It is proved that when v<<c , then speed of the light measured in the laboratory frame is , u = c/n + v -v/n^2 .
Given ,
The motion of a transparent medium influences the speed of light .
The water moves with speed v in a horizontal pipe .
Assume that the light travels in the same direction as the water moves .
The speed of the light with respect to the water is c/n
Where n = 1.33 is the refractive index of water .
Let us assume ,
u' be the speed of light in water , in the frame moving with the water .
u' is related to the refractive index of water ,n as :
u'=c/n
where , c is the speed of light .
let , u be the speed of light in water in the lab frame .
Now , u and u' are related as : u = (u'+ v )/(1+ u'v/c^2)
Here v is the speed of water in the horizontal pipe .
we know the value of u' , so by substituting the value , we will get ,
u= (c/n+ v)/(1+cv/nc^2)
u= c/n(1+ nv/c)/(1+v/nc)
(b) We have , v<<c
v/c<<1 .
so , (1+v/nc )^-1 = (1-v/nc)
Now substituting this , we will get ,
u = c/n(1+nv/c) (1-v/nc)
u≈c/n(1+ nv/c-v/cn)
u≈c/n + v - v/n^2
Hence , it is proved that when v<<c , then speed of the light measured in the laboratory frame is , u = c/n + v -v/n^2 .
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Disclaimer : incomplete question , here is the complete question .
Question: The motion of a transparent medium influences the speed of light. This effect was first observed by Fizeau in1851. Consider a light beam in water. The water moves with speed v in a horizontal pipe. Assume the light travels in the same direction as the water moves. The speed of light with respect to the water is c / n , where n=1.33 is the index of refraction of water.(a) Use the velocity transformation equation to show that the speed of the light measured in the laboratory frame isu = c/n (1 + nv/c / 1+ v/nc) . (b) show that for v<<c , the expression from part (a) becomes , to a good approximation , u ≈ c/n + v - v/n^2 .
Will the following pair of atomic orbitals interact constructively, destructively, or with no net overlap if they approach along the indicated axis?.
If the troughs of the atomic orbitals overlap with each other and indicate out-of-phase combinations then they interact destructively.
However, (+), and (-) pair of atomic orbitals interact destructively.
In Chemistry, molecular orbital theory(MOT) indicates that atoms merge together to form atomic orbitals in a molecule. Atomic orbitals overlap to form molecular orbitals.
In a molecule, there are two types of orbitals: bonding orbitals (BO) and anti-bonding orbitals(ABO).
According to MOT theory, when atoms join together through atomic wavefunction then the electrons display wave-like nature.
The presence of electrons in the bonding orbitals increases the molecular stability increases as compared to their presence in anti-bonding orbitals.
To put it simply, when only the crusts of waves overlap in molecule orbitals they form constructive interference while overlapping of troughs causes destructive interference.
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Describe the change in motion F = 300 N. V = 0 m/s F = 450 N
When a moving body's direction changes, its velocity doesn't always go to zero. Only when the body's total displacement is zero does velocity become zero.
A change in the body's state of motion is reflected in either a change in the body's speed or its direction of motion. A force is an attempt to alter the status of an object, whether it is stationary or moving. The speed shift might indicate acceleration or slowdown (deceleration). Acceleration measures the change in speed as opposed to velocity, which measures speed in a vector (also in a vector). The velocity is zero, which indicates that although the item is not moving, there is a force exerted on it due to acceleration.
Hence the change in motion is zero
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M A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB . This level is too loud for your baby, who yells at 75.0 dB. (a) What total sound intensity engulfs you?
A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 db. This level is too loud for your baby, who yells at 75.0 db. 155 is the total sound intensity can engulf me.
What is intensity?In physical science, the force or motion of brilliant energy is the power moved per unit region, where region is estimated on the plane opposite to the heading of spread of the energy.
The formula for intensity is given by, I = P A. Where I am the intensity, P is the power and A is the area of cross section.
Light force assumes an essential part. With expanded light the fish' s vision improves, and they will turn out to be more careful about hunters. The sun' s point decides how much light entering the water. As would be normal, the most elevated measure of sun-based force happens on the globe right where the sun is above and as the point of the sun brings down, the sun-oriented power declines.
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I NEED HELP ASAP!!!
23. Formulating Hypotheses Suppose you want
to know if objects with different masses fall to
the ground at different rates. State a hypothesis
about falling objects.
