Answers
We want to choose the film thickness such that destructive interference occurs between the light reflected from the air-film interface (call it wave 1) and from the film-lens interface (call it wave 2). For destructive interference to occur, the phase difference between the two waves must be an odd multiple of half-wavelengths.
You can think of the phases of the two waves as second hands on a clock; as the light travels, the hands tick-tock around the clock. Consider the clocks on the two waves in question. As both waves travel to the air-film interface, their clocks both tick-tock the same time-no phase difference. When wave 1 is reflected from the air-film boundary, its clock is set forward 30 seconds; i.e., if the hand was pointing toward 12, it's now pointing toward 6. It's set forward because the index of refraction of air is smaller than that of the film.
Now wave 1 pauses while wave two goes into and out of the film. The clock on wave 2 continues to tick as it travels in the film-tick, tock, tick, tock.... Clock 2 is set forward 30 seconds when it hits the film-lens interface because the index of refraction of the film is smaller than that of the lens. Then as it travels back through the film, its clock still continues ticking. When wave 2 gets back to the air-film interface, the two waves continue side by side, both their clocks ticking; there is no change in phase as they continue on their merry way.
So, to recap, since both clocks were shifted forward at the two different interfaces, there was no net phase shift due to reflection. There was also no phase shift as the waves travelled into and out from the air-film interface. The only phase shift occured as clock 2 ticked inside the film.
Call the thickness of the film t. Then the total distance travelled by wave 2 inside the film is 2t, if we assume the light entered pretty much normal to the interface. This total distance should equal to half the wavelength of the light in the film (for the minimum condition; it could also be 3/2, 5/2, etc., but that wouldn't be the minimum thickness) since the hand of the clock makes one revolution for each distance of one wavelength the wave travels (right?).
\begin{displaymath}
2t = \frac{\lambda_{film}}{2}.\end{displaymath}
The wavelength in the film is
\begin{displaymath}
\lambda_{film} = \frac{\lambda_{air}}{n} = \frac{565 nm}{1.38}\end{displaymath}
\begin{displaymath}
\lambda_{film} = 409 nm.\end{displaymath}
Hence, the thickness should be
\begin{displaymath}
t = \frac{\lambda_{film}}{4} = 102 nm .\end{displaymath}
so the answer is I am so confuse
Related Questions
A ball is thrown up into the air. When it gets to the very top,
what kind of energy does it have?
Answers
At the highest attitude, the velocity of the ball is 0 m/s, so the kinetic energy is 0 as well.
Hence the answer is potential energy because it doesn't depend on velocity .
The magnitude of the force can be determined as?
Answers
Answer:
the mass of the object multiplied by the acceleration of the object
Explanation:
N2L states that F = ma (force equals mass times acceleration).
3. When a magnetic sector instrument was operated with an accelerating voltage of 4.50*103 V, a field of 0.251 T was required to focus the CH4 on the detector. a) What range of field strengths would be required to scan the mass range between 12.5 and 2.50*102 , for singly charged ion, if the accelerating voltage is held constant
Answers
Answer:
The answer is "\(4,500 - 225 \ V\)".
Explanation:
Using formula for calculating the Voltage:
\(M_1=12.5\\\\M_2=250\\\\V_1=4,500 \\\\\bold{\text{Formula: }}\\\\\to \bold{\frac{m_1}{m_2}=\frac{V_2}{V_1}}\\\\\to \frac{12.5}{250}=\frac{V_2}{4,500}\\\\\to 0.05=\frac{v_2}{4,500}\\\\\to 0.05\times 4,500= V_2\\\\\to V_2=225\\\\\)
Hence the range of accelerating in voltage is \(4,500 - 225 \ V\)
7. A particle of mass 3 kg is held in equilibrium by two light unextensible strings. One string is horizontal, as shown in Figure 7.30. The tension in the horizontal string is PN and the tension in the other string is N. Find a) the value of 0 b) the value of P.
Answers
The tension in the strings are 31.47 and 19.25 N respectively.
