The energy of the scattered photon is approximately 2.712 x 10^6 eV.
The energy of a photon is related to its wavelength by the equation:
E = hc/λ
where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.
The Compton scattering formula can be used to determine the change in wavelength of a photon after it scatters off an electron:
Δλ = (h/mec) * (1 - cos(θ))
where Δλ is the change in wavelength, me is the mass of the electron, θ is the scattering angle, and c is the speed of light.
We can first use the given wavelength of the incident photon to calculate its energy:
E = hc/λ = (6.626 x 10^-34 J s) * (2.998 x 10^8 m/s) / (0.00229 x 10^-9 m) = 2.717 x 10^6 eV
Using the Compton scattering formula with θ = 60.0∘ and the electron mass me = 9.109 x 10^-31 kg, we can calculate the change in wavelength:
Δλ = (h/mec) * (1 - cos(θ)) = (6.626 x 10^-34 J s / (9.109 x 10^-31 kg) * (1 - cos(60.0∘)) = 1.15 x 10^-12 m
The final wavelength of the scattered photon is the sum of the incident wavelength and the change in wavelength:
λf = λi + Δλ = 0.00229 x 10^-9 m + 1.15 x 10^-12 m = 0.00229115 nm
Finally, we can use the equation for photon energy to calculate the energy of the scattered photon:
E' = hc/λf = (6.626 x 10^-34 J s) * (2.998 x 10^8 m/s) / (0.00229115 x 10^-9 m) = 2.712 x 10^6 eV
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The energy of the scattered photons is approximately 1.03 keV. This energy is calculated using the Compton scattering formula, taking into account the initial wavelength, scattering angle, Planck's constant, mass of the electron, and the speed of light.
Determine the energy?To calculate the energy of the scattered photons, we can use the Compton scattering formula: Δλ = λ' - λ = (h / mₑc) * (1 - cosθ), where Δλ is the change in wavelength, λ' is the wavelength of the scattered photons, λ is the initial wavelength, h is the Planck's constant, mₑ is the mass of the electron, c is the speed of light, and θ is the scattering angle.
Rearranging the formula, we have Δλ = (h / mₑc) * (1 - cosθ) = h / (mₑc) * (1 - cosθ). Solving for λ', we get λ' = λ + Δλ = λ + h / (mₑc) * (1 - cosθ).
Given λ = 0.00229 nm (or 2.29 x 10⁻¹² m), θ = 60.0°, h = 6.626 x 10⁻³⁴ J·s, mₑ = 9.109 x 10⁻³¹ kg, and c = 2.998 x 10⁸ m/s, we can substitute these values into the equation to find Δλ and then calculate λ'.
Finally, we can use the equation E = hc / λ' to calculate the energy of the scattered photons. Substituting the values of h, c, and λ', we find E ≈ 1.03 keV.
Therefore, the scattered photons possess an energy of around 1.03 kiloelectronvolts (keV).
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Which of the following areas takes visual information from one side of the body and conveys it to the opposite side
The optic chiasm is the point where the optic nerves cross the midline, allowing the opposite side of the brain to process sensory data from one side of the body.
What is the optic chiasm and where is it located?Since the optic nerves cross in the optic chiasm, also known as the optic chiasma, it plays a crucial role in the visual pathway. Within the suprasellar cistern, it is situated 10 mm above the pituitary gland and 10 mm beneath the hypothalamus near the base of the brain.
The optic chiasm's function is to make sure that visual impulses reach both hemispheres of the brain. The thalamus receives and processes the majority of brain impulses, which are then transmitted to various parts of the occipital lobe. Half of each divided optic nerve's fibers travel to the opposing side. Due to the anatomical configuration, injury to the optic nerve system results in particular patterns of vision loss.
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Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds. approximately how far away is vega from the sun?
Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds, approximately Vega will be 25.076 Light year or 7.692 Parsec away from the sun
The parallax angle is the angle between the Earth at one time of year, and the Earth six months later, as measured from a nearby star.
