The thicker the glass, the slower the ramp speed. The temperature must increase or decrease slowly enough that the surface of the glass is not so.
Temperature is a bodily quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
And it's by far one of the freshest locations in the world partly because its excessively steep valley partitions trap hot air within the valley floor instead of freeing it. because the sun reheats air hundreds, dying Valley's temperature will increase.
It's miles usually held that the maximum temperature at which humans can continue to exist is 108.14 degrees Fahrenheit or forty-two.3diploma Celsius. A better temperature may denature proteins and purpose irreparable harm to the mind. actually put, the human body can become a scrambled egg.
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Suppose you were far from a planet that had a very strong gravitational field and you were watching a clock on the surface of the planet. During the time in which your own clock ticks out a time of 1 hour, how much time does the clock on the planet tick out?
Less than 1 hour (but more than zero)
The answer is: Less than 1 hour (but more than zero)
What is gravitational field?
In physics, a gravitational field is a model used to describe the effect of a massive object extending into the space around it and creating a force on another massive object. Gravitational fields are therefore used to describe gravitational phenomena and are measured in Newtons per kilogram (N/kg). It is therefore measured in square meters per second (m/s2).
In the original concept, gravity was the force between point masses. Borrowing from Isaac Newton, Pierre-Simon Laplace attempted to model gravity as a kind of radiation field or fluid. Since the 19th century, explanations of gravity have usually been taught in terms of field models rather than point attraction
In the field model, instead of two particles attracting each other, the particles distort space-time with their mass. This distortion is perceived and measured as a 'force' that moves in a certain way depending on the curvature of spacetime. And either gravity doesn't exist or gravity is an imaginary force.
Therefore, The answer is: Less than 1 hour (but more than zero)
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A wiring device (switch or receptacle) is mounted on one yoke (strap). The number of conductors to be deducted from the maximum permitted conductor fill for the box as indicated in 314.16(B) is: _________two conductors
For a wiring device installed on a single yoke (strap), two conductors must be subtracted from the maximum permissible conductor fill.Section 314.16(B) of the National Electrical Code outlines this requirement (NEC).
A regionally adopted standard for the secure installation of electrical wiring and equipment in the United States is the National Electrical Code (NEC), often known as NFPA 70.
The National Fire Protection Organisation (NFPA), a private trade association, publishes the National Fire Code series, which includes this document.
The National Electrical Code (NEC), published by the National Fire Protection Association (NFPA®), provides guidance on how electrical equipment and systems should be installed and used in buildings and other structures in order to assist safeguard people and property from potential risks.
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describe the sizes of stars along the main sequence. what are stars like near the top of the main sequence, the middle, and the bottom
The sizes of stars Super Giant Stars, Giant Stars ,Main Sequence White Dwarf Stars .Based on their temperature, the stars are categorized, with O being the hottest and M being the coldest. O-B-A-F-G-K-M
What are stars known as?Any big, large celestial mass that is personality and produces light from its own internal renewable resources is referred to be a star. Only a very small portion of the hundreds of milliards of trillions of in the observable cosmos are visible.
Why is a star created?When light element atoms are compressed put under a lot compression allowing their nuclei to fuse, a star is created. All stars are still the consequence of an equilibrium of forces gravity pulls interstellar gas's atoms together until fusion reactions start.
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The average kinetic energy of gas molecules is ________ proportional to the absolute temperature.
The average Kinetic energy of the molecules of a gas is directly proportional to the absolute temperature.
How is K.E proportional to absolute temperature?We know that Kinetic energy is given by the equation ,
[tex]K = \frac{1}{2} mv^{2}[/tex]
where ,
K = kinetic energy
m = mass
v = velocity
Since the square of a particle's velocity is precisely proportional to the kinetic energy of a gas, kinetic energy likewise rises when temperature rises.As a result, the relationship between a gas's kinetic energy and absolute temperature is linear.The kinetic energy of the gas molecules increases as the temperature rises, increasing their rate of motion.The speed of the gas molecules' motion, or their kinetic energy, falls as the temperature drops.A gas's average molecular kinetic energy is inversely related to its absolute temperature.What is absolute temperature?The Kelvin scale, where 0 represents absolute zero, is used to measure absolute temperature. The temperature at which matter's particles move the least and cannot cool down is known as the zero point (minimum energy). A thermodynamic temperature reading does not include a degree symbol because it is "absolute" in nature.