24. Designing Experiments Explain how you can
test the hypothesis in Question 23. What will be
the manipulated variable in your experiment?
What will be the responding variable?
I already have a hypothesis for 23 I just need to know how I will test my hypothesis.
Also I don’t know if Im right but would the manipulated variable be the Weight??
A plausible hypothesis in this case is; "different masses of objects fall to the ground at different rates".
What is a hypothesis?A hypothesis is a plausible explanation for an observation. A hypothesis is always formulated prior to an experiment. The experiment would now confirm or disprove the hypothesis that has been put forward.
Recall that an experiment must have a dependent variable and an independent variable. The independent variable is the variable that we have to continue to manipulate while the dependent variable is the variable that dependent variable changes with the independent variable.
A plausible hypothesis in this case is; "different masses of objects fall to the ground at different rates". The independent variable would now be mass of the object while the dependent variable would be the rate at which the object falls.
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Will the following pairs of atomic orbitals interact constructively, destructively, or with no net overlap if they approach along the indicated axis?.
If the atomic orbitals are oppositely charged then they interact destructively.
In Chemistry, molecular orbital theory refers to the pattern of electron movement in a molecule.
It states that electrons have wave-like nature and their combination is the result of the atomic wavefunction.
According to this theory, there are two types of orbitals: bonding orbitals (BO) and anti-bonding orbitals(ABO).
Electrons in bonding orbitals make the molecule more stable as compared to electrons of anti-bonding orbitals.
Atomic orbitals form molecular orbitals and the combination of waves in molecule orbitals forms constructive and destructive interference. In-phase waves give rise to constructive interference.
While the combination of out-of-phase waves results in destructive interference that results in a straight line with no amplitude.
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A string of length L , mass per unit length μ , and tension T is vibrating at its fundamental frequency. (i) If the length of the string is doubled, with all other factors held constant, what is the effect on the fundamental frequency?(a) It becomes two times larger.(b) It becomes √2 times larger. (c) It is unchanged.(d) It becomes 1 /√2 times as large. (e) It becomes one-half as large.
Fundamental frequency will be [tex]\frac{1}{{2} }[/tex] times that of original frequency on doubling the length of the string which is option (e) .
Fundamental frequency, also called simply fundamental wave, is defined as the lowest frequency of a periodic waveform. In music, the root is the pitch of the note that is perceived as the lowest partial present.A wave traveling on the string is reflected at the other end. Standing waves are created as a result of interference between incident and reflected waves propagating in opposite directions. The fundamental frequency of the standing wave of a taut string is given by [tex]f=\frac{1}{2l} \sqrt{\frac{T}{u} }[/tex] ....(1) where T is the tension in the string, u is the mass per unit length of the string , l is the length of the string.From equation (1) it can be seen clearly that fundamental frequency in inversely proportional to the length of the string.
On putting double the length of the string in equation (1) keeping the all factor same , we get
[tex]f'=\frac{1}{2\times2l} \sqrt{\frac{T}{u} }\\\\f'=\frac{1}2 } f[/tex]
Where f ' is the new frequency and f is the original frequency .
Thus, If the length of the string is doubled, with all other factors held constant, then the fundamental frequency will reduce to half.
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a baseball pitcher throws a fastball at a speed of 37 m/s. the acceleration occurs as the pitcher holds the ball in his hand and moves it through an almost straight-line distance of 3.5 m. calculate the acceleration, assuming that it is constant and uniform.
The acceleration of the ball during the throwing motion is 5.28m/s².
Acceleration is defined as rate of change of velocity w.r.t time.
a = dv/dt
velocity is the rate of change of displacement with respect to time.
final velocity ,
v = 37m/s
initial velocity,
u = 0m/s
distance, s = 3.5m
acceleration = ?
equation of motion describes simple Concept of the motion make position, velocity, acceleration of an object.
Using the equation of motion
v² = u² + 2as
using above values we get
(37)² =(0)² + 2× a × 3.5
a = 37/7
a = 5.28m/s²
The acceleration of the ball during the throwing motion is 5.28m/s².
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What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?.
E = 1.024 10⁻⁷ N/C is the size of an electric field where a proton experiences an electric force that is equal to its weight.
What is an electric field?The term "electric field" refers to the physical field that surrounds electrically charged particles and pulls or attracts all other charged particles nearby. Additionally, it describes the physical environment of a system of charged particles.