Mathematically it can be understood as that the parallax angle is the angle which is taken from a point at one time on the earth and again after six months later from the same point on the earth. The parallax angle is the semi-angle of inclination between the two lines to sight.
Stellar parallax is the basis for the parsec, which is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond.
Distance (in parsec) = 1 / (parallax angle ( arcsec))
given
parallax angle = 0.13 arcseconds
Distance (in parsec) = 1/ 0.13 = 7.692 Parsec
if 1 Parsec = 3.26 Light year
So, 7.692 Parsec will be equal to = 3.26 * 7.692 = 25.076 Light year
≈ 25.076 Light year
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A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection
The angle of projection is θ = 53°
What is the angle of projection?The angle between the initial velocity of a body from a horizontal plane through which the body is thrown, is known as angle of projection.Motion in A Plane. Show that there are two angles of projection for which horizontal range is the same. Thus horizontal range is the same for angle of projection θ and α = 90°–θ.The maximum height achieved by a projectile ignoring the air resistance is given by HM=U2Sin2 θ 2g.where U is the initial velocity, θ is the angle of projection and g is the acceleration due to gravity.
R = 3H
R = v²sin2θ/g = 2v²sinθcosθ/2 = 3v²sin²θ/2g
tan θ = 4/3
θ = 53°
So, the angle of projection is θ = 53°
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Describe and explain your observations using the law of conservation of charge and the properties of the conductors.
What is Law of conservation of charge?
Law of conservation of charge states that, "the total electric charge in an isolated system is always constant".
It can also be stated as, "Charge can neither be created nor destroyed but can only be converted from one form of energy to another".
What are the properties of conductors?
There is movement of electrons and ions in the conductor. Free charges exist on the surface of the conductor.The charge density of a conductor is zero.All points of a conductor are at the same potential.The electric field of a conductor is zero. This allows the electrons to flow within them.To learn more about Law of conservation of charge: https://brainly.com/question/4158552
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A 100-lb child stands on a scale while riding in an elevator. What does the scale read while the elevator slows to stop at the lowest floor
Answer: A 100-lb child stands on a scale while riding in an elevator. Then, the scale reading approaches to 100lb, while the elevator slows to stop at the lowest floor
Explanation: To find the correct answer, we need to know more about the apparent weight of a body in a lift.
What is the apparent weight of a body in a lift?Consider a body of mass m kept on a weighing machine in a lift.The readings on the machine is the force exerted by the body on the machine(action), which is equal to the force exerted by the machine on the body(reaction).The reaction we get as the weight recorded by the machine, and it is called the apparent weight.How to solve the question?Here we have given with the actual weight of the body as 100lbs.This 100lb child is standing on the scale or the weighing machine, when it is riding .During this condition, the acceleration of the lift is towards downward, and thus, a force of ma .There is also mg downwards and a normal reaction in the upward direction.when we equate both the upward force and downward force, we get,[tex]ma=mg-N\\N=mg-ma[/tex] i.e. during riding the scale reads a weight less than that of actual weight.
When the lift goes slow and stops the lowest floor, then the acceleration will be approaches to zero.Thus, from the above explanation, it is clear that ,when the elevator moves to the lowest floor slowly and stops, then the apparent weight will become the actual weight.
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According to the theory of a symmetry breaking, at the moment of quark confinement, when the universe was 10-6 seconds old, what were the relative numbers of neutrons and antineutrons
At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
What is quark confinement?Note that one quark is never found on its own but if particles are said to be smashed together and quarks are found, they are said to be like ends of rubber bands that expands.
Hence, At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
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The spectral type of this star is listed as K5V. (V means it is a main sequence star.) Based on the table below, how does the surface temperature of this star compare with that of HIP 87937
It turns out that the star in question belongs to the K5V star class. Thus, the surface temperature of this must be between 5200 K and 3700 K. It has a surface temperature of 6200 K to 5200 K and is a G2V class star, commonly known as Bernard's star. In other words, the star in question has a colder surface than HIP 87937. This is further explained below.
