determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point o . the material has a mass per unit area of 28 kg/m2 . (figure 1)

Answers

Answer 1

The mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O is 0.113kgm^2

Two sections of the plate are possible. Segment (2) should be viewed as a negative part because it is a hole. The perpendicular distances from each segment's center of mass to point O are also shown.

The formula used to calculate the moment of inertia of segments (1) and (2). is Mass Moment of Inertia

m1 = π(0.2^2)(28) = 3.51kg

m2 = (0.2)(0.2)(28) = 1.12 kg

The parallel-axis theorem can be used to calculate the plate's moment of inertia for each segment along an axis perpendicular to the page and passing through point O.

I = ΣI' + md^2

I = [1/2x(3.51)x(0.2 )^2+3.51x(0.2 )^2]–[ 1/12x(0.8)x(0.2^2 + 0.2^2)+0.8x(0.2)^2]

I  = 0.113kg⋅m^2

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Determine The Mass Moment Of Inertia Of The Thin Plate About An Axis Perpendicular To The Page And Passing

Related Questions

In which graph is acceleration the slope?
A. Distance versus time

B. Acceleration versus time

C. Velocity versus time

D. Position Versus time

Answers

The graph of the slope's acceleration depicts velocity vs time.

reveals the solution.

The distance an object has travelled over time is displayed on a distance-time graph.

A straight-line graph of the time versus distance results is shown. The Y-axis displays the distance. The X-axis displays a time plot. Velocity changes occur more quickly on the graph with the sharpest slope.

It picks up speed the fastest. The acceleration of an item is shown by the slope of a velocity graph. As a result, the value of the slope at a particular time determines the item's acceleration at that specific instant.

A moving item is shown by a sloped line on a distance-time graph. The object's speed is equal to the gradient or slope of the line on a distance-time graph.

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Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency?

Answers

The frequency of the wave of the wind gusts is determined as 40 Hz.

What is frequency of a wave?

The frequency of a wave is the number of waves that pass a fixed point in a given amount of time. In other words, is the number of cycles completed by a wave in a given time period.

Mathematically, the relationship between frequency, velocity and wavelength of a wave is given as;

v = fλ

f = v / λ

where;

f is the frequency of the wavev is the velocity of the waveλ is the wavelength

f = (2 m/s) / (0.05 m)

f = 40 Hz

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Treating the nucleus as a Fermi gas, estimate the time it takes for a typical bound nucleon to cross the nucleus. Now, calculate the time for one revolution of a rigid rotor with j=2, I=5000amu fm2, and A= 208. You may find this helps justify the Nilsson model, where we treat the nucleon as if its orbiting around an essentially stationary rotor.

Answers

The time taken for one revolution of a rigid rotor to cross the nucleus is 6,240,000×10⁻¹⁵ sec .

Microwave rotational spectroscopy utilizes microwave radiation to quantify the energies of rotational advances for atoms in the gas stage. It achieves this through the communication of the electric dipole snapshot of the particles with the electromagnetic field of the astonishing microwave photon.

To test the unadulterated rotational advances for particles, researchers use microwave rotational spectroscopy. This spectroscopy uses photons in the microwave reach to cause changes between the quantum rotational energy levels of a gas particle.

We know that time taken to complete one revolution of a rigid rotor is

given by the formula J×(J+1)× B × h

where J is rotational quantum number,

B  or I is rotational constant

and h or A is value of atomic mass of the nucleus.

So, on putting we get

=>t=2×(2+1)×5000×208

=>t=2×3×5000×208

=>t=6,240,000fm-sec or

=>t=6,240,000×10⁻¹⁵ sec  

Hence, required time is 6.240,000×10⁻¹⁵ sec .

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a projectile is fired at an angle of 55 above the horizontal and has a maximum up[ward vertical diusplacement

Answers

A projectile being fired at 55 degrees after the magnitude of the horizontal component of the projectile's displacement is 40.2m

Initial velocity of projectile (v) = 35 m/s

Given Angle (θ)= 55°

Estimating, horizontal components of velocity

[tex]v_{x}[/tex] = v cosθ

= 35 cos 55°

= 20.1 m/s

Calculating the horizontal components of displacement after t = 2

d₂ = [tex]v_{x}t[/tex]

= 20.1 x 2

= 40.2 m

Projectile motion refers to the motion of an object or particle that is launched into a gravitational field, such as from the surface of the Earth, and travels along a curved path while only being influenced by gravity. An object that is fired into the air and only reacts to the acceleration of gravity is called a projectile.

