you look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (fig. 34.33). because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to be where extensions of the intercepted rays cross, at depth da instead of d. assuming that the intercepted rays in fig. 34.33 are close to a vertical axis through the coin, show that da da = d=n.
Answers
The water is medium 1, so
n₁ = n(w)
which we simply write as n. The air is medium 2, for which
n₁≈ 1
We refer to points where the light rays strike the water surface as A (on the left side of Figure) and B (on the right side of the picture). The point midway between A and B (the center point in the picture) is C. The penny P is directly below C, and the location of the “apparent” or virtual penny is V.
We note that the angle ∠CVB (the same as angle ∠CVA) is equal to θ₂ and the angle ∠CPB (the same as angle ∠CPA) is equal to θ₁.
The triangles CVB and CPB share a common side, the horizontal distance from C to B (which we refer to as x).
Therefore,
tan θ₂ = x / dₐ
tan θ₁ = x / d
Using the small-angle approximation (so a ratio of tangents is nearly equal to a ratio of
sines) and the law of refraction, we obtain
tan θ₁ / tan θ₂ = sin θ₁ / sin θ₂
⇒ (x / dₐ) / (x / d) ≈ n₁ / n₂
⇒ d / dₐ ≈ n
⇒ dₐ = d / n
Therefore, the above calculations shows that using law of refraction, dₐ = d / n. Hence, proved.
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Related Questions
A group of students were investigating the force of gravity. They began by dropping a foam ball from a height of 3 meters into a bucket of sand. The ball hit the sand in 0. 306 seconds. They dropped additional balls of approximately the same diameter, but of different masses. Here is the data they collected. Based on this experiment and the collected data, what would their conclusion be?.
Answers
Based on this experiment and the collected data, their conclusion be: mass becomes a factor affecting speed of a falling object when it is dropped at a great distance from the surface of the Earth
What is gravitational force?Gravitational force is that type of force by which an object attracts other objects into its center of mass. We are able to stand on the ground because of the gravitational pull of earth.
The force of gravitation depends on the mass of the object : as mass increases then the speed of the falling object also increases because it experiences more gravitational pull from earth.
Here, ball with greater mass hit the ground with less time as compared to the one with lesser mass.
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What can happen to solar radiation when it enters Earth’s atmosphere?
Answers
It is reflected by the surface of the Earth, reflected by clouds, and upper atmosphere.
What is Earth-Atmosphere Energy?The energy balance between the earth and atmosphere is reached when the energy from the Sun equals the energy that is lost by the Earth back into space. When it reaches the Earth, a portion of it is absorbed by the atmosphere, a portion is reflected back into space by clouds, and a portion is absorbed at the planet's surface. The Earth emits lesser (long wavelength) infrared light than the Sun because it is much cooler than otherwise.
The various surfaces that the solar radiation comes into contact with provide it the opportunity to undergo a variety of varied experiences. When solar radiation strikes the Earth, some of it is absorbed by the planet and some is reflected back into space.
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a force of 30 n acts on a 2 c charge in a 5 t magnetic field. if the charge is moving perpendicularly to the field, how fast is it moving?
Answers
The velocity by which charge is moving is 3m/sec if a force of 30N acts on it in a 5Tesla magnetic field.
We know very well that a moving charge can produce both magnetic field and electric field. Static charge is only able to produce electric field.
Moving charge has velocity due to that it is able to produce magnetic field.
Now, direction of charge is very important as it will decide whether force act on the charge applied by the magnetic field or not.
Now, We know very well that force exerted by magnetic field on the charge is given by(F)=qvBsinθ where
q is the amount of charge,
v is the velocity of charge
F is the amount of force
B is the amount of magnetic field and
sinθ is the angle made by the charge with the plane of magnetic field.
Since charge is moving perpendicularly to the field, therefore value of sinθ=1
Now, F=qvBsinθ
=>v=F/qvBsinθ
=>v=30/(2×5×1)
=>v=30/10
=>v=3m/sec
Hence, velocity of charge is 3m/sec.
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serenity asks carlos what conditions are needed to observe interference of waves from two sources. which responses are correct? (select all that apply.)