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a beam of monochromatic light with a wavelength of 580 nm in air travels into water. what is the wavelength of the light in water? give your answer in nanometers
The wavelength of the light which travels from air to water is 436.09 nm
The wavelength of the light in air = 580 nm
The light travels from air to water is
μ = 4/3
The formula to find the wavelength of the light in the air can be found using the formula
ν = c/μ
It can be rewritten as
λₙ = λ₀ / μ
where λₙ is the wavelength of light in water
λ₀ is the wavelength of light in water
μ is the relative refractive index
Let us substitute the known values in the above equation, we get
λₙ = 580 x 10⁻⁹ / 1.333
= 436. 09 nm
Therefore, the wavelength of light in water is 436.09 nm
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The student decides to build a model transformer.
The transformer is a step-up transformer which doubles the input voltage.
Describe how they could build this step-up transformer in a science laboratory.
Answer:
hhh
Explanation:
how, if at all, does the ground state energy change if these electrons are subject to a uniform magnetic eld of strength b?
The ground state energy does not change when the electrons are subject to a uniform magnetic field of strength b. This is because the ground state energy is determined only by the number of electrons and the Coulomb repulsion between them, which is not affected by the magnetic field.
What is magnetic field?
The magnetic influence on moving electric charges, pulsed electrical, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is moving through a magnetic field. The magnetic field of a permanent magnet pulls on ferromagnetic substances like iron and attracts as well as repels other magnets. Paramagnetism, diamagnetism, as well as antiferromagnetism are three additional magnetic effects that a nonuniform magnetic field can have on "nonmagnetic" materials, though these forces are typically so minute that they can only be discovered by laboratory equipment. Electric currents, such as those found in electromagnets, as well as electric fields that change in time produce magnetic fields that surround magnetised materials.
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a car is traveling at 104 km/h when the driver sees an accident 80 m ahead and slams on the brakes. what minimum constant deceleration is required to stop the car in time to avoid a pileup? (round your answer to two decimal places.)
Answer:
below
Explanation:
104 km/hr = 104 000 / 3600 = 28.889 m/s
average velocity = 28.9 / 2 = 14.44 m/s
80 m / 14.4 m/s = 5.538 seconds to stop
vf = 0 = vo + at
= 28.9 + a (5.538) shows a = - 5.22 m/s^2
two particles of mass m and 3m are moving with the same speed v in a vacuum at right angles with the particle of mass m moving in the x-direction and the particle of mass 3m moving in the negative y-direction. a
If the two particles are moving at the same speed in a vacuum, then their kinetic energy will be the same. The kinetic energy of a particle is given by the equation:
KE = (1/2)mv^2
Where KE is the kinetic energy of the particle, m is its mass, and v is its speed.
In this case, the kinetic energy of the particle with mass m will be:
KE = (1/2)m*v^2
And the kinetic energy of the particle with mass 3m will be:
KE = (1/2)3mv^2 = (3/2)mv^2
Since the particles have the same kinetic energy, we can set the two equations equal to each other and solve for v:
(1/2)mv^2 = (3/2)mv^2
(1/2)*v^2 = (3/2)*v^2
1/2 = 3/2
This equation does not have a valid solution, which means that the two particles cannot be moving at the same speed in a vacuum if one has a mass of m and the other has a mass of 3m.
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A carbon atom usually has 6 protons and 6 neutrons. Carbon-14 is a type of carbon with atoms that contain 6 protons and 8 neutrons. Carbon-14 can be used to find the age of certain fossils. Carbon-14 is an example of a(n).
Carbon-14 is an example of an Isotopes.
Isotopes can be defined as variants of chemical elements that have the same number of protons and electrons but different numbers of neutrons.
In other words, isotopes are variants of elements that differ in the number of nucleons (the total number of protons and neutrons) due to the difference in the total number of neutrons in their respective nuclei.A carbon atom usually has 6 protons and 6 neutrons.
Also, Carbon-14 contains an atomic nucleus of 8 neutrons along with 6 protons.
Both the carbon atoms have the same number of protons, but different number of neutrons, hence they can be termed as the isotopes.
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in the past, asteroids striking the earth have produced disastrous results. if we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. intense surface heating from the laser could cause surface material to be ejected into space at high speed.
By focusing a laser on the surface of a asteroid, the intense surface heating from the laser could cause surface material to be ejected into space at high speed due to change in the momentum
Since the surface material is ejected into space at high speed, it has significant momentum. And since the asteroid and all of its component are considered as an isolated system, the total momentum is conserved according to law of conservation of momentum.
