is produced when the loop is positioned in the earth's magnetic field without moving. When the magnetic field starts rotating, the area and magnetic field strength stay constant, but the angle between the plane of the area's normal and the field lines continues to alter or fluctuate. Due to the magnetic flux's relationship to angle and the time dt at which an average emf is produced in the coil, this results in a change in the net magnetic field across the loop.
The flux φ = BAcosθ
E = - dφ/dt = - d(BAcosθ)/dt
As "B" & "A", both are constant
so, E= - BAd(cosθ)/dt
where, θ = the function of time
θ = ωt
where, ω = angular frequency (rad/sec)
E = -BAd(Cosωt)/dt
E = - (-ω)BA Sinωt = ωBA Sinωt
E = ωBASinωt
E = -d(BACosθ)/dt
The plane is now parallel to the field, and the normal is now perpendicular to the field.
θ=90°
Therefore, E= ωBASin90° = ωBA(1) = ωBA
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If a current of 2. 4 a is flowing in a wire of diameter 2. 0 mm, what is the average current density?
The average current density is 7.6 × 10⁵ A/m².
To calculate the current density current will be 2.4 A.
Diameter of a wire = 2mm.
The cross-sectional area of the wire is given by r = d/2
where r is the radius of the wire.
Then, the cross-sectional area is = 0.00000314159265
= 3.1 × 10⁻⁶ m².
What is average current density?Consider a current carrying conductor, the current density depends upon the current flow in the conductor. If the current flow in the conductor will be high then the current density will also be high. Using the average current flowing through the conductor, the average current density will be found.
Average current density j = I / A Ampere/ meter².
By substituting the values in the formula,
j = 2.4 / ( 3.1 × 10⁻⁶)
= 7.6 × 10⁵ A/m².
Hence, the current density can be calculated.
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