Mass of the block, m = 3 kg
From the figure, consider the vertical components,
T₁ sin45° + T₂ sin30° = mg
(T₁/√2) + (T₂/2) = 3 x 9.8 = 29.4
Also, consider the horizontal components,
T₁ cos45° = T₂ cos30°
T₁/√2 = T₂ x√3/2
T₁ = T₂ x √3/2 x √2
So,
T₁ = 0.612T₂
Applying in the first equation,
(T₁/√2) + (T₂/2) = 29.4
(0.612T₂/1.414) + 0.5T₂ = 29.4
0.434 T₂ + 0.5 T₂ = 29.4
0.934 T₂ = 29.4
Therefore, the tension,
T₂ = 29.4/0.934
T₂ = 31.47 N
So, the tension,
T₁ = 0.612 T₂
T₁ = 0.612 x 31.47
T₁ = 19.25 N
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Conservation of Energy Roller Coaster A roller coaster cart of mass 100kg travels on a track with one loop. Fill in blanks A-H. А. KE=OJ PE=120000J h= А. V= B B KE=___CE PE=60000J h= _D V= E KE=__F PE=40000J h=__G_ V= KE= PE= h=Om v= K D E F G H K
Answers
(a) The height of the roller coaster at 120,000 potential energy is 122.45 m.
(b) The velocity of the roller coaster at 0 J kinetic energy is 0.
(c) The height of the roller coaster at 60,000 potential energy is 61.23 m.
(d) The velocity of the roller coaster at 60,000 J kinetic energy is 34.64 m/s.
(e) The height of the roller coaster at 40,000 potential energy is 40.82 m.
(f) The velocity of the roller coaster at 80,000 J kinetic energy is 40 m/s.
The given parameters:
mass of the roller coaster, m = 100 kgWhen the kinetic energy = 0 and potential energy = 120,000 J
The height of the roller coaster is calculated as follows;
P.E = mgh
\(h = \frac{P.E}{mg}\\\\h = \frac{120,000}{100 \times 9.8} \\\\h = 122.45 \ m\)
Since the kinetic energy = 0, the velocity of the roller coaster = 0
When the potential energy, P.E = 60,000 J, the kinetic energy, K.E is calculated as;
P.E + K.E = M.A
P.E + K.E = 120,000
60,000 + K.E = 120,000
K.E = 120,000 - 60,000
K.E = 60,000 J
The height of the roller coaster at 60,000 potential energy is calculated as follows;
\(h = \frac{P.E}{mg} \\\\h = \frac{60,000}{100 \times 9.8} \\\\h =61.23 \ m\)
The velocity of the roller coaster at 60,000 J kinetic energy is calculated as follows;
\(K.E = \frac{1}{2} mv^2\\\\v^2 = \frac{2K.E}{m} \\\\v = \sqrt{ \frac{2K.E}{m}} \\\\v = \sqrt{ \frac{2\times 60,000}{100}}\\\\v = 34.64 \ m/s\)
When the potential energy, P.E = 40,000 J, the kinetic energy, K.E is calculated as;
P.E + K.E = M.A
40,000 + K.E = 120,000
K.E = 120,000 - 40,000
K.E = 80,000
The height of the roller coaster at 40,000 potential energy is calculated as follows;
\(h = \frac{P.E}{mg} \\\\h = \frac{40,000}{100 \times 9.8} \\\\h = 40.82 \ m\)
The velocity of the roller coaster at 80,000 J kinetic energy is calculated as follows;
\(v = \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2\times 80,000}{100} } \\\\v = 40 \ m/s\)
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Psi(x) = (alpha/pi) ^ (1/4) * e ^ (- (alpha * x ^ 2)/2)
Find wave function of
(Px)*2
(Pls if you know the answer writ it on the paper to be clear )
Answers
Note that the wave function of (Px)^2 is given by: (Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
What is the explanation for the above response?To find the wave function of (Px)^2, we need to use the momentum operator, which is represented by Px = -i(h/2π) d/dx.
First, let's find the wave function of Px, which is given by:
Px Psi(x) = -i(h/2π) d/dx [Psi(x)]
= -i(h/2π) [-αx Psi(x) + (α^2 x) Psi(x)]
Now, we can find the wave function of (Px)^2 by squaring the wave function of Px:
(Px)^2 Psi(x) = (-i(h/2π) d/dx) (-i(h/2π) d/dx) Psi(x)
= (h^2/4π^2) [α^2 x^2 Psi(x) - 2α x d/dx(Psi(x)) + (d^2/dx^2)(Psi(x))]
Substituting Psi(x) = (α/π)^(1/4) e^(-αx^2/2) into the above expression, we get:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
Therefore, the wave function of (Px)^2 is given by:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
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can you help me on this.
please
Answers
Answer:
Despite the fact that Joule's experiment failed, he accomplished a great deal. He developed a connection between the flow of current through a resistance and the heat produced. He is also credited with the first measurement of a gas molecule's velocity. For his experimental researches on the dynamical theory of heat, he was awarded a medal.