So, as the surface material is ejected with momentum, this causes a change in the momentum of the asteroid in the opposite direction. This change reduces the speed of the asteroid gradually decreasing its momentum, or it gives the asteroid a speed in a different direction causing it to be deflected from its path.
The given question is incomplete. The complete question is:
In the past, asteroids striking the earth have produced disastrous results. If we discovered the asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed. How would this deflect the asteroid?
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is only capable of pushing a car with a force of 800 n. how fast must the car be moving at the bottom of the hill so that his 800 n force will be just enough to get it to the top of the hill
It will depend on your frame of reference, assuming no energy is lost in the conversion of energy to motion.
Newton's first law asserts that an object in motion will remain in motion until acted on by a force. The car will remain in motion as long as the forces on it are balanced. However, we currently consider a motion to be moved relative to a frame of reference; depending on your perspective, the car could be traveling forward, backward, or not moving at all.
An external force is described as a change in mechanical energy, which can be either kinetic or potential energy in an item. External agents cause these forces. Friction, normal force, and air resistance are examples of external forces. Because stationery is simply a constant speed of 0. So the pace is constant.
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what range of spring constant values will cause the motion of the system to have damped oscillation?
The range of spring constant values is less than 2√Km that will cause the motion of the system to have damped oscillation is given.
[tex]\beta =\left \{ {{y=2\sqrt{km} } \atop {y > 2\sqrt{km} }} \right.[/tex]
[tex]\beta =\left \{ {{b\leq 2\sqrt{Km}----under-damping }[/tex]
When b≤ 4mk, the damping constant, is low, the system oscillates while the motion's amplitude decays exponentially. Then this system is underdamped.After displacement, a body will oscillate on its own accord at its natural frequency. However, as the oscillation continues to lose amplitude, it eventually comes to an end.Non-conservative forces like friction within the oscillation system are what lead to the decrease in amplitude. The term "dissipative forces" also refers to the non-conservative forces.
The oscillations eventually stop if the friction between the box's surface and the floor is not ignored. The force that dampens the oscillation is referred to as the damping force.
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What is the fastest motion that can be measured in any frame of reference? (1 point).
Speed of light is the fastest motion that can be measured in any frame of reference.
A frame of reference is a reference point combined with a set of directions.A frame of reference is similar to the idea of a reference point. A frame of reference is defined as a reference point combined with a set of directions.Something is in motion if it is changing position. It could be a fast-moving airplane, a leaf swirling in the wind, or water trickling from a hose.For example, when you see a ball roll down a street, you can tell the ball is moving because the frame of reference is the streets, whatever may be on the side of the roads, or the Earth.To know about Frame of reference visit:
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A coil 4.40 cm radius, containing 470 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 2.90×10−5 T/s4 )t4. The coil is connected to a 530-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.
Part A
Find the magnitude of the induced emf in the coil as a function of time.
E= 1.09×10−2 V +( 1.06×10−4 V/s3 )t3
E= 3.43×10−2 V +( 8.29×10−5 V/s3 )t3
E= 3.43×10−2 V +( 3.32×10−4 V/s3 )t3
E= 1.09×10−2 V +( 3.32×10−4 V/s3 )t3
SubmitMy AnswersGive Up
Correct
Part B
What is the current in the resistor at time t0 = 4.50 s ?
I =
The current in the resistor at time 4.50 s is 1.2179 X 10⁻⁴ A and the magnitude of induced EMF in the coil is (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³.
Number of turns of coil = N = 470
Radius of the coil = R = 4.40 cm = 0.044 m
Magnetic field varying according to time = B = ( 1.20×10⁻² T/s )t +(2.90×10⁻⁵ T/s⁴ )t⁴
Resistance of the resistor = 530 Ω
Part A :
The flux over the coil is = φ =
= φ = nBA
= φ = 470 X B X (π X 0.044)
= φ = 2.85 (( 1.20 × 10⁻² T/s )t +(2.90×10⁻⁵ T/s⁴ )t⁴)
The magnitude of EMF is = E =
= E = dφ / dt
= E = 2.85 (1.20 × 10⁻² + 11.60 × 10⁻⁵ t³)
= E = (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³
Part B:
The current in the coil = I =
= I = E / R
= I = (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³ / 530
= I = 1.2179 X 10⁻⁴ A
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A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450m above the ground.
a) Find position function s(t) of the stone above the ground level at time t. Assume g=9.8 m/s2.
b) How long does it take the stone to reach the ground?
c) What is the impact velocity of the stone when it hits the ground? d) If the stone is thrown downward with a speed of 5m/s. How long does it take to reach the g
Since the acceleration of gravity can be considered a constant for this situation the below formulas can be derived:
The acceleration due to gravity value of 9.8 m/[tex]s^2[/tex] means that the velocity of a body falling freely changes by 9.8 m/s every second.