What is surface temperature?Generally, The temperature at a surface is referred to as the surface temperature. In particular, it may refer to the surface air temperature, which is the temperature of the air that is relatively close to the earth's surface.
In conclusion, The star in question is of the K5V type. Therefore, the temperature of the surface of this must be somewhere between 5200 and 3700 kelvin. The star with the designation HIP 87937, often known as Bernard's star, is of the G2V type. Stars of this type have a surface temperature that falls anywhere between 6200 and 5200 degrees Celsius. Therefore, it should come as no surprise that the surface temperature of the given star is lower than that of HIP 87937.
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Answer: It is hotter because K is before M
Explanation:
The actual surface temperature of this star is 4600 KK compared to 3100 KK for the M4 star in Parts A and B.
Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1. 00 mol of photons with a wavelength of 370. Nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to? energy mol submit answer try another versiorn 2 item attempts remaining.
The energy of photon in kJ/mol is 329kJ/mol.
Wavelength of radiation is 370nm. The frequency of given wavelength is
ν = c / λ
ν = 3×10^8 / 370×10^-9
ν = 8.11 × 10^14 s^-1
Now the energy of photon is:
E = hν
E = 6.63×10^-34 J.s/photon × 8.11×10^14s^-1
E = 5.41× 10^-19 J/photon
To find in mole
E = 5.41× 10^-19 × 6.022×10^23
E = 3.29 ×10^ 5 J/mol
So, the energy of mole of photon is equal to 329 kJ/mol.
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what is the frequency of a wave that has a wavelength of 0.20m and a speed of 22 m/s?
Answer:
f=110HZ
Explanation:
Calculate the frequency of a wave
Based on equation λ= VT but T= 1/f
=> λ=V/f
=> f= V/λ
by V=22m/s
λ= 0.20m
=> f= 22/0.20= 22/(2×10-¹) = 110Hz
So the frequency of a wave is f=110Hz
Answer:
110
Explanation:
velocity=wavelength×frequency
22=0.20f
divide both sides by 0.20
22/0.20=0.20f/0.20
f=22/0.20
f=110
A stone ‘X’ of mass 2 kg is at the height of 20m in two minutes, calculate the power delivered. [g=10 m/s-2]
400 J power will be delivered by lifting a stone of mass 2 kg at the height of 20m in two minutes.
What is power?The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as an activity in ancient writings. A scalar quantity is a power.
Work completed and time is linked in the power equation. Since forces may move objects and we know that forces perform work, we might anticipate that by understanding the power, we can gain insight into how a body moves through time. This outcome may be especially beneficial.
Given that, a stone ‘X’ of mass 2 kg is lifted to the height of 20m in two minutes, and g=10 m/s-2
Power Delivered = Work done in lifting the stone
Work Done = Potential energy = mgh
Work done = 2 × 10 × 20
Work done = 400 J
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A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
What is convex lens?A convex lens is the name given to any converging lens.
A converging lens or convex lens is a lens that converges rays of light that are traveling parallel to its principal axis.
What is focal length?The focal length, f of a lens is the distance between the center of a lens and its focus.
Object placed between infinity and 2fFor an object that is placed between infinity and double of the distance from focal point, along a line perpendicular to the center of the lens,
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
Thus, for an object placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
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How much longer (percentage) is a one-mile race than a 1500-m race (""the metric mile"")?
Answer:
1 m = 39.37 in = 3.281 ft
1500 m * 3.281 ft / m = 4922 ft
(5280 - 4922) / 4922 = .073 = 7.3 %
(Note - 1600 m often replaces the 1 mi run)
A 7.55 × 1014 hz electromagnetic wave travels in carbon tetrachloride with a speed of 2.05 ×108 m/s. what is the wavelength of the wave in this material?
Answer:
2.72×10^-7
Explanation:
velocity = frequency × wavelength
2.05×10^8=7.55×10^14 wavelength
wavelength = 2.05×10^8/7.55×10^14
wavelength = 2.72×10^-7
Consider vectors u and v, where u = ⟨1, –1⟩ and v = ⟨1, 1⟩. what is the measure of the angle between the vectors?