The answer to the question is that the electric force's strength is proportional to its weight.
F(q) = Weight.
F(q) = E × q
where;
E = electric field magnitude
q = charge on an electron.
Therefore;
E × q = m × g
E = (1.67 × 10^-27 × 9.81)/1.60× 10^-19
E = 1.024 × 10^-7 N/C
Therefore, the magnitude of the electric field is E = 1.024 10⁻⁷ N/C.
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During eeg measurements, 6-10 electrodes are attached to the scalp and produce line drawings that represent __________. a. brain patterns b. mental activity c. x-rays d. brain waves please select the best answer from the choices provided a b c d
During eeg measurements, 6-10 electrodes are attached to the scalp and produce line drawings that represent brain waves.
EEG stands for electroencephalogram and eeg measurements refer to the recording of brain activities in the form of neuron signals.
In this test, micro sized sensors or electrodes are attached to the head or scalp of a person and electrical signals are recorded released by the brain neurons.
On the EEG recorder, the brain activities show up in the form of wave signals or wavy lines indicating that brain communicates through electrical currents signals.
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Answer:
brain waves
Explanation:
the takeoff speed for an airbus a320 jetliner is 78 m/s . velocity data measured during takeoff are as follows:
The acceleration of the Jetliner during takeoff = 2.1 [tex]m/s^2[/tex]
The given dataset of time in seconds and takeoff speed in m/s is:
t (s) v(m/s)
0 0
10 21
20 42
30 63
As we can see the rate of change of velocity (Δv) is uniform in each interval.
That is, in each interval, Δv = 21 m/s and Δt = 10s
We need to find the jetliner's acceleration during the takeoff.
Acceleration of a moving body is defined as the rate of change of velocity. Here since the rate of change of velocity is constant, we can simply use the following formula to find the acceleration.
Acceleration during takeoff, a = Δv / Δt = 21/10 = 2.1 [tex]m/s^2[/tex]
The question is incomplete. Find out the complete question here:
The takeoff speed for an airbus a320 jetliner is 78 m/s . velocity data measured during takeoff are as follows:
t (s) v(m/s)
0 0
10 21
20 42
30 63
What is the jetliner's acceleration during takeoff, in m/s2?
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what are the components of the displacement vector from camp to summit? choose the x axis east, y axis north, and z axis up.
Consider east-west direction along x-axis and north-south direction along y-axis, x = x- component of the displacement vector = - 4580 Sin32.4 = - 2454.1 m
y = y- component of the displacement vector = 4580 Cos32.4 = 3867.02 m
z = z-component of the displacement vector = 2450 m
magnitude of displacement vector is given as
magnitude = sqrt(x² + y² + z²) = sqrt((- 2454.1)² + (3867.02)² + (2450)²) = 5194.13 m
Work is the result of displacement and a part of force acting in the displacement direction. 2. The result of force and displacement is work. 3. Work is a result of force and a part of displacement that moves in the force's direction.
When examining a force's geometric representation or its algebraic equivalent, the components of a force can be viewed as horizontal and vertical changes. The vertical and horizontal forces that combine to create the resulting force are represented by a force's components.
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Is a rocket in the process of launching, Balanced or Unbalanced force?
The forces during rocket launching are unbalanced as, without unbalanced force, there can not be any motion.
Forces constantly balance and become out of balance during a rocket flight. On the launch pad, a rocket is balanced. Gravity tries to pull the rocket down, but the surface of the pad pushes it upward.
When the rocket's engines are lit, the thrust from them causes the forces to become out of balance, which causes the rocket to ascend. For a rocket to launch from a launch pad or for a spacecraft to change speed or direction, an unbalanced force must be applied.
Therefore, when the rocket is in the process of launching, the forces that act on the rocket are unbalanced.
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if an electron is released from infinity, how fast will it be traveling after falling to within 1 x 10-10 m of a proton?
If an electron is released from infinity, after falling to within 1x10-10 m of a proton its speed will be 2.25x10^-6 m/s.
What is speed?
Speed is typically characterized as rapidity in motion, travel, or action; swiftness; and celerity. The speed of light and the speed of sound are two instances of speed. Speed of motion or forward movement; relative quickness in moving, progressing, etc.: we're moving really quickly. the fullest, highest, or most efficient pace of motion: The car just needs nine seconds to accelerate to its top speed. According to special relativity, the maximum speed at which energy or information may move is equal to the speed of light in a vacuum, which is equal to c = 299792458 meters per second (about 1079000000 kilometers per hour or 671000000 mph).