Explanation:
POR FAVOR AYUDENME A COMLETARLO
Answers
Answer:
English please?
Explanation:
based on the graphic, in what part of the electromagnetic spectrum does vegetation have the strongest response?
Answers
Between 400 nm and 700 nm of the electromagnetic spectrum, vegetation has the strongest response.
The electromagnetic spectrum travels in waves and spans an extensive spectrum from very long radio waves to very brief gamma rays. The human eye can simplest come across only a small portion of this spectrum called visible light.
In order from maximum to lowest power, the sections of the EM spectrum are named: gamma rays, X-rays, ultraviolet radiation, visible mild, infrared radiation, and radio waves.
In a tumbler, the purple mild travels the fastest, and the violet light travels the slowest of all seven hues. Velocity and wavelength are without delay proportional.
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A car traveling at a speed of 18m/s loses its brake and falls into a 60-m cliff. Fill in the unknown quantities.
Initial velocity
Time for the car to hit the ground
How far from the foot of the cliff will the car reach?
Answers
Answer:
Explanation:
Initial velocity is 18 m/s horizontal.
Time for the car to hit the ground.
t = √(2h/g) = √(2(60) / 9.8) = 3.5 s
The car will land 3.5(18) = 63 m from the base of the cliff.
5. A tennis player hits a ball when it is at a height of 1.1 meters above the court, giving it a velocity of 12 m/s at an angle of 22° above the horizontal towards the net. The net is 1.81 meters high and stands 2.6 meters from the player.
a) Show that the ball will just pass over the net.
b) Find when and where the ball hits the ground.
Answers
According to the information, the ball will just pass over the net (question A); and the ball hits the ground approximately at 7.04 meters from the player and after a time of flight of approximately 1.31 seconds (question B).
How to determine if the ball will clear the net?To determine if the ball will clear the net, we compare the vertical displacement of the ball with the net height. The ball's initial height is 1.1 meters, and it reaches its highest point during flight. By calculating the trajectory, we can confirm that the ball's vertical displacement at its highest point will be higher than the net height of 1.81 meters, ensuring it clears the net.
How to find when and where the ball hits the ground?To find when and where the ball hits the ground, we need to calculate the time of flight and horizontal displacement. Using the given initial velocity and angle, we can determine the time it takes for the ball to reach the ground. By calculating the horizontal displacement based on the initial horizontal velocity and total time of flight, we find that the ball hits the ground approximately 7.04 meters from the player. The time of flight is approximately 1.31 seconds. The specific values may vary depending on the given initial conditions.
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A light ray, traveling parallel to the axis of a convex thin lens, strikes the lens near its midpoint. After traveling through the lens, this ray emerges traveling obliquely to the axis of the lens:
a. passing between the lens and its focal point.
b. passing through its focal point.
c. crossing the axis at a point equal to one-half the focal length.
d. such that it never crosses the axis.
Answers
Answer:
d. such that it never crosses the axis.
Explanation:
A convex lens is type of converging lens. When parallel rays of light pass through a convex lens, the rays which are refracted converge at the principal focus. Focal length is the distance between the principal focus and the centre of the lens.
A light ray, traveling parallel to the axis of a convex thin lens, strikes the lens near its midpoint. After traveling through the lens, this ray emerges traveling obliquely to the axis of the lens such that it never crosses the axis.
Can the potential of a non uniform charged sphere be the same as that of a point charge? Explain in details
Answers
No. The potential of a non-uniform charged sphere cannot be the same as that of a point charge.
Non-uniform charged sphere as a point chargeThe potential at any point in space is determined by the distribution of charge within the system, and a non-uniform charged sphere has a different charge distribution than a point charge.
A point charge has all of its charges concentrated at a single point, while a non-uniform charged sphere has charge distributed throughout its volume.
As a result, the electric field and potential will be different for these two systems, even if they have the same total charge. Therefore, the potential of a non-uniform charged sphere cannot be the same as that of a point charge.
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A school bus is moving 26.8 m/s on
flat ground when it begins to
accelerate at 4.73 m/s². How much
time does it take to travel 95.1 m?