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
Angle between the vectorsThe angle between the vectors describes the direction of the vector and the value of the angle can be determined from the horizontal and vertical components of the vectors as shown below.
The sum of the horizontal components and vertical components of the vectors is calculated as follows;
Sum of the horizontal component of the vectors, x = 1 + 1 = 2
Sum of the vertical component of the vectors, y = -1 + 1 = 0
The angle between the vectors is calculated as follows;
θ = arc tan (y/x)
θ = arc tan (0/2)
θ = arc tan (0)
θ = 0⁰
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
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Answer: C. 90°
Explanation:
Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses:________
A. increases by a factor of 4.
B. increases by a factor of 2.
C. increases by a factor of 16.
D. decreases by a factor of 4.
E. decreases by a factor of 16.
Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses: C. increases by a factor of 16.
Gravitational force is an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.
Force between two masses = G M1 M1 / [tex]R^{2}[/tex]
since , gravitation force d follows an inverse square law
F is directly proportional to 1/[tex]R^{2}[/tex]
If distance between two masses is decreased by a factor of 4
Let initial distance : R
when distance between two masses is decreased by a factor of 4 = 4R
Force = G M1 M1 / [tex](4R)^{2}[/tex]
Force = G M1 M1 / [tex]16R^{2}[/tex]
16 Force = G M1 M1 / [tex]R^{2}[/tex]
since , there is an inverse relation , so if distance is decreased , gravitation force will increase .
hence, gravitational force will increase by factor of 16
correct option C. increases by a factor of 16.
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A train is traveling at 30.0 m/sm/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 HzHz. The speed of sound in air should be taken as 344 m/sm/s .
frequency fapproach is heard by a passenger = 302.05 Hz
frequency frecede is heard by a passenger = 228.37433 Hz
Given :
speed of train to the ground = 30.0 m/s
frequency emitted by the train whistle = 262 Hz
speed of sound in air = 344 m/s
To Find :
(A) frequency fapproach (B) frequency frecede
Solution :
The frequency of approach is given by
f' = f v + v(relative)
v - v(air)
= 262x 344 + 18
344 - 30
f' = 302.05 Hz
The frequency of approach is 302.05 Hz
The frequency of recede is given by
f' = f v - v(relative)
v + v(air)
= 262 x 344 - 18
344 + 30
The frequency of recede is 228.37433 Hz
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You look at a light source through a polarizer. As you turn the polarizer you see no change in intensity. Is the light emitted by this source polarized
No, the light emitted from the source is not polarized
Bypassing it through a polarizing filter or other polarizing substance, light can be made polarized. After passing through a polarizing filter, the intensity of polarized light I is equal to the original intensity I0 cos2, where I0 is the original intensity and is the angle formed by the polarization's direction and the filter's axis.
Unpolarized light is diminished by a factor of 12 when it travels through a polarizer. Along the polarizer's axis, the transmitted light is polarized. The only parameter that is unaffected by any phenomenon, including reflection, refraction, interference polarization, etc., is frequency. The polarization phenomenon has no effect on light frequency.
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When a person is standing upright, the weight of anything being lifted and carried in the hands is first reflected onto the:
Pelvic girdle
In human anatomy, the pelvis is a complex of bones that connects the trunk and the legs, supports and balances the trunk, and houses and supports the intestines, the urinary bladder, and the internal organ. It is sometimes referred to as the bony pelvis or the pelvic girdle.
One is located on the left side of the body and the other is located on the right. They come together to make the pelvic girdle, a portion of the pelvis. The hip bones are attached to the upper portion of the skeleton at the sacrum.
The pelvic girdle's main function is to support the upper body's weight while seated and transfer that weight to the lower limbs while standing. For the muscles in the trunk and lower limbs, it functions as attachment point.
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1. Determine the energy released per kilogram of fuel used.