Answers
The sources of the waves must be coherent, which means they emit identical waves with a constant phase difference. The waves should be monochromatic - they should be of a single wavelength.
What is interference of waves ?In physics, interference is the overall result of two or more wave trains travelling in parallel or converging directions. At each place impacted by many waves, the effect is that of adding the individual wave amplitudes.
Interference comes in two flavours positive interference and destructive interference. Additionally, when wave amplitudes reinforce one another and cause an increase in wave amplitude, constructive interference occurs.
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If one of the rocks that you were analyzing for density suddenly split in two, and you were only able to measure the mass and volume of a smaller piece, would that change the outcome of your calculation?.
Answers
The answer is C) No, and that is called an intensive property.
What is mass?mass is a very large amount of number or something.
Intensive properties are those that do not depend on the mass or size of a body. If the system is divided into several subsystems its value will remain unchanged, therefore they are not additive
Examples of intensive properties are elasticity, speed, specific volume (volume occupied by the unit of mass), density, boiling point, melting point, viscosity, hardness, concentration, solubility, odor, color, taste, conductivity, porosity, pressure, temperature, etc., in general, all those that characterize a substance distinct from others.
For instance if we have a liter of water, your boiling point is 100 °C (at 1 pressure atmosphere). If another liter of water is added, the new system, made up of two liters of water, has the same boiling point as the original system. This illustrates the non-additivity of intensive properties.
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which sentence describes newton's second law
Answers
according to the socioemotional selectivity theory, recently retired joyce will likely seek familiar social contacts that reinforce all of these except:
Answers
According to the socioemotional selectivity theory, recently retired joyce will likely seek familiar social contacts that reinforce all of these except: Joy
What is socioemotional selectivity theory?
The Socio-Emotional Selectivity Theory (SST; developed by psychologist Laura L. Carstensen at Stanford University) is a lifelong motivational theory. According to this theory, as time spans shorten, as usually happens with age, people become increasingly selective and invest more resources in emotionally meaningful goals and activities. Changes in motivation also affect cognitive processing. Aging is associated with a relative preference for positive information over negative information among people who have formed rewarding relationships. This selective narrowing of social interactions maximizes positive emotional experiences and minimizes age-related emotional risks for individuals. According to this theory, older adults systematically strengthen their social networks to ensure that available social partners meet their emotional needs.
This theory also focuses on the types of motivations individuals seek to achieve. Knowledge-related goals cover knowledge acquisition, career planning, building new social relationships, and other endeavors that will yield results in the future. Emotion-related goals are aimed at regulating emotions, seeking emotionally satisfying interactions with social partners, and other pursuits whose benefits are currently realizable.
Thus, According to the socioemotional selectivity theory, recently retired joyce will likely seek familiar social contacts that reinforce all of these except: Joy
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A car battery is rated at 40 Ah. In theory, how long does this suggest the battery could light a headlamp bulb which draws 2 A from the battery?
Answers
The battery will light the headlamp bulb for 20hours
What is battery run time?A battery run time is the total time in hours that a battery can sustain a certain power output.
Battery run time can also be defined as the ratio of the battery capacity in( Ah) and the current of the load in( A) i.e
Battery Life (in hours) = Battery Capacity (in Ah) / Load Current (in A).
The battery capacity is 40Ah and the the load takes a current of 2A
therefore the time it will take the battery to run out is
40/2= 20hours
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what is the acceleration of a car that starts at 0 and goes to 45mph in 5 seconds
Answers
The acceleration of the car will be 9m/s2.
What is acceleration?Acceleration is the rate of change in velocity. Involves a change in speed and direction. When acceleration involves a change in speed only: Positive acceleration it occurs when an object speeds up. Negative acceleration occurs when an object slows down. Acceleration is a change of velocity over a period of time.
Using the formula;
[tex]a = \frac{v-u}{t}[/tex]
v = final velocity (45mph)
u = initial velocity (0)
t = 5 seconds
[tex]a = \frac{45 - 0}{5}[/tex]
a = 9m/s2.
In conclusion, the acceleration of the car will be 9m/s2.