The projectile's path is the name for the object's trajectory. A projectile is any object that is sent into space with only gravity acting on it. The primary force affecting a projectile is gravity. This doesn't mean that other forces don't have an impact; it just means that they have a much smaller one compared to gravity.

Note that the full question is:

A projectile is fired at an angle of 55° above the horizontal with an initial speed of 35.0 m/s. What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s?

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the op-amp circuit that has a capacitor as the feedback component and resistor at the inverting input is called a(n) . unity follower differentiator integrator summing amplifier

Answers

An integrator is an operational amplifier (op-amp) circuit with a resistor at the input terminal and a capacitor serving as the feedback component.

What purpose does a capacitor serve?

A capacitor is an insensitive electric component that contains an electrostatic signal of energy. Two components that are arranged close to and are electrically insulated from one another make up a capacitor, a device used to store electrical energy. A linear capacitor is a simple example of one such flash drive.

What rules the basic operation of a capacitor?

A capacitor works under the assumption that its permeability increases as a single conductor is brought close to another conductor. The upshot is that the structure has two major plates that are offset against one another and pointed in different directions.

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The index of refraction of a glass plate is 1.60. What is the Brewster's angle when the plate isin the following substances?(a) air1°(b) water2

Answers

The Brewster's angle when the plate is in the air is 58° and 50° when in water for the given refractive index of the glass plate.

What is Brewster's angle?

In most cases, at least a portion of the optical power of the light is reflected when it strikes a flat boundary between two different transparent materials. However, given a specific incidence angle known as Brewster's angle.

What is Refractive Index?

The refractive index of an optical material is a dimensionless quantity that indicates how well that material bends light. The refractive index controls how much light is refracted or curved when it enters a medium.

Calculations:

Brewster angle

       θB = tan-1 (n2 /n1)

For air

          θB= tan-1 (1.60 /1)

              = 58°

For water

          θB = tan-1 (1.60 / 1.33)  =50.2°

Hence, Brewster's angle when the plate is in the air is 58° and 50° when in water for the given refractive index of the glass plate.

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certain minerals are only stable in a small range of temperatures and as such can tell us what temperature the rock metamorphosed at. we call these geothermometry.

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Certain minerals are only stable in a small range of temperatures and as such can tell us what temperature the rock metamorphosed at. we call these geothermometry. This statement is false.

The 3 foremost minerals (magnetite, pyrrhotite, and ilmenite)  strongly interested in a magnet. Two varieties of rock – serpentine and ironstone are nearly usually magnetic.

As magma or lava cools, those minerals start to shape. At this point, the molten rock has no longer completely solidified, so the magnetic minerals floating inside the molten mass, end up aligned with the magnetic subject.

Water is discovered in interior rocks nearly anywhere, even very deep underneath the earth's floor where it's far particularly warm. The water inside hot rocks may be very warm as well, and when the fluid comes to the earth's floor, it can generate electricity.

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44Point Question and Brainliest.
two people need to answer or it won't let me give Brainliest.

During WWII Allied forces dropped food on German-occupied, famine-inflicted Netherlands called Operation Manna and Operation Chowhound. Food was dropped in bags from planes flying low (~ 400 ft). There were no parachutes. From a physics perspective imagine the food hitting the ground and how it would be different if parachutes were attached to the bags of food.

In three to five sentences, explain how the real and imagined scenarios falls compare. Include the effects of gravity, mass, and air resistance.

Answers

In the real scenario, the bags of food would have been dropped from the planes without parachutes, so they would have fallen to the ground under the force of gravity.

How will the real and imagined situation compare?

The food bags would have been dropped from the planes in the real scenario without parachutes, allowing gravity to bring them to the ground. They would have fallen faster because of the acceleration brought on by gravity. Air resistance would have caused the bags to descend a little more slowly as well. Depending on their mass and speed when they hit the ground, they would have impacted with a specific amount of kinetic energy.

The food bags would have been dropped with parachutes attached in the imagined scenario. The bags' descent would have been slowed by the parachutes, lowering the acceleration brought on by gravity. This would have decreased the bags' kinetic energy and speed before they touched the ground. The bags would have encountered air resistance as well, but due to the slower speed, this would have been less noticeable. If the bags had been dropped with parachutes, they would have landed with less force and kinetic energy overall.

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n empty bottle has a mass of 35.00 grams. When filled with water, it has a mass of 98.44 grams. Of the same bottle is filled with a different fluid, the mass is 89.22 grams. What is the specific gravity of this other fluid

Answers

The specific gravity of the liquid is 0.85

What is specific gravity of a liquid?