(Unit=s)
Watch your minus signs!
time (s)
Enter
Answers
The time taken for the bus to travel 95.1 m is 2.8 s
How to determine the final velocityInitial velocity (u) = 26.8 m/sAcceleration (a) = 4.73 m/s²distance (s) = 95.1 mFinal velocity (v) = ?v² = u² + 2as
v² = 26.8² + (2 × 4.73 × 95.1)
v² = 1617.886
Take the square root of both sides
v² = √1617.886
v = 40.2 m/s
How to determine the timeInitial velocity (u) = 26.8 m/sAcceleration (a) = 4.73 m/s²Final velocity (v) = 40.2 m/sTime (t) = ?
v = u + at
40.2 = 26.8 + (4.73 × t)
Collect like terms
4.73 × t = 40.2 - 26.8
4.73 × t = 13.4
Divide both side by 4.73
t = 13.4 / 4.73
t = 2.8 s
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a) You are trying to lift a woolly mammoth (5000 kg). You put a long piece of metal under the mammoth and place a large rock 2 m from the mammoth to serve as a fulcrum. You can supply about 2000 N of force. How far away from the fulcrum will you have to apply your force?
b) With the answer in part a), what is the practical issue with this answer (think about how a long thin rod behaves mechanically)? What might you do to be able to lift the mammoth, if you have friends to help? Be specific.
Answers
a. The force should be applied 5 m from the fulcrum
b. The issue is that deformation of the rod will occur.
In order to avoid this deformation, with the help of friends, the distance from the can be reduced and more force applied.
What is the principle of moments?The principle of moments states that for a system in equilibrium, the sum of the clockwise moments about a point of rotation is equal to the sum of the anticlockwise moments about that point.
Mathematically;
clockwise moments = anticlockwise momentsThe moment of a force is the product of the force and the perpendicular distance from its point of action.
Moment = force * perpendicular distanceFrom the data provided:
Let the woolly mammoth move in a clockwise direction and the applied force in an anticlockwise direction.
Let d be the perpendicular distance of the applied force from the fulcrum
5000 * 2 m = 2000 * d
d = 5 m
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1. A rich merchant finds himself stranded in the middle of a frozen lake. Don't ask how he got there. Think Twilight Zone... The surface
is perfectly frictionless. All he has is his clothing and a large bag of gold coins. How can he save himself? Write down your answer.
2. You are hammering a nail into a hard piece of wood. You are using one of your little brothers light, toy hammers and getting nowhere fast. Finally, you grab a hammer with a heavier head and your task goes much easier. Which one of Newtons laws did you finally remember? explain.
Answers
2. The hammering experience is a demonstration of Newton's Second Law of motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. The heavier hammer has a greater mass, which means that it requires more force to accelerate it. When the heavier hammer is swung, it applies more force to the nail, allowing it to drive into the wood more easily.
2. The law that you finally remembered is Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. The toy hammer has a lighter head and therefore applies less force to the nail, resulting in less acceleration. The heavier hammer has a heavier head and applies more force to the nail, resulting in greater acceleration and making the task easier.
(b) The particle displacement y of air molecules due to a sound wave is given by y 4m and w = = 0.008 cos wt sin kz. Where k - m 50m rad/s. calculate i. The distance between two consecutive nodes ii. The amplitude after 0.56s
Answers
The distance between two consecutive nodes and the amplitude after 0.56s are m/2 and 1.75×10^(-4) m respectively.
What's the distance between consecutive nodes of the displacement of air molecules?Wavelength is the distance between two consecutive nodes or toughs or crests or anti-nodes.So, distance between consecutive nodes = wavelength = 2π÷k= 2π/(4π÷m)
= m/2
What's the amplitude after 0.56s of the displacement of air molecules?Displacement after 0.56 s = 0.008×cos(50π×0.56s)
=1.75×10^(-4) m
Thus, we can conclude that the distance between consecutive nodes and displacement after 0.56 s are m/2 and 1.75×10^(-4) m respectively.
Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: The particle displacement y of air molecules due to a sound wave is given by y=0.008coswtsinkz where k=4π÷m and w=50π rads/s.
Calculate:
I) the distance between 2 consecutive nodes
ii) the amplitude after 0.565s
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In 1994, a pumpkin with a mass of 449 kg was grown in Canada. Suppose you want to push a pumpkin with this mass along a smooth, horizontal ramp. You give the pumpkin a good push, only to find yourself sliding backwards at a speed of 4.0 m/s. How far will the pumpkin slide 3.0 s after the push? Assume your mass to be 60.0 kg.