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The radius of magnesium atom is 0.16NM the radius of a nucleus is about 1/10,000 that of an atom calculate the radius of magnesium nucleus give your answer in standard form. And explain
The radius of magnesium atom is 0.16NM and radius of nucleus is 1\10,000 of atom so radius of magnesium nucleus will be 1.6E-5 NM.
Given,
radius of magnesium atom is 0.16NM
radius of nucleus is about 1\10,000 of an atom
So radius of magnesium nucleus will be :
radius of magnesium atom * 1\10,000
0.16 NM *1\10,000
1.6e-5 NM
Hence radius of magnesium nucleus will be 1.6E-5 NM by simple unitary method.
We can also put it in SI units by using the same unitary method and get the values in meters which will be equal in values to 1.6 e-14 m.
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Describe how atoms form positive ions by losing electrons or negative ions by gaining electrons
Atoms form positive ions by losing electrons or negative ions by gaining electrons through a special type of chemical combination called electrovalent or ionic combination.
How atoms of sodium and chlorine combine together to form their ionsIt follows that metals are electropositive elements which donates its valence electrons to the nonmetals. The atoms which donates its electrons become positively charged while the species that recieve electrons become negatively charged.
In the formation of sodium chloride, sodium donates its 1 valence electron to chlorine become positively charged; Na+ and chlorine which recieves the electron to add to it's 7 valence electrons become negatively charged; Cl-
Na + Cl ---- Na+Cl-
So therefore, atoms form positive ions by losing electrons or negative ions by gaining electrons through a special type of chemical combination called electrovalent or ionic combination.
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Because most particles fired at metal foil passed straight through, rutherford concluded that.
Because most particles fired at metal foil passed straight through, Rutherford concluded that only a small area of an atom is positively charged called the nucleus.
According to Rutherford's atomic model, the atom is a tiny particle that is made up of fundamental objects called electrons, protons, and neutrons.
In the center of an atom, there is a dense, micro-sized, and positively charged nucleus.
All the mass of an atom resides in the nucleus around which small and negatively charged particles revolve in orbitals called electrons.
However, this model suggests that when electrons were bombarded on gold metal foil, most of them went straight and only a few changed their path after colliding with the positively charged nucleus.
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You push on a couch with a force of 200
N. The couch and floor have a coefficient
of static friction of 0.6, and there is a
normal force of 700 N. What is the
maximum static friction between the
couch and floor?
Answer: 420 N
Explanation:
coefficient of static friction * normal force=maximum static friction force
0.6 * 700N=maximum static friction force
6/10 * 700N=
700*6/10=
4200/10=420 N
based on the knowledge you gained from the video and the data that you’ve seen, what do you think is creating the data that kepler gathered? explain your answer
https://youtu.be/gypAjPp6eps
The telescope created the data gathered by Kepler and his team.
What is a star?
A star is a large luminous astronomical body which produces light and heat energy as well as radiation.
There are billions of stars in the universe organized into galaxies.
The Sun is the star of our solar system.
The Kepler project produced a wide range of data products and documentation to assist the community in using data from the mission to help study both exoplanets and other astrophysical areas.
In the video, a mysterious star was observed which is 50 percent bigger and 1,000 degrees hotter than the Sun.
By mean of telescopes, it was observed that the dimming seen in the diet was dues to dust particles.
These data produced ranges from engineering data on the detectors to lists of planet candidates and includes many of the intermediate data products in the data processing path.
The Kepler first mission came to an end after four years when two of the four reaction wheels, used to point the spacecraft malfunctioned.
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A plane travels 2.5km at an angle of 35 degrees to the ground and then changes direction and travels 5.2km at an angle of 22 degrees to the ground. What is the magnitude and direction of the plane's total displacement?
The magnitude and direction of the plane's total displacement will be 7.66 km, 26.20° to the ground.
What is displacement?It should be noted that displacement is a vector quantity which explains the change in the distance to the overall change in position of the object.
The sine and cosine function can be used to solve for the resultant x and y components.