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The acceleration of the car moving with a velocity of 13.37m/s in 5s is 2.67m/s²
What is acceleration?Acceleration is the rate of change of velocity with time. It is the measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is a vector quantity.
Acceleration = change in velocity/ time
therefore a= (v-u)/t
where v = final velocity and u= initial velocity, t is the time
since 1meter = 0.000621miles and 60×60 seconds is 1hour, then
45 mph to m/s is 45×1609.344/60×60
= 48120.48/3600= 13.37m/s
a= (13.37-0)/5
a= 13.37/5
a= 2.67m/s²
therefore the acceleration of the car is 2.67m/s²
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in each of the four scenarios shown in the images, a large bat lets out a short burst of ultrasonic sound, which a smaller bat hears a moment later. if the large bat flies at 3.750 m/s and the small bat flies at 13.60 m/s , order the frequencies that the smaller bat detects in the four scenarios from highest to lowest. assume that the speed of sound is 343.0 m/s . a. the large bat is on the left and is flying to the right. the small bat is on the right and is flying to the right. b. the large bat is on the left and is flying to the left. the small bat is on the right and is flying to the right. c. the large bat is on the left and is flying to the right. the small bat is on the right and is flying to the left. d. the large bat is on the left and is flying to the left. the small bat is on the right and is flying to the left.
Answers
The frequency from highest to lowest will be C, A, D, B
Given,
Velocity of large bat = 3.750 m/s
Velocity of small bat = 13.60 m/s
Speed of sound = 343 m/s
Frequency of initial signal = 40.20 kHz
To find,
Frequency heard by small bat in scenario C is
f' = f(V +V₀) / V - V(s)
f' = (40.2)(343 + 2.54) / (343 - 15.2)
f' = 42.3755 Hz
The reflected wave heard by large bat is
f'' = f'(V + V₀) / V - V(s)
f'' = (42.3755)(343 + 15.2) / (343 - 2.54)
f'' = 44.5836 kHz.
Therefore, the total sound frequency of the two bats is 44.5836 kHz and the order of sound frequencies of the bats are C, A, D, B.
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true or false: the eye is spherical, measuring about 5 centimeters in diameter, and most of it is receded into the orbit of the skull.
Answers
The answer to this question is false. The eye of an adult is about 21 mm to 27 mm in total length and width.
What is dry eye?Tears may be insufficient and unsteady. The discomfort of dry eyes is felt. The stinging or burning of your eyes could be a sign of dry eyes.
On an airplane, in an air-conditioned room, while riding a bike, or after staring at a computer screen for a while, are a few examples of scenarios when you could get dry eyes.
You may feel more comfortable using treatments for dry eyes. Changes in lifestyle and eye drops are two possible treatments.
To manage the signs of dry eyes, you'll probably need to keep up with these precautions indefinitely.
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how much heat (in kj) is required to warm 15.0 g of ice, initially at to steam at . the heat capacity of ice is , and that of steam is .
Answers
The ice must be warmed with 4.719 kJ of heat.
How do you calculate heat to melt ice?Let's have a look at the energy required to melt one kilogramme of ice at absolute zero to create one kilogramme of water at absolute zero. We determine that Q = mLf = (1.0 kg)(334 kJ/kg) = 334 kJ is the energy required to melt a kilogramme of ice using the equation for a change in temperature and the value for water from Table 1.The quantity of heat energy required to transform materials from a solid to a liquid is known as the heat of fusion (melting.)The heat of fusion calculation formula is q = mHf.2090 Joules/kg C is the specific heat of ice.Given data :
The mass of ice is, m = 10.0 g.The initial temperature is, T = - 10 degree Celsius.The final temperature is, T' = 110.0 degree Celsius.The heat capacity of ice is, c = 2.09 J/g C.The heat capacity of steam is, c' = 2.01 J/g C.When ice absorbs heat, the conversion takes place from ice to water (liquid) and from the liquid to steam at 110 degree Celsius. So,
The amount of heat absorbed is given as,
Q = m[c(T' - T) + c'T']
Q = 10 [ 2.09 ( 110 - ( -10) + ( 2.01 x 110) ]
Q = 4719 J
Convert in kJ as,
Q = 4719/1000
Q = 4.719 kJ
Thus, we can conclude that the amount of heat required to warm the ice is 4.719 kJ.