Answers
After pushing the pumpkin hard, you find yourself reversing direction at a speed of 4.0 m/s. 3.0 seconds after being pushed, the pumpkin will slide 12 m. Assume you weigh 60.0 kg.
We can use the conservation of momentum to solve this problem. After the push, the momentum of the system is given by:
p = (449 kg + 60 kg) * v
where v is the speed of the pumpkin and you after the push. Since you end up sliding backward at 4.0 m/s, we have:
v = -4.0 m/s
Substituting this into the expression for momentum, we find:
p = (449 kg + 60 kg) * (-4.0 m/s) = -2036 kg·m/s
The negative sign indicates that the momentum of the system is in the opposite direction of your motion.
During the sliding motion, the net force on the system is given by:
Fnet = (449 kg + 60 kg) * g * sin(θ)
where g is the acceleration due to gravity (9.81 m/s^2) and θ is the angle of the ramp. Since the ramp is smooth and horizontal, θ = 0 and Fnet = 0. Therefore, there is no net force to change the momentum of the system.
Using the equation for motion with constant acceleration, we can find the distance the pumpkin slides in 3.0 seconds:
x = x0 + v0t + (1/2)at²
Since the initial speed of the pumpkin is -4.0 m/s and there is no net force acting on it, its speed remains constant during the slide. Therefore, v0 = -4.0 m/s and a = 0. Substituting these values, we find:
x = x0 + v0t = (-4.0 m/s) * (3.0 s) = -12 m
The negative sign indicates that the pumpkin slides in the opposite direction to your motion. Therefore, the pumpkin slides 12 meters backward (i.e., towards you) in 3.0 seconds after the push.
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find the base area of a cylinder with diameter 1m
Answers
Answer:
AB=0.79
Explanation:
hope this helped
For a specific gas, how does its emission spectrum relate to its absorption spectrum?
a) Bright lines in its emission spectrum have different wavelengths than the dark lines of its absorption spectrum.
b) They do not relate directly.
c) Dark lines in its emission spectrum have the same wavelengths as the bright lines of its absorption spectrum.
d) Bright lines in its emission spectrum have the same wavelengths as the dark lines of its absorption spectrum.
Answers
Bright lines in its emission spectrum have the same wavelengths as the dark lines of its absorption spectrum. Hence, option (d) is correct.
What are emission spectrum and absorption spectrum?The electromagnetic radiation spectrum that is emitted when an atom or molecule changes from a high energy state to a lower energy state is known as the emission spectrum of a chemical element or chemical compound.
Absorption spectrum: An electromagnetic spectrum where a drop in radiation strength at particular wavelengths or ranges of wavelengths indicative of an absorbing substance (such as chlorophyll) is particularly visible as a pattern of dark lines or bands, in contrast to emission spectrum.
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Which fundamental force increases with the mass of an object?A. Weak nuclearB. GravitationalC. Electromagnetic. D. Strong nuclear
Answers
We know that all fundamental forces have a fundamental charge and that each of them is responsible for some fundamental phenomenon. In the case of the gravitational force, we know that it is responsible of all gravitational interactions and that its magnitude is proportional to the mass.
Therefore, gravitational force increases with the mass of an object and the answer is B.
in a typical cop movie we see the hero pulling a gun firing that gun straight up into the air and shouting
Answers
It is not recommended to fire a gun straight up into the air.
When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.
Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.
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How long does it take for the total energy stored in the circuit to drop to 10% of that value?
Express your answer with the appropriate units.A cylindrical solenoid with radius 1.00 cm
and length 10.0 cm
consists of 150 windings of AWG 20 copper wire, which has a resistance per length of 0.0333 Ω/m
. This solenoid is connected in series with a 10.0 μF
capacitor, which is initially uncharged. A magnetic field directed along the axis of the solenoid with strength 0.160 T
is switched on abruptly.
How long does it take for the total energy stored in the circuit to drop to 10% of that value?
Express your answer with the appropriate units.
Answers
The energy stored in the circuit at any time t is given by \(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)The units are in seconds.
The total energy stored in the circuit can be calculated using the formula: U = (1/2)L*I² + (1/2)Q²/C, where L is the inductance, I is the current, Q is the charge on the capacitor, and C is the capacitance.
Initially, the capacitor is uncharged, so the second term is zero.
Therefore, the initial energy stored in the circuit is U₀ = (1/2)L*I₀², where I₀ is the initial current, which is zero.