Resultant x = 2.5 cos 35 + 5.2 cos 22
= 6.87 km
Resultant y = 2.5 sin 35 + 5.2 sin 22
= 3.38 km
The resultant displacement is calculated using hypotenuse equation:
displacement = ✓(6.87² + 3.38²)
displacement = 7.66 km
The resultant angle will be:
θ = tan^-1 (3.38 / 6.87)
θ = 26.20°
Therefore the magnitude and direction will be 7.66 km, 26.20° to the ground.
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if the outside air temperature increases during a flight at constant power and at a constant indicated altitude, the true airspeed will
If the outside air temperature increases during a flight at constant power and at a constant indicated altitude, the true airspeed will Increase and true altitude will increase.
What is Altitude?This refers to the vertical elevation of a body and is the measurement of the height above the sea or ground level. An airplane's altitude is directly proportional to the airspeed as long as the power is constant.
This means that increase in airspeed will lead to an increase in altitude and vie versa. This is the reason why as it runs fast, it can be observed that it begins to elevate.
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the density of liquid mercury is 13.5 g/cm3. what mass (in kg) of mercury is required to fill a 2.00 l container?
27.00 kg of liquid mercury is needed to fill a 2.0 L container.
The required mass of mercury in kg to fill a 2.0 L container can be determined through proper conversion of units.
Conversion of cm3 to L:
1 cm3 = 1 mL and 1000 mL = 1L
1000 cm3 = 1 L
Conversion of g to kg:
1000 g = 1 kg
Determine the product of density and volume of the container to solve for the required mass of mercury.
(13.5 g/cm3) x ( 1000 cm3/1 L) x (2.0 L) = 27,000 g
27,000 g * (1 kg/1000 g) = 27 kg of mercury
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The average bond dissociation energy of a carbon-carbon bond is 410 kj/mol. What wavelength in nanometers of ultraviolet radiation has an energy of 410 kj/mol?.
The wavelength of nanometers of ultraviolet radiation has an energy of 410 kj/mol is 292 nm.
The energy content of ultraviolet light with a wavelength of 300 nm is approximately 95.3 kcal, Einstein, which is sufficient to spontaneously break carbon-carbon bonds. Wavelength can be calculated using the formula Wavelength Wave Speed, Frequency. Wavelength is usually expressed in meters. The symbol for wavelength is the Greek lambda.
As every engineer knows, calculating energy is easy. The unit of electrical energy is the kilowatt hour kWh. It is determined by multiplying the amount of electricity consumed kilowatts, kW by the number of hours the electricity was consumed. Multiply this by the cost per kWh to get the total energy cost. For methane, you can calculate the energy required to split 1 mole of methane gas into gaseous carbon and hydrogen atoms.
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3. How does the shape of a sail affect the distance a boat will travel?
Independent Variable:
Dependent Variable:
Answer:
IV: Sail shape
DV: Travel distance
Explanation:
The independent variable is the variable we are changing to see its effects. If we are seeing how the shape of a sail affects travelling distance, the independent variable will be the shape of the sail. This could be achieved by using different dimensions or different geometric shapes.
The dependent variable is the one we are measuring in response to the independent variable. In this case it will be the distance that the boat travels. This could be measured using a ruler or distance meter.
Hope this helped!
An x-ray photon is scattered by an originally stationary electron. Relative to the frequency of the incident photon, is the frequency of the scattered photon (a) lower. (b) higher.(c) unchanged?
The frequency of the scattered photon will be lower which is option (a).
A quantum is the smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation. The energy of radiation absorbed or emitted is directly proportional to the frequency of the radiation.According to the quantum concept of radiation, radiation consists of packets of energy called photons. The photon energy is given by
[tex]E=hv=\frac{hc}{\lambda}[/tex] ....(1)
where 'h' is the Planck's constant
[tex]v=\frac{c}{\lambda}[/tex] ...(2)
where 'v' is the radiation frequency
As x-ray photon is scattered by an electron , there will be loss in the energy of scattered photon.
From equation (1) energy and wavelength have inverse relation which means that due to loss in the energy of scattered photon there will be an increase in the wavelength of scattered photon.
From equation (2) frequency and wavelength have inverse relation due to which increment in the wavelength of scattered photon will lower the frequency of the scattered photon.
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Consider a sign suspended on a boom that is supported by a cable, as shown. What is the proper equation to use for finding the net force in the y direction?