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The light energy that falls on a square meter of ground over the course of a typical sunny day is about 20 MJ . The average rate of electric energy consumption in one house is 1.0 kW .
Part A got answer for part A and is correct
On average, how much energy does one house use during each 24 hr day?
Express your answer using two significant figures.
=86 MJ
Part B
If light energy to electric energy conversion using solar cells is 15%efficient, how many square miles of land must be covered with solar cells to supply the electrical energy for 250,000 houses? Assume there is no cloud cover. A=___________mi^2
Answers
86.4×10^6 joule is energy does one house use during each 24 hr day.
20 MJ of light energy
Consumption of electricity is 1 kW.
The energy consumption lasts for 24 hours.
energy=power×time
energy=10^3×24×3600
energy=86.4×10^6 joule
Energy in physics is the ability to perform work. Different shapes, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc., may be assumed by it. Other examples of energy being transferred from one body to another include heat and work. Energy is always distributed after it has been transported in accordance with its type. Thus, heat transfer could result in thermal energy, whereas work could result in mechanical energy.
Motion is a trait shared by all forms of energy. For instance, if a body is moving, it has kinetic energy. Due to the object's design, which incorporates potential energy, a tensioned object, like a spring or bow, has the ability to move even when at rest.
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what is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?
Answers
The magnitude of the cross product of both the given vectors is 6.91.
Given that, the magnitude of first vector is 2m and is pointing east
a = 2 (cos 0° i + sin 0° j) = 2 i
The magnitude of second vector is 4m pointing 30° west of north.
b = 4 (-cos 30° i + sin 30° j) = -4* 0.866 i + 4* 0.5 j = -3.46 i + 2 j
The total angle between a and b is 120°. (as one vector is on the east and the other is 30° west of north.
The formula for the cross product of two vectors is given by,
a × b = |a| |b| sinθ
where, |a| is the determinant of a
|b| is the determinant of b
θ is the angle between a and b
|a| = √(2)² = 2
|b| = √(-3.46)² + (2)² = 3.99
a × b = |a| |b| sinθ = 2* 3.99* sin 120° = 7.98* sin 120° = 6.91
Thus, the magnitude of cross product is 6.91.
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a 1.5 kg 1.5 kg ball rotates on the end of a 3 m 3 m string in a vertical circle with a speed of 7 m/s 7 m/s. what force does the ball exert on the rope at the top of the vertical circle?
Answers
The ball pulls on the rope with a force of 24.5 N. Force is an outside factor that has the power to alter an object's motion or velocity.
It can also be explained as the result of acceleration and mass.
Mathematically, the ball's mass is 1.5 kg and force F = m*a.
3 meters is the circle's radius.
The ball rotates at a speed of 7 m/s.
The ball is subject to centripetal force since it is rotating in a vertical circle.
A rotating object experiences centripetal force, which is different from gravitational force, which is zero in a vertical circle.
Centripetal force has the formula Fc = mv2/r.
Fc = 1.5 * (7)²/ (3) (3)
Fc = 24.5 N
At the top of the vertical circle, there is a 24.5N force applied by the ball to the rope.
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the temperature is increased from 20°c to 100°c. by what factor does the rms speed of an ideal molecule change?
Answers
In version 1.1, the temperature is raised to 100°C from 20°C. what variable affects the ideal molecule's rms speed.
What is temperature and what is its unit in physics?The kelvin is the fundamental unit of heat in the European System of Units (SI). Its identifier is K. The Celsius measure, in which 0 degrees corresponds approximately to the freezing temperature and 100 degrees to its boiling temperature at sea level, is frequently practical for use in common applications.
Briefing:Create the equation for the gas's RMS speed.
Vrms = [tex]\sqrt{3RT}/M[/tex]
In this case, R stands for the air constant, T for temperature, and M for molecular size.
The numerator of the temperature is approximately equal to the RMS speed of both the gas, according to the expression above.