The specific gravity of a liquid is the relative weight of that liquid compared to an equal volume of water. It can also be called relationship density. Specific gravity has no unit

Therefore specific gravity of a liquid = weight of the liquid/ weight of water OR mass of the liquid / mass of water.

Mass of water = 98.44-35.00 = 63.44g

mass of the liquid = 89.22-35.00 = 54.22

Therefore the specific gravity of the liquid = 54.22/63.44= 0.85

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Which of the following statement is true of ATP? A. ATP stands for adenosine triphosphate
B. ATP consists of one adenosine atom and three phosphate atoms
C. ATP consists of one adPOenosine atom and two phosphate atoms
D. The breakdown of ATP provides the energy needed to fuel muscle contraction

Answers

The one that is accurate is that when the phosphate is broken down into ADP, ATP releases energy.

Does ATP save its energy in glucose form?

The energy that cells need is produced through the breakdown of glucose. More energy cannot be stored by ATP molecules than is released by the cells. In actuality, ATP doesn't retain as much energy as a glucose molecule. See the equation in the question; roughly 38 ATP molecules are produced for every glucose molecule.

How does ATP store energy?

The cell stores extra energy by reattaching a free phosphate molecule to ADP, converting it back into ATP. This extra energy can come from the breakdown of food that has been ingested or, in the case of plants, energy produced during photosynthesis.

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(a) Suppose a blood vessel’s radius is decreased to 89 % of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?

Answers

a). The pressure along the vessel in order to keep the flow rate at constant is 89 pascal.

b). Turbulence try to decreases flow rate, so that the pressure must need to increase after more to compensate at 89%.

The primary unit of stress is the pascal, described because the stress exerted through a pressure of 1 newton perpendicularly upon a place of 1 rectangular metre. In North America, however, the United States Customary System is preferred.

This is primarily based totally on Imperial devices which includes the pound (lb) and inch (in) or foot (ft). First, the resistance of float is inversely associated with the radius of the pipe. In different words, because the radius increases, there's extra room for the fluid to float through, and consequently the float charge increases.

a). Let x be the radius

then [tex]r_{2}[/tex] = x-89

pressure is inversely proportional to radius so, since pressure is constant there will be no change.

[tex]\frac{p_{2} }{p_{1} } =\frac{r_{1 }}{r_{2} } }\\\\\frac{p_{1} }{p_{1} } = \frac{x }{x-89+p } }\\\\\\1 = \frac{x }{x-89 } }\\\\x-89+P=x\\p=89[/tex]

So, pressure =89 pascal

b).  Turbulence try to decreases flow rate, so that the pressure must need to increase after more to compensate at 89%.

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A rotating wheel accelerates at a constant rate from an angular speed of 24 rad/s to 36 rad/s in a time interval of 3 s. What is the angle in radians through which the wheel rotates?

Answers

The angle in radians through which the wheel rotates is [tex]14207.511^{\circ}[/tex].

What is angular velocity?

In physics, angular velocity or rotational velocity, also known as angular frequency vector, is a pseudovector representation of how fast the angular position or orientation of an object changes with time.

Given

initial angular velocity [tex]$\omega_1=25 \mathrm{rad} / \mathrm{s}$[/tex]

Final Angular velocity [tex]$\omega_2=36 \mathrm{rad} / \mathrm{s}$[/tex]

time interval [tex]$t=3 \mathrm{~s}$[/tex]

using

[tex]$$\begin{aligned}& \omega_2=\omega_1+\alpha t \\& 36=25+2 \\& \alpha=1.5 \mathrm{rad} / \mathrm{s}^2\end{aligned}$$[/tex]

(b)Average angular speed [tex]$\frac{\Delta \theta}{\Delta t}$[/tex]

[tex]$$\begin{aligned}& \theta=\omega_1 t+\frac{1}{2} \alpha t^2 \\& \theta=25 \times 8+\frac{1}{2} \times 1.5 \times 8^2 \\& \theta=200+48=248 \mathrm{rad}\end{aligned}$$[/tex]

average angular speed [tex]$=\frac{\Delta \theta}{\Delta t}$[/tex]

[tex]=\frac{248}{8}=31 \mathrm{rad} / \mathrm{s}$$[/tex]

(c)Angle rotated =248 radians

(d)angles in degree [tex]$=14207.511^{\circ}$[/tex]

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I have multiple voltage sources of different rating like 5V,6V,1V and 20V draw schematic diagram using these sources to power a light of rating 11 volt

Answers

Answer:

add molecules

calculate the acceleration due to gravity on the surface of the sun. you can find the relevant data in appendix c of the text.