Given MeV per reaction, calculate energy in joules per kilogram of reactants.
Consider 1 mole of tritium plus 1 mole of deuterium to be a mole of “reactions” (total molar mass = 5 grams).
2. Determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years.
Energy use per person per year in the United States = 3.5 × 1011 joules.
Base your calculations on a current population of 310,000,000.
1MeV = 1.6 x 10-13 J and 3.5 x 1011 joules of energy is energy in joules per kilogram of reactants.
The amount of fuel needed to meet US expectations for energy consumption over the next ten years.
In the US, each person uses 3.5 x 1011 joules of energy annually. 310,000,000 people make up the present population, thus use 1MeV = 1.6 x 10-13 J in your calculations.
In the US, annual energy consumption per person is equal to 3.5 x 1011Joules (estimated, varies by source, August 2009)
USA population: 310,000,000, roughly.
One mega electron volt, or one million electron volts, is designated as MeV. A particle with one electron charge will gain one MeV of energy when it passes through a potential difference of one million volts in a vacuum.
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A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is:
A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
To find the answer, we need to know about the magnetic field due to a solenoid.
What is the magnetic field due to a solenoid?A solenoid is an insulated wire wound in the form of a helix. Its length is very large compared to its diameter.The magnetic field due to solenoid carrying current [tex]I[/tex] can be written as,[tex]B=[/tex] μ₀n [tex]I[/tex]
[tex]n=\frac{N}{l}[/tex]
We have an expression for magnetic flux as,Φ [tex]= BA[/tex] Where, A is the area.
Substituting above value of magnetic field in the expression of magnetic flux, we get,Ф [tex]= \frac{NIA}{l}[/tex] μ₀
In terms of inductance, we can express the magnetic flux linked with the coil as,Ф [tex]= LI[/tex]
By equating above two equations of magnetic flux, we get the expression for inductance as,μ₀ ( [tex]\frac{N^2A}{l}[/tex] ) [tex]I[/tex] [tex]=LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
Thus, we can conclude that the expression for inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
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The inductance of a solenoid having N number of turns, area A and a length l will be equal to μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
We need to understand the magnetic field created by a solenoid in order to determine the solution.
What does a solenoid's magnetic field look like?An insulated wire twisted into a helix is what makes up a solenoid.Compared to its diameter, its length is significantly larger.It is possible to express the magnetic field caused by a solenoid carrying current as,[tex]B=\frac{NI}{l}[/tex]×μ₀
We can express magnetic flux as follows:[tex]flux=BA[/tex] , A is the area.
In the formula for magnetic flux, we obtain by substituting the above magnetic field value:[tex]flux=\frac{NIA}{l}[/tex] times the μ₀.
The magnetic flux associated with the coil can be expressed in terms of inductance as follows:[tex]flux=IL[/tex]
We obtain the expression for inductance as, by combining the aforementioned two magnetic flux equations.μ₀ ( [tex]\frac{N^2AI}{l}[/tex])= [tex]LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
As a result, we can say that the inductance expression is [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
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A toy car is placed at 0 on a number line. It moves 9 cm to the left, then 4 cm to the right, and then 6 cm to the left. What is the total distance the toy car traveled?
1 cm
5 cm
11 cm
19 cmis the displacement of an object during a specific unit of time.
The total distance the toy car traveled is D. 19cm
Calculations and ParametersThe total distance of the toy car traveled in cm would be calculated
We would add the sum:
D = 9 + 4 + 6 cm
D = 19 cm
Therefore, the total distance the toy car traveled in cm is 19 cm.
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Dalton's law of partial pressures states that for a mixture of gases, the pressure is the of the partial pressures of the individual gases. (assume that the gases do not react with each other.)
True. The partial pressure of gas that is made up of a mixture of gases is the sum of the individual pressure of the gases.
What is Dalton's law of partial pressure?Dalton's law of partial pressure of gases is one of the gas laws that take into consideration the fact that a gas can be made from a mixture of non-reacting gases.