(Vrms)₁/(Vrms)₂ = [tex]\sqrt{T1}[/tex]/[tex]\sqrt{T2}[/tex]
= [tex]\sqrt{20+273 K}[/tex]/[tex]\sqrt{100+273 K}[/tex]
= [tex]\sqrt{293 K}[/tex]/[tex]\sqrt{373 K}[/tex]
= 0.886 (Vrms)₂
= 1.12 (Vrms)₁
The complete question is-
If the temperature of a gas is increased from 20°C to 100°C, by what factor does the rms speed of an ideal molecule change?
A) 1.1
B) 1.3
C) 2.2
D) 1.6
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which properties of our universe are well-explained by the standard big bang model, and which properties are not well-explained?
Answers
The universe's mass-energy density would be similar to the critical density based on the characteristics, which are comparative abundances of the exceptionally light elements.
What are properties in science?Properties are the features that allow us to distinguish between different types of materials. A feature of material that is unrelated to its chemical makeup is called a physical property. Attributes include things like density, color, hardness, melting and liquid and a gas, and electrical conductivity.
What do you mean properties?Anything that a individual or a company has legal ownership is considered property. Property can relate both to real objects, like homes, automobiles, or appliances, as well as intangible items with the potential for future value, like stock and bond certificates.
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if two objects, a and b, of different temperatures come into direct contact, what is the relationship between the heat lost by one and the heat gained by the other? what is the relationship between the temperature changes of these two objects?
Answers
The heat lost by one object is equal to the heat gained by the other.
What is heat?
heat is the energy that moves from one body to another when temperatures are different. Heat flows from the hotter to the colder body when two bodies with various temperatures are brought together. Usually, but not always, this energy transfer results in a rise in the temperature of a colder body and a fall in the temperature of a hotter body. By transitioning from one physical state (as well as phase) to another, such as from a phase from solid to liquid (melting), from the a solid to the a vapour (sublimation), from the a liquid to a vapour (boiling), either from one solid form to another, a substance can absorb heat without increasing in temperature.
This is because of the law of conservation of energy, which states that energy cannot be created or destroyed. As a result, the temperature of both objects will change until they reach the same equilibrium temperature. This is known as the law of thermal equilibrium, which states that the temperature of any two objects in thermal contact will eventually reach the same temperature.
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if every sun-like star had an earth-like planet in an earth-like orbit, how many could be detected by a transit?
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If every sun-like star had an earth-like planet in an earth-like orbit, then the transit would be 1 in 200.
Explain in detail.
The transit technique has been used to find the majority of known exoplanets. When a planet passes in front of an observer and a star, it is said to be transiting. When Venus or Mercury pass in front of Earth and the Sun, transits inside our solar system can be seen from the planet.Less than 1% of the stars Kepler will observe are located within 600 light-years of Earth. Kepler cannot witness the transits necessary to find planets the size of Earth from stars more than 3,000 light years away because to their faintness.To know more about Kepler here
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Physics is hard and my brain hurts
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(a) The frictional force acting on the 19 kg mass is 120.45 N.
(b) The largest angle that the incline can have so that the mass does not slide the incline is 39⁰.
What is the frictional force acting on the 19 kg mass?
The frictional force acting on the 19 kg mass is calculated by applying Newton's second law of motion as follows;
F = μFn
where;
μ is the coefficient of static frictionFn is the normal force on the 19 kg massThe normal force on the 19 kg mass is calculated as follows;
Fn = mg cosθ
where;
θ is the angle of inclination of the planeg is acceleration due to gravity = 9.8 m/s²F = μmg cosθ
F = 0.81 x 19 x 9.8 x cos(37)
F = 120.45 N
The largest angle that the incline can have so that the mass does not slide the incline is calculated as follows;
the net force on the block must be equal to zero
∑F(net) = 0
parallel force - force of friction = 0
mg sinθ - μmg cosθ = 0
mg sinθ = μmg cosθ
sinθ = = μ cosθ
μ = sinθ/cosθ
μ = tanθ
θ = arc tan(μ)
θ = arc tan(0.81)
θ = 39⁰
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a 34 kg child is riding a playground merry-go-round that is rotating at 15 rev/min. what centripetal force must she experience to stay on the ride if she is 1.2 m from its center?