(a) acceleration = g = constant = -9.81 m/[tex]s^2[/tex] dv/dt
(b) velocity =[tex]V_0[/tex] -gt = ds/dt
(c) Position s=[tex]s_0[/tex]+[tex]V_0[/tex]t -1/2g[tex]t^2[/tex]
a) Therefore in this problem [tex]s_0[/tex]= 450 m and [tex]V_0[/tex] = 0, s(t) = 450 -1/2g[tex]t^2[/tex]
b) The time to reach the ground is found by solving the position equation for s=0 yielding 9.58 sec
c) The impact velocity is found by solving 2) for t= 9.58 sec yielding -94 m/s ( neg means down).
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Sam, whose mass is 75 kg, straps on his skis and starts down a 50-m-high, 20 ^\circ frictionless slope. A strong headwind exerts a horizontal force of 200 N on him as he skies.
a)Find Sam's speed at the bottom using work and energy.
b)Find Sam's speed at the bottom using Newton's laws.
At the base of the incline, Sam is moving at a speed of 15.73 m/s. who weighs 75 kg puts on his skis and begins to descend a 50 m-high, 20 frictionless slope.
Sam's bottom-of-the-screen speed is determined using the Work-Energy Theorem as follows: An object moves parallel to the plane on a slope with no friction. Both the normal force and the gravitational perpendicular component cancel each other out because they are acting in the same speed. Therefore, an object on a frictionless slope is solely accelerated by the gravitational parallel component. On a surface on an inclined plane with no friction, any item accelerates.
delta W is equal to the delta kinetic energy for frictionless slope
(36750 - 27472) = 1/2*75*(v2 -0).
9278=37.5(v^2)
v^2 = 9278/37.5(v2)
v^2 = 247.4v = 15.73 m/s
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Light is refracted through a diamond. If the angle of incidence is 30°, and the angle of refraction is 12°, what is the index of refraction?.
The index of refraction is 2.45
This can be found by Snell's law. This law is defined as
“The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given color and for the given pair of media”. It is also known as Snell–Descartes law and the law of refraction.
The data given in the question is as follows;
Θi = 30°
Θr = 12°
μ = ?
The formula which is used here will be;
μ = [tex]\frac{sin i}{sin r}[/tex]
By putting values in the formula we will get the answer as follows
μ = [tex]\frac{sin 30}{sin 12}[/tex]
μ = [tex]\frac{0.5}{0.2079}[/tex]
μ = 2.45
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in an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. which pebble is traveling faster when it reaches the ground? responses
They hit at the same time.
Correct answer is C.
What happens to velocity when a ball is thrown horizontally?
Gravity produces a downward vertical acceleration with a magnitude of 9.8 m/s/s, but a projectile's horizontal velocity is constant (a value that never changes). The vertical velocity of a projectile varies by 9.8 m/s per second and is independent of its horizontal motion.
When a ball is thrown horizontally and another is dropped which will be faster?
Since both balls experienced the same acceleration, their time to reach the ground should have been the same. same vertical speed, thus. It goes without saying that a ball thrown horizontally will move quicker.
What is Acceleration?
Acceleration is the term used to describe how quickly a velocity varies over time.
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I understand that the question you are looking for
In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. which pebble is traveling faster when it reaches the ground?
A) The thrown pebble hits first.
B) The dropped pebble hits first.
C) They hit at the same time.
D) We cannot tell without knowing which pebble is heavier.
A force of 5. 0 n moves a 6. 0 kg object along a rough floor at a constant speed of 2. 5 m/s. (a) how much work is done in 25 s? (b) what power is being used? (c) what force of friction is acting on the object?.
Total work done by 5N force is 312.5 J and power used is 12J/s
Speed of object = 2.5 m/s
Time the object moves = 25 s
Since no acceleration is given,
Distance = Speed * Time
Distance = 2.5 * 2.5
Distance = 6.25
i.e. Distance travelled by the block is 62.5m.
F= Force on object = 5N
Work done = Force * Displacement
W = F * S
W = 5 * 62.5
W = 312.5 J
Total work done by 5N force is 312.5 J.