According to him, if a gas is made as such, the pressure of the gas would be the sum of the individual pressure of the component gases. This means that each gas contributes partially to the overall pressure of the gas mixture.
Thus, if gas A is a mixture of gas B and gas C. The pressure, P, of gas A is given as:
P = Pb + Pc where Pb and Pc are the partial pressure of gases B and C respectively.
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Pearl labels a diagram of a charged capacitor as shown. Which change would correct the error in the diagram?
A) changing +2Q to +Q
B) changing +2Q to –2Q
C) reversing the direction of the arrows
D) reversing the labels for Conductors and Insulator
To correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
What is a capacitor?A capacitor is device that is used for storing electric charge. We know that the capacitor is composed of two conductors separated by an insulator.
In order to correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
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Answer:
A
Explanation:
A 67 V power supply is connected to three identical resistors in series. If the current through the resistors is measured at 0.95 A, what is the value of each resistor? Round your answer to 2 decimal places.
The value of each resistor is 23.51 ohms.
Value of each resistor
The value of each resistor is calculated as follows;
R₁ = R₂ = R₃ = R
Total resistance, Rt = 3R
V = IRt
V = I(3R)
R = V/3I
R = (67)/(3 x 0.95)
R = 23.51 ohms
Thus, the value of each resistor is 23.51 ohms.
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The spectral type of this star is B7V. The order of spectral types, from hottest to coolest, is OBAFGKM. How does the surface temperature of this star compare with the other stars we have observed
The hottest celebrity is this one.
The majority of stars fall under a select few spectral categories. The hottest to the coldest stars are listed in the spectral types of the Henry Draper and Bright Star Catalogues (see stellar classification). The letters O, B, A, F, G, K, and M are used to indicate these categories in decreasing order of temperature.
What is Spectral type of star ?Using spectral types, we can categorise stars based on their colour or the spectral lines that are visible in their light. The spectral types are OBAFGKM, with the hottest stars being O and the coldest being M. To humans, cooler stars appear redder and hotter stars appear bluer.
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A 540 gram object is attached to a vertical spring, causing the spring’s length to change from 70 cm to 110 cm.
What is the spring constant k?
Group of answer choices
130 N/m
33 N/m
13 N/m
330 N/m
Answer:
Approximately [tex]13\; {\rm N \cdot m^{-1}}[/tex] (assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].)
Explanation:
Let [tex]F_{\text{s}}[/tex] denote the force that this spring exerts on the object. Let [tex]x[/tex] denote the displacement of this spring from the equilibrium position.
By Hooke's Law, the spring constant [tex]k[/tex] of this spring would ensure that [tex]F_\text{s} = -k\, x[/tex].
Note that the mass of the object attached to this spring is [tex]m = 540\; {\rm g} = 0.540\; {\rm kg}[/tex]. Thus, the weight of this object would be [tex]m\, g = 0.540\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \approx 5.230\; {\rm N}[/tex].
Assuming that this object is not moving, the spring would need to exert an upward force of the same magnitude on the object. Thus, [tex]F_{\text{s}} = 5.230\; {\rm N}[/tex].
The spring in this question was stretched downward from its equilibrium by:
[tex]\begin{aligned} x &= (70\; {\rm cm} - 110\; {\rm cm}) \\ &= (-40)\; {\rm cm} \\ &= (-0.40) \; {\rm m}\end{aligned}[/tex].
(Note that [tex]x[/tex] is negative since this displacement points downwards.)
Rearrange Hooke's Law to find [tex]k[/tex] in terms of [tex]F_{\text{s}}[/tex] and [tex]x[/tex]:
[tex]\begin{aligned} k &= \frac{F_{\text{s}}}{-x} \\ &\approx \frac{5.230\; {\rm N}}{-(-0.40)\; {\rm m}} \\ &\approx 13\; {\rm N \cdot m^{-1}}\end{aligned}[/tex].