Answers

Use these uncertainties to estimate the biggest and smallest possible values you could get for gravity:

    g (low) = 2h / ( t + Δt )²

    g(high) = 2h / ( t - Δt )²

What is a simple definition of gravity?

The force that pulls items toward the center of a planet and other entity is called gravity. Each of the planets are kept in orbits around the sun by gravity.

Briefing:

First, choose an area where you can dump your small thing. Drop from a height that is sufficient to reduce the relative proportion of time needed to start and stop the stopwatch but not excessive enough to start affecting the outcome due to air resistance  One narrative is a decent middle ground.

The fall distance of the object is measured in meters. The entire course uses metric measurements only!

At least twenty times, time the thing falling.

Use the relationship to get the earth's acceleration owing to gravity (derived from calculus))

    g = 2h / t2

where t is the median fall time and h is the fall height.

To calculate your random uncertainty, use your spread in t values:

    Δt = (largest duration – lowest duration) / 2.

     g (low) = 2h / ( t + Δt )²

    g (high) = 2h / ( t - Δt )²

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The magnetic field inside a 4.0cm diameter superconducting solenoid varies sinusoidally between 8.0T and 12.0T at a freqency of 10Hz.
a) what is the maximum electric field strength at a point 1.5cm from the solenoid axis?
b) What is the value of B at the instant E reaches its maximum value

Answers

E max = 0.942 V/m is the maximum electrical field amplitude at a position 1.5 cm away from the solenoid axis.

An electric field is what?

The physical force that surrounds ionised objects and exerts force on every other energetic particles with in field, either attracting of repel them, is known as an electric field (or E-field). It can also refer to a collection containing charge particles' physical field.

Briefing

Diameter, D, equals 4 cm = 400 parts per million m

R = d/2 ≈ 0.04/2 = 0.02 metres for the circumference.

The electric potential is provided by Faraday's law;

Frequency; f = 10 Hz

From Faraday’s law, the electric field is given by;

E = -(r/2)(dB/dt)

We can formulate the magnetic field's equation as follows based on the magnetic field's variation:

B(t) = B_c + B_o*sin (2πft)

B(t) = 2sin(2*10t) + 10

Thus;

dB/dt = 40π cos 20πt

When cos 20t = -1, the electric field is at its maximum value.

(dB/dt)_max = -40π

Thus, with respect to the solenoid axis, at r = 1.5 centimeter = 0.015 m, we obtain;

E = -(0.015/2) × -40π

E = 0.942 V/m

What are the units used to measure mass and weight?; Are mass and weight measured in the same units?; What unit is mass measured in kilograms pounds Newton's?

Answers

Kilogram are the units used to measure mass and weight. The same units are used to measure mass and weight. A body's mass can be thought of as a measurement of its amount of matter.

And the SI unit of mass is Kilogram (kg). Weight is a measurement of how much gravity is pulling on a body. Weight is calculated using the method w = mg. Each item in physics has a unit that establishes its common measurement. Consequently, a physical quantity like mass has a unit as well. In International systems, SI, the mass is measured in Kilograms symbolised by symbol kg. Weight in this context is a vector quantity denoted by N and measured in Newton.

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Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.)
Largest Diameter
- main-sequence star of spectral type A
- Jupiter
- one-solar-mass white dwarf
- the moon
- a two-solar-mass neutron star
- the event horizon of a two-solar-mass black hole
Smallest Diameter
Feedback: Correct
The main-sequence star is obviously much larger than a planet such as Jupiter. A one-solar-mass white dwarf is about the size of Earth, which makes it larger than the Moon. A neutron star will be larger than a black hole of the same mass, because while light can escape from a neutron star, the same mass in a black hole must be more concentrated so that its gravity is strong enough to prevent light from escaping.

Answers

Objects based on their diameter, from largest to smallest are:

-main-sequence star of a spectral type A

-Jupiter

-a one-solar-mass white dwarf

-the Moon

-a two-solar-mass neutron star

-the event horizon of a two-solar-mass black hole

Earlier than then, observers had seen best 5 planets-Mercury, Venus, Mars, Jupiter, and Saturn. The sun is a celeb and is the most important object in the sun gadget. Its diameter is ready 1.4 million km. The sun is made normally of hydrogen gasoline.

From largest to smallest they're Universe, galaxy, sun machine, celebrity, planet, moon, and asteroid.

Astronomers at the NANOGrav Physics Frontiers middle have found the biggest neutron star ever recorded, which is nearly too huge to be in life. The pulsar, J0740+6620, is 2.17 times the mass of the sun and has a diameter of about 15 miles.