We know that: Power = Work/time
i.e. Power = 312.5/25 = 12 J/s
So power being used is 12 J/s
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some of the light also reflects off the surface of the water. if the incident light is initially unpolarized, the reflected light will be
Whereas if incident light is originally updates, the diffraction pattern will be slightly horizontally polarized, according to the stated assertion.
What exactly are incident and reflected light?The light that strikes the object as incident light from the source but also reflects off it is alluded to as refract. It makes no difference what the flashlight is or what you are photographing. When light strikes anything, it will always be transformed and reflected.
How does incident light behave?A portion of the light is dispersed when incident light hits a sample. Rayleigh scattering is the process wherein most of the dispersed light shares the same frequency as the incoming light. A portion of the light is dispersed around a different wavelength; this is called Raman scattering.
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(a) if you move the particle of charge q from point a to point d, is the change in the electric potential energy of the three-particle system positive, negative, or zero?
Answer: The change in the electric potential energy of the three-particle system positive, negative, or zero is negatively charged particle
Reason:
The change in the electric potential energy of the three-particle system, when moved from A to D, is zero. The work done by the net electric force on the particle when moved from A to D is negative.
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The electrochemical gradient that determines how a charged ion will move through a permeable membrane depends upon the electrical forces acting on that ion the difference in concentration of that ion on either side of the membrane the ratio between the charge on the ion and its atomic mass athe combined effects of electrical forces and concentration differences across the membrane Allof the choices for this question are correct
The combined effects of electrical forces and concentration differences across the membrane.
Since there are less positive ions within the cell due to the ion gradient, the interior is negative in comparison to the exterior forces. The ensuing membrane potential favors positively charged ions entering the cell and negatively charged ions exiting the cell. A combination of a concentration gradient and an electrical field gradient, the electrochemical gradient controls the direction in which ions will flow through an open ion channel. These two gradients may be taken into account individually. Energy can be released when the ions return down their electrochemical gradients, which primary active transport creates. The energy stored in these gradients is used in secondary active transport to move other materials against their own gradients.
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suppose you are on a ship in the north pacific ocean. you notice that the wind is blowing out of the west toward the east. if you look over the edge of the ship, to which direction would the net ekman transport be directed?
To south direction would the net ekman transport be directed when the wind is blowing out of the west toward the east.
When the wind is coming from the north, upwelling happens along the western coasts of the Northern Hemisphere because the net transport of near-surface water is away from the shore. Along the eastern shores of the Northern Hemisphere, winds from the south cause upwelling. Ekman transport occurs when wind-induced friction forces on ocean surface waters have an impact. The top 10-100 meters of the water column are pulled along by the friction force that the wind creates as it blows on the ocean's surface.
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what would happen to your percent recovery of a solid on filter paper if you do not take account for the mass of the filter paper?
The percent recovery will be larger than expected.
How does a gravity filter work?The process of utilizing gravity to force liquid through a filter to remove contaminants from solutions is known as gravity filtration. Gravity and vacuum/suction filtration are the two basic types employed in laboratories. Gravity filtration is frequently employed in chemical laboratories to remove residual reactants, unacceptable side products, drying agents, and precipitates from precipitation operations. Vacuum filtration is most frequently utilized for this purpose, while it can also be used to filter out powerful compounds.Transport and attachment are two processes in the removal of suspended materials. When particles pass through the filter paper and migrate to a different location, this mode happens.It is simple to remove precipitation or solid contaminants from an organic liquid using gravity filtering.To learn more about filter, refer to
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light that is incident upon the eye is refracted several times before it reaches the retina. as light passes through the eye, at which boundary does the majority of the overall refraction occur?
Eye refraction is the dimension of the specified energy for a person’s eyeglasses or touch lenses. This is calculated through a refraction test (additionally called a vision test).
Where and how refraction occurs maximum?
Most of the refraction takes place on the outer floor of cornea whilst mild enters the attention. Refraction is described as bending of mild from its authentic direction whilst mild travels from one medium to some other. Refraction additionally relies upon at the refractive index of the medium. More the distinction in refractive index of mediums, extra might be the refraction. So while mild enters the attention maximum distinction in refractive index is gift among the air and outer floor of cornea. Here most refraction takes place. Whereas the internal components of the attention, the distinction of refractive index isn't always plenty in comparison to that of air.