Answers
100.56N to maintain her position. A force that causes a body to maintain a curved path is known as a centripetal force. .
What is the centripetal force calculation formula?The formula for centripetal force is supplied by the mass, velocity, and radius. f c = m v 2 / r. Where m = mass; v = velocity; and r = radius, fc = centripetal force. We must be aware that this formula resembles the traditional formula for the force in several ways.
Briefing:Given
The child's mass= (34 kg)
Weight (mg)= (34x9.8=333.2N)
And distance from the center
(w=215/60=1.570),
The distance from the center is 1.2 meters.
She applies centripetal force of
F=m(w)*2xr
F=34x(1.570)*2x1.2
F=100.56N to maintain her position.
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A proton and an electron are placed in an electric field. Which undergoes the lesser acceleration?.
Answers
An Electron will undergoes the lesser acceleration
What is Proton and Electron ?An electron is a negatively charged particle of equivalent magnitude to a proton, which is positively charged. Therefore, they will feel the same amount of electric force when exposed to an electric field. As a result, the relationship between acceleration and mass will be inverse. An electron will accelerate more quickly than a proton because an electron has a lower mass.
Due to their opposite polarity, an electron and a proton are attracted to one another by an electrical force of equal strength when they are placed in an electric field. However, because of their opposing charges, the force will act in the opposite direction.
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7. the fact that voltage can be created by exerting force on a crystal is used for which type of sensor?
Answers
A knock sensor is used where voltage is created by exerting force on a crystal.
What is a force?A force is a pushing or pulling that an object feels as a consequence of engaging with another thing. Every time two objects contact, a force is applied to everything in the system. When the interaction is finished, the force is no more sensed by the two objects. Forces are merely interactions; they do not exist in isolation.
what does a sensor do and what are some examples?A sensor is a tool that collects physical information from its surroundings and transforms it into information that can be used by either a machine or a human to understand. Most sensors (which transform the data into electronic data) are electronic, but some are simpler, such as a glass thermometer that displays visual data.
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bilingual children and adults outperform others on tests of inhibition, sustained and selective attention, flexible thinking, analytical reasoning, concept formation, and false-belief understanding. the benefits of sustained bilingual education have inspired u.s. educators to devise two-way programs. these programs are growing rapidly in u.s. public schools.
Answers
Literature suggests that bilingual immersion programs are beneficial for elementary school students. Because this program will help fill the grade gap for elementary school students improve their academic performance and embrace their culture and new ones.
Bilingual education means teaching subjects in two different languages. It can be easily applied to help students transition from their native language to the language of the country in which they currently live, but can also be used to teach academic content in two languages at the same time.
Students can connect effectively with people from different cultures and backgrounds improve their ability to empathize with others and develop emotional intelligence. Teachers and students can use her two languages. One is the target language to learn and the other is the native language to reach the target language English.
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dsl achieves high throughput over regular telephone lines by using data modulation techniques at the physical layer of the osi model.
Answers
Equal download and upload speeds are provided by symmetric DSL (SDSL), which evenly divides the upstream and downstream frequencies.
2 Mbps may be available both upstream and downstream on this connection. Small businesses typically favor it.You won't need to invest in pricey phone system modifications because a DSL connection uses your current telephone wiring.Cost-Effective - DSL internet offers the best connectivity and is a very cost-effective method.DSL modems are offered by the service providers.Users are able to utilize the internet and telephone lines simultaneously. And the reason for that is that voice and digital signals utilize different frequencies to be sent.
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What can happen to solar radiation when it enters Earth’s atmosphere?
Answers
When solar radiation is enters Earth’s atmosphere it absorbed or reflected as it travels to the earth's surface.
What is Solar Radiation?The electromagnetic radiation that the sun emits is known as solar radiation, sometimes referred to as the solar resource or just sunshine. With the use of various technologies, solar radiation may be absorbed and converted into usable forms of energy like heat and electricity.
When solar radiation penetrates the earth's atmosphere, it travels and collides with the ground. The earth absorbs some of the rays, while the remainder are reflected back into the atmosphere. A layer of gas called a blanket of greenhouse gases in the atmosphere absorbs some of the reflected rays, while a minute fraction escapes back into space.