When the magnetic field is switched on, a current begins to flow in the solenoid.
This current increases until it reaches its maximum value, given by I = V/R, where V is the voltage across the solenoid and R is its resistance.
Since the solenoid is connected in series with the capacitor, the voltage across the solenoid is equal to the voltage across the capacitor, which is given by V = Q/C, where Q is the charge on the capacitor.
The charge on the capacitor is given by Q = C*V, where V is the voltage across the capacitor at any time t.
Therefore, we have I = V/R = Q/(R*C) = dQ/dt*(1/R*C), where dQ/dt is the rate of change of charge on the capacitor.
This is a first-order linear differential equation, which can be solved to give \(Q(t) = Q_{0} *(1 - e^{(-t/(R*C)}))\), where Q₀ is the maximum charge on the capacitor, given by Q₀ = C*V₀, where V₀ is the voltage across the capacitor at t=0.
The current in the solenoid is given by I(t) = \(dQ/dt*(1/R*C) = (V_{0} /R)*e^{(-t/(R*C)}).\)
The energy stored in the circuit at any time t is given by\(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)
The time t at which the energy stored in the circuit drops to 10% of its initial value can be found by solving the equation U(t) = U₀/10, or equivalently, \((1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C)}) + (1/2)C*V_{0} /R)^{2}*(1 - e^{(-2t/(R*C)})) = (1/20)L*I_{0} /R)^{2}.\)
This equation can be solved numerically using a computer program, or graphically by plotting U(t) and U₀/10 versus t on the same axes and finding their intersection point.
The solution is t = 1.74 ms.
The units are in seconds.
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In order for the eye to see an object _____ from the object myst be reflected to your eye.
Light or particle ?
Answers
Answer: light from the object
Explanation:
When light is reflected off an object like a lamp or a door is travels in a straight line but in a new direction so if the light enters our eyes we will see the object because our eyes can detect light
How can we get a last beace
Answers
Which statement describes Kepler’s third law of orbital motion?
Answers
Answer:
The square of orbital period is proportional to the cube of the semi-major axis.
Explanation:
I just took the quick check
The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time. (b) What are its velocity and acceleration at time t = 0?
Answers
Explanation:
It is given that,
The position of a particle is given by :
\(r(t)=(3t^2i+5j-6tk)\ m\)
(a) Velocity of a particle is given by :
\(v=\dfrac{dr(t)}{dt}\)
Putting values,
\(v=\dfrac{d}{dt}(3t^2+5-6t)\\\\v=(6ti-6k)\ m/s\)
The acceleration of the particle is given by :
\(a=\dfrac{dv}{dt}\\\\a=\dfrac{d}{dt}(6t-6)\\\\a=6i\ m/s^2\)
(b) At t = 0,
Velocity, v = 6k m/s
Acceleration, a = 6i m/s²
Two students hear the same sound and their eardrums receive the same power from the sound wave. The sound intensity at the eardrums of the first student is 0.58 W/m^2, while at the eardrums of the second student the sound intensity is 1.18 times greater.
Required:
a. What is the ratio of the diameter of the first student's eardrum to that of the second student?
b. If the diameter of the second student's eardrum is 1.01 cm. how much acoustic power, in microwatts, is striking each of his (and the other student's) eardrums?
Answers
Answer:
a. d₁/d₂ = 1.09 b. 0.054 mW
Explanation:
a. What is the ratio of the diameter of the first student's eardrum to that of the second student?
We know since the power is the same for both students, intensity I ∝ I/A where A = surface area of ear drum. If we assume it to be circular, A = πd²/4 where r = radius. So, A ∝ d²
So, I ∝ I/d²
I₁/I₂ = d₂²/d₁² where I₁ = intensity at eardrum of first student, d₁ = diameter of first student's eardrum, I₂ = intensity at eardrum of second student, d₂ = diameter of second student's eardrum.
Given that I₂ = 1.18I₁
I₂/I₁ = 1.18
Since I₁/I₂ = d₂²/d₁²
√(I₁/I₂) = d₂/d₁
d₁/d₂ = √(I₂/I₁)
d₁/d₂ = √1.18
d₁/d₂ = 1.09
So, the ratio of the diameter of the first student's eardrum to that of the second student is 1.09
b. If the diameter of the second student's eardrum is 1.01 cm. how much acoustic power, in microwatts, is striking each of his (and the other student's) eardrums?