Around 80% of general refraction takes place on the cornea and ultimate 20% takes place inner the attention. Since it's far a herbal phenomena, refraction of mild can not be stopped. The eye is likewise full of aqueous humor which additionally performs a essential position for refraction. There is any other component in the attention which plays refraction is the lens. The lens converges mild rays to retina to shape an image. The quantity of refraction right here continues to be much less than on the cornea.
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A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength. Which of the following statements about these particles are accurate? (There may be more than one correct choice.)A) Both particles have the same speed.B) The electron has more momentum than the proton.C) The electron has more kinetic energy than the proton.D) Both particles have the same kinetic energy.E) Both particles have the same momentum.
A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength and both particles have the same momentum and the electron has more kinetic energy than the proton.
The electron is a subatomic particle with a bad standard electric charge. Electrons belong to the primary technology of the lepton particle's own family and are typically thought to be fundamental particles because they have no recognized additives or substructure.
For most realistic purposes, an electron is a structureless particle with an intrinsic angular momentum or spin. simply two numbers — the electron's mass and its electric price — gasoline the equations that describe its behavior. From this 'sensible electron' version, physicists constructed present-day microelectronics.
By using the best values for the wavelength and the scattering by a matter of tough X-rays and ?-rays, the radius of the electron is anticipated as approximately 2 × 10-10 cm.
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If you were to travel at a speed close to the speed of light, you could notice that your own.
As per the special theory of relativity, if the body moves with the speed of light, then the mass of the body increases, and the time decreases.
What happens if you travel close to the speed of light ?First off, reaching the speed of light causes your mass to expand infinity-times, which causes you to slow down. The more mass you have, the faster you move, according to relativity. Driving down a freeway on Earth functions the same way.
We wouldn't even be able to recognise our surroundings at close to light speed. Similarly, the Doppler effect would make things so bright that we couldn't tell what they were at all.
A thing would have infinite mass if it ever managed to travel faster than light. The energy needed to move the object would then have to be infinite as well, which is impossible.
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Determine which the following are defined Whenever they occur denctes multivariable function and denotes vector field both of which are twice continuously differentiable on common domain_ (Select all that apply.) V . (F . Vf) V. (V x Vf) V x (V . F) V x (V x f) V x (V x F) V . (V x F)
Yes, all of these are defined whenever they occur, and they denote multivariable functions and vector fields that are twice continuously differentiable on a common domain.
What is multivariable function?
The extension with one calculus to calculus with functions of multiple variables, or the differentiation as well as integration of functions involving different variables as opposed to just one, is known as multivariable function(also recognised as multivariate calculus). Calculus with multiple variables can be seen as an introduction to more complex calculus. Check out calculus on Euclidean space for advanced calculus. The term "vector calculus" refers to the special particular instance of calculus throughout three dimensional space.
For example, V . (F . Vf) denotes a multivariable function and vector field that is twice continuously differentiable. This expression can be interpreted as the dot product of the vector V and the product of the function F and the vector field Vf.
Similarly, V x (V x f) denotes a multivariable function and vector field that is twice continuously differentiable. This expression can be interpreted as the cross product of the vector V and the cross product of the vector V and the function f.
Likewise, V x (V x F) and V . (V x F) denote multivariable functions and vector fields that are twice continuously differentiable. These expressions can be interpreted as the cross product of the vector V and the cross product of the vector V and the function F, and the dot product of the vector V and the cross product of the vector V and the function F, respectively.
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What is the energy, in J, of light that must be absorbed by a hydrogen atom to transition an electron from n = 3 to n = 6? Submit an answer to three signficant figures.
It takes [tex]1.815 * 10^{-19}[/tex] Joules of energy for a hydrogen atom to transition an electron from n=3 to n=6.
Energy absorbed by photon (eV)
[tex]E = 13.6 Z^{2} ( \frac{1}{n_{1} ^{2} } -\frac{1}{n_{2} ^{2} } )[/tex]
where Z is the atomic number
[tex]n_{1}[/tex] lower energy state
[tex]n_{2}[/tex] higher energy state
[tex]E =13.6* 1^{2} ( \frac{1}{3 ^{2} } -\frac{1}{6 ^{2} } )\\\\E = 13.6 (\frac{1}{9} -\frac{1}{36} )= \frac{13.6 *3}{36}[/tex]
E = 1.133 eV
To convert energy into J from eV
Multiply it by [tex]1.602 * 10^{-19}[/tex]
E = [tex]1.133 *1.602 * 10^{-19}[/tex]
E = [tex]1.815 * 10^{-19}[/tex] J
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