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a solid cylinder has a mass of 5 kg and a radius of 30 cm. a torque of 40 nm is applied to the cylinder. what will be its angular acceleration?
Answers
A solid cylinder has a mass of 5 kg and a radius of 30 cm. a torque of 40 Nm is applied to the cylinder, then its angular acceleration 177.77 m/s^2.
Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics, torque is what causes an object to acquire angular acceleration. Angular acceleration is a quantitative expression of the change in angular velocity per unit time.
Let T be the torque, I be the Inertia and a be the angular acceleration.
In the angular form of Newton's second law, rotational inertia replaces mass and torque (tau) replaces force. The relationship between angular acceleration and torque is true when an object's rotational inertia is constant.
F = ma
T= I x a (1)
and I = 1/2 x M x R^2
I = 1/2 x 5 x (0.3)^2 Kgm^2
According to equation 1
a = T/I
a= 40/0.225 = 177.777 m/s^2.
Therefore, angular acceleration is 177.77 m/s^2.
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consider a piezoelectric common rail injector. what happens to the actuator when current is initially applied to the crystals?
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According to the piezoelectric actuator's operating principle, when voltage is applied, the piezoelectric actuator produces a little displacement with a large amount of force.
As a result, they are utilized in a variety of applications such as ultra-precize positioning, high force handling, and force generating under fixed or dynamic settings. The Piezoelectric Injector is crucial to the operation of contemporary common rail technology. In Piezo diesel injectors, when an electrical voltage is applied, Piezo crystals slightly expand, changing their structural properties in less than a thousandth of a second. Electric potential difference between two sites is referred to as voltage, also known as electric pressure, electric tension, or (electric) potential difference. The work required to transport a unit of charge in a static electric field correlates to this.
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what is the minimum thickness of film required? assume that the wavelength of the light in air is 480 nanometers.
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Assuming a wavelength of 500 nm for light in air, the minimum film thickness required is 83.9 nm.
How do you calculate destructive interference?refractive index of polystyrene; η_p = 1.49
Refractive index of fablite; η_f = 2.409
The wavelength of light in air is 500nm.
To answer this question, we know that light is first reflected twice.
Once from the top coating layer and once from the contact between the coating and the polystyrene material.
The additional path of light in the coating is 2t, but the path difference is 2tp. Therefore, the minimum required film thickness is given by the formula used in destructive interference, namely 2tη_p = λ/2.
t = λ/2 * 1/2η_p
t = λ/(4η_p)
t = 500/(4 * 1.49)
t = 83.9 nm
So, assuming a wavelength of 500 nanometers for light in air, the minimum required film thickness is: 83.9 nanometers
The full question is:
A thin polystyrene film is used as an anti-reflection coating on fablites (known as substrates). Polystyrene has a refractive index of 1.49 and fablite has a refractive index of 2.409. What is the minimum film thickness required? Suppose the wavelength of light in air is 500 nanometers.
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rank the block based on its electrical resistance along the three illustrated coordinate directions (x, y, and z).
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The resistance is halved and ranking is y, z, x
Let x. = 3 cm., y = 10 cm., z. = 4 cm.
resistance is proportional to L/A where L is the length along the current, A is the area of cross section,
along x direction: L = x, A = yz, so L/A = x/yz = 3/40 = 0.075
along y direction: L = y, A = xz, so L/A = y/xz = 10/12 = 0.833
along z direction: L = z, A = xy, so L/A = z/xy = 4/30 = 0.133
a) rank: y, z, x
Depending on its shape and the material it is made of, an object's resistance varies. We can learn more about the resistance of more complex shapes by using the straightforward analysis of the cylinder resistor in Figure 1. The cylinder's electric resistance R, which is comparable to a pipe's resistance to fluid flow, is directly proportional to its length L, as one might anticipate. More collisions will occur between charges and its atoms the longer the cylinder is. A cylinder's capacity to carry more current increases with its diameter. The cylinder's cross-sectional area A and R are actually inversely proportional.
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