Fnety = (FT)(sin 32°) + Fg
Fnety = (FT)(sin 32°) – Fg
Fnety = (FT)(cos 32°) + Fg
Fnety = (FT)(cos 32°) – Fg
The proper equation to use for finding the net force in the y direction is B. Fnety = (FT)(sin 32°) – Fg
What is net force?The total force acting on an object is its net force. The net force can be determined using Newton's second law, which states that F = ma, where: F is the net force. The object's mass is given by m. Acceleration is a.
The total of all forces acting on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. The net force is a word used in a system where there is a substantial number of forces.
In this case, the proper equation to use for finding the net force in the y direction is B. Fnety = (FT)(sin 32°) – Fg.
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Answer:
B. Fnety = (FT)(sin 32°) – Fg
Explanation:
just did it!
What is simple slope/ what is the simple slope equation?
The slope of a line is also referred to as the gradient and it is the number which describes both the direction and the steepness of the line.
What is Slope equation?This type of formula is used to calculate how steep a line is and is usually denoted as m. The formula can be seen below:
m = y2-y1 / x2-x1
Slope can be defined as the ratio of the vertical change between two points to the horizontal change between two points and measures the steepness of a line.
The chosen answers provided are therefore the most appropriate in this context.
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A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm . The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony?
The physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.
How fast was the physicist traveling, according to his own testimony?Using the formula for doppler shift for light,
λ' = λ√[(1 + v/c)/(1 - v/c)] where
λ = wavelength of source, λ' = wavelength of observer, v = speed of source and c = speed of lightGiven that the driver is moving away from the stop light, we take the driver as the source. Since, the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm. we have
λ' = wavelength of source = 650 nm, λ' = wavelength of observer = 520 nmSo, substituting the values of the variables into the equation, we have
λ' = λ√[(1 + v/c)/(1 - v/c)]
520 nm = 650 nm√[(1 + v/c)/(1 - v/c)]
520/650 = √[(1 + v/c)/(1 - v/c)]
0.8 = √[(1 + v/c)/(1 - v/c)]
Squaring both sides, we have
0.8² = (1 + v/c)/(1 - v/c)
0.64 = (1 + v/c)/(1 - v/c)
0.64(1 - v/c) = (1 + v/c)
0.64 - 0.64v/c = 1 + v/c
0.64 - 1 = v/c + 0.64v/c
-0.36 = 1.64v/c
-0.2195 = v/c
v = -0.22c
v = -0.22 × 3 × 10⁸ m/s
v = -0.66 × 10⁸ m/s
v = -6.6 × 10⁷ m/s
So, the physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.
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at what temperature both celsius and fahrenheit scale show the same reading? show by calculation.
Answer:
The two scales have different zero points and the Celsius degree is bigger than the Fahrenheit. However, there is one point on the Fahrenheit and Celsius scales where the temperatures in degrees are equal. This is -40 °C and -40 °F.
Explanation:
Review. (a) Show that a magnetic dipole in a uniform magnetic field, displaced from its equilibrium orientation and released, can oscillate as a torsional pendulum (Section 15.5) in simple harmonic motion.
The answer is τ is proportional to θ
What is SHM?A motion in which the restoring force is directly proportional to the body's displacement from its mean position is known as a simple harmonic motion, or SHM. This restoring force always moves in the direction of the mean position. The French mathematician Joseph Fourier made the discovery that any regularly recurring motion or wave, regardless of how complex its shape, may be thought of as the sum of a collection of straightforward harmonic motions or waves in 1822.
Consider a magnetic dipole that has been liberated from its equilibrium orientation in a homogeneous magnetic field. Let the angle between the magnetic moment and the magnetic field be θ. The torque on the dipole due
to the external field is, τ=μXB
and magnitude of, τ=μB sinθ
if the angle is small, then, τ=μBθ
or, τproportionalθ
which is the equation for a restoring torque, so the dipole tends to turn the dipole toward its equilibrium
orientation if displaced from its original position. So a magnetic dipole in a uniform magnetic field can oscillate as
a torsional pendulum in SHM if displaced from its equilibrium position.
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GP A series RLC circuit contains the following components: R=150Ω, L=0.250H, C=2.00µF, and a source with Δ Vmax=210V operating at 50.0Hz. Our goal is to find the phase angle, the power factor, and the power input for this circuit. (a) Find the inductive reactance in the circuit.