A helicopter blade starts to rotate from rest with a constant angular acceleration of 0.82 radians/second2. How many revolutions will the blade make before it is rotating at 500 revolutions per minute (RPM)
Revolutions made by the blade will be 266 rev
Given:
Constant angular acceleration = 0.82 radians/second^2
number of revolution per minute = 500
To Find:
number of revolution
Solution: Angular Acceleration is defined as the time rate of change of angular velocity. It is usually expressed in radians per second per second.
Initial speed of the helicopter blade, w₁ = 0
The final speed of the blade, wf = 500 rpm = 500 x 2π/60 rad/s = 52.35 rad/s
We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is θ
So,
wf^2 - wi^2 = 2αθ
θ = wf^2/2α = 1671 rad
Let there are n number of revolutions made by the blade. So,
n = θ / 2π
n = 1671 / 2 x 3.14 = 266 rev
So, the revolutions made by the blade will be 266 rev
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Three charges, qA is +6.0 μC, qB is –5.0 μC, and qc is +6.0 μC, are located at the corners of a square with each
side length at 5.0 cm as shown in the diagram. Calculate the electric field at point D.
The net electric field at point D is determined as 3.95 x 10⁷ N/C.
Electric field at D due to charge A
E = kq/r²
where;
r is the distance between A and Dq is charge AE(AD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(AD) = 2.16 x 10⁷ i N/C
Electric field at D due to charge B
E = kq/r²
where;
r is the distance between A and Bq is charge Br² = 5² + 5²
r² = 50
r = √50
r = 7.07 cm
E(BD) = (9 x 10⁹ x 5 x 10⁻⁶)/(0.0707²)
E(BD) = 9 x 10⁶ N/C
in x - direction = 9 x 10⁶ N/C x cos(45) = 6.36 x 10⁶ i N/C
in y - direction = 9 x 10⁶ N/C x sin(45) = 6.36 x 10⁶j N/C
Electric field at D due to charge CE = kq/r²
where;
r is the distance between C and Dq is charge CE(CD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(CD) = 2.16 x 10⁷ j N/C
sum of electric field in x directionEi = 2.16 x 10⁷ i N/C + 6.36 x 10⁶ i N/C
Ei = 2.796 x 10⁷ i N/C
sum of electric field in y directionEj = 2.16 x 10⁷ j N/C + 6.36 x 10⁶j N/C
Ej = 2.796 x 10⁷ j N/C
Resultant electric field at DE = √Ei² + Ej²
E = √[(2.796 x 10⁷)² + (2.796 x 10⁷)²]
E = 3.95 x 10⁷ N/C
Thus, the net electric field at point D is determined as 3.95 x 10⁷ N/C.
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In the simulation, select the pressure tab, then select the right-most of the three reservoir configurations (top left). By putting weights into the small column of water and using the pressure gauge to measure the water and air pressure, estimate the cross-sectional area of the left column of water. Which of the following best represents the cross-sectional area
The volume of any rectangular solid, including a cube, is calculated mathematically as V = l × w × h
How to find a cross-sectional area?In a given calculation, if you are given the:
Length WidthHeightTo find this, you would have to use the area of its base which is:
Length * Width * Height.
Furthermore, if the cross-section is parallel, then you would have to solve it thus:
Length * Width which is the area of the section from top to bottom.
Although your question is incomplete, the general idea of how to find the cross-sectional area of the volume of any rectangular solid.
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The acceleration due to gravity is lower on the Moon than on Earth. Which of the following is true about the mass and weight of an astronaut on the Moon's surface compared to Earth
Mass is the same, weight is less
What is the Weight and mass on Moon ?As we know that the mass of the object is the measurement of the quantity of the matter that is present in it
So here we can say that if the mass of the object is m then its total quantity of the matter that is present in it is given as
mass = (density) × (volume)
Now for the weight of the object is defined as the force of gravity due to planet
Fg = mg
so the weight of the object is depending on the acceleration due to gravity of the planet
As we know that the gravity of moon is smaller than the gravity of the earth so here weight on the moon will be smaller than the weight on the Earth
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