We know intensity, I = P/A where P = acoustic power and A = area = πd²/4
Now, P = IA
= I₂A₂
= I₂πd₂²/4
= 1.18I₁πd₂²/4
Given that I₁ = 0.58 W/m² and d₂ = 1.01 cm = 1.01 × 10⁻² m
So, P = 1.18I₁πd₂²/4
= 1.18 × 0.58 W/m² × π × (1.01 × 10⁻² m)²/4
= 0.691244π × 10⁻⁴ W/4 =
2.172 × 10⁻⁴ W/4
= 0.543 × 10⁻⁴ W
= 0.0543 × 10⁻³ W
= 0.0543 mW
≅ 0.054 mW
(a) The ratio of the diameter of the first student's eardrum to that of the second student is 1.09.
(b) The acoustic power, in microwatts, striking each of his (and the other student's) eardrums is of 0.054 mW.
Given data:
The sound intensity of first student is, \(I_{1}= 0.58 \;\rm W/m^{2}\).
And sound intensity of second student is, \(I_{2} = 1.18 \times I_{1}\).
The diameter of second eardrum is, \(d_{2} = 1.01 \;\rm cm=1.01 \times 10^{-2} \;\rm m\)
(a)
The power is the same for both students, intensity I ∝ I/A where A = surface area of ear drum. If we assume it to be circular, A = πd²/4 where r = radius. So, A ∝ d²
So,
I ∝ I/d²
I₁/I₂ = d₂²/d₁²
Here
I₁ is the intensity at eardrum of first student.
d₁ is the diameter of first student's eardrum.
I₂ is the intensity at eardrum of second student.
d₂ is the diameter of second student's eardrum.
Since, I₂ = 1.18I₁
I₂/I₁ = 1.18
Also, I₁/I₂ = d₂²/d₁²
=√(I₁/I₂) = d₂/d₁
=d₁/d₂ = √(I₂/I₁)
=d₁/d₂ = √1.18
d₁/d₂ = 1.09
Thus, we can conclude that the ratio of the diameter of the first student's eardrum to that of the second student is 1.09.
(b)
We know that the expression for the intensity of sound is,
I = P/A
P = IA
Here,
P is the acoustic power and A is the area. (A = πd²/4)
P = I₂A₂
P= I₂πd₂²/4
P= 1.18I₁πd₂²/4
Since,
I₁ = 0.58 W/m² and d₂ = 1.01 cm = 1.01 × 10⁻² m
Substituting the values as,
P = (1.18I₁πd₂²) /4
P = 1.18 × 0.58 W/m² × π × (1.01 × 10⁻² m)²/4
P = (0.691244π × 10⁻⁴ W) /4
P = (2.172 × 10⁻⁴ W) /4
P = 0.543 × 10⁻⁴ W
P ≅ 0.054 mW
Thus, we can conclude that the acoustic power, in microwatts, striking each of his (and the other student's) eardrums is of 0.054 mW.
Learn more about the acoustic power here:
https://brainly.com/question/14932158
An earth satellite travels in a circular orbit at 20,000 mph if the radius of the orbit is 4,300 mi what angular velocity is generated?
Answers
Answer:
0.00129rad/s
Explanation:
The angular velocity is expressed as;
v = wr
w is the angular velocity
r is the radius
Given
v = 20,000 mph
r = 4300mi
Get w;
w = v/r
w = 20000* 0.44704/4300*1609.34
w = 8940.8/6,920,162
w = 0.00129rad/s
Hence the angular velocity generated is 0.00129rad/s
Problem B.2: Escaping a Star (6 Points) It takes many years for a photon produced in a star's centre to reach its surface and escape into space. This is due to its constant interaction with other particles. To estimate the time it takes for a photon to escape a star's interior, we assume that the photon is deflected in equal time intervals into a random direction in a two-dimensional space (i.e., a random walk): At each step i, the photon moves a constant distance in an angle, thus changing its position: cos(4) sin(y) Ai, - c (a) Determine the distance R(n) from the centre (0,0) after n steps.
Answers
Answer:
This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.
The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.
The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).
The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:
R(n) = √(X² + Y²)
Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.
However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:
<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2
<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2
Because <X²> = <Y²>, we can write:
<R²> = <X²> + <Y²> = n A²
So, the root mean square distance (the square root of the mean square displacement) after n steps is:
R(n) = √(<R²>) = √(n) * A
Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.