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which of the following graphs best predicts the solar energy output in the country in the northern hemisphere in december?

Answers

B graphs best predicts the solar energy output in the country in the northern hemisphere in December.

Any form of energy produced by the sun is known as solar energy.

Nuclear fusion occurs in the sun, which is how solar energy is produced. When two hydrogen atoms hit forcefully and combine to form a helium atom at the sun's core, fusion takes place.

This procedure, also referred to as a PP (proton-proton) chain reaction, produces a significant quantity of energy. The sun's core burns around 620 million tons of hydrogen per second. Other stars that like our sun in size experience the PP chain reaction, which supplies them with constant energy and heat. On the Kelvin scale, these stars have a temperature of roughly 4 million degrees (about 4 million degrees Celsius, 7 million degrees Fahrenheit).

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briefly outline the eight trace minerals reviewed in this week's readings, highlighting their primary function in the body and major food sources.

Answers

Answer:

college money

Explanation:

4. Two equal weights of 20 N are attached to the ends of a thin string which passes over three smooth pegs in a wall arranged in the form of an equilateral triangle with one side horizontal. Find the tension on each peg.​

Answers

Answer:

Tension in topmost peg = 40rt(5/3)

Tension in other pegs = 40/rt(3)

Explanation:

Note point: I am taking T as a vector quantity and not scalar.

If the tension in the horizontal pegs is T, then the tension in the topmost peg will be T + T.

Lets find the magnitude of the vector T

|T| = 20/cos 30 can be easily seen by drawing FBD

    = 40/rt(3)

Then, tension in topmost peg = rt{1600/3 + 1600/3 + (3200/3)*1/2}

= rt{(3200/3)*(5/2)} = rt(8000/3)

5. A 1500-kg car makes a u-turn with a radius of 25m. If the coefficient of static friction between the tires and the road μs = 0.42, what is the greatest speed the car can have without skidding (m/s)?

Answers

The maximum speed of the car was found to be 10.14 ms-1.

Define coefficient of static friction ?

A number that expresses how sticky an object is to its contact surface while it is stationary is known as the coefficient of static friction.

It is the ratio of the normal force imposed on the body to the static friction present between two contact surfaces.

Consider the three categories of dry friction: rolling friction, kinetic friction, and static friction.

Generally speaking, rolling friction and kinetic friction coefficients are lower than the coefficient of static friction.

Because static friction is greater than kinetic friction and rolling friction, this is the case.

This suggests that if an item is immobile, it will take greater effort to start it moving.

Rolling friction often has the least friction since it is greater in kinetic friction than rolling friction.

Fr=μs|n|

g=9.81

Fc=mv^2max/R

mv^2max/R=μsmg

v^2max=μsgR

vmax=√(0.42)(9.81)(25)

=√103.005

vmax =10.14 ms-1

The maximum speed of the car was found to be 10.14 ms-1.

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If m1 is 50 kg and has a velocity of 4 m/s, and m2 is 75 kg and has a velocity of -1 m/s, then what would be the final velocity of object 2 if the two objects collide and bounce off of each other and object 1 has a final velocity of -2 m/s?

Answers

The final velocity of object 2 is: 3 m/sec

What is the conservation of mass?

According to the rule of conservation of mass, no atoms are created or destroyed during a chemical process. Instead, the atoms combine in a variety of ways to create goods. This explains why each element has the equal amount of atoms on both sides of an equation with balanced symbols.

According to conservation of mass,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Given that,

m₁ = 50 kg

m₂ = 75 kg

u₁ = 4 m/s

u₂ = -1 m/s

v₁ = -2 m/s

v₂ = ?

Now, putting the values,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(50 × 4) + [75 × (-1)] = [50 × (-2)] + (75 × v₂)

or, 125 = -100 + 75 v₂

or, 75 v₂ = 225

or, v₂ = 3 m/sec.

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The dynamo theory states that Earth's magnetic field is created in the ...

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The dynamo theory states that Earth's magnetic field is created in the planet's outer core.

The dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field.

Dynamo theory describes the process through which a rotating, convecting  and electrically conducting fluid acts to maintain a magnetic field. This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies.

There are three requisites for a dynamo to operate:

An electrically conductive fluid medium, Kinetic energy provided by planetary rotation, An internal energy source to drive convective motions within the fluid.

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when light strikes a window pane some rays will be reflected back and forth in between the two glass surfaces. why do these reflected rays not produce visible colored interference fringes?

Answers

Yes, and the colors you see will now be the colors your eye perceives when you see the wavelengths producing the interference patterns.

In physics, the wavelengths is the length over which a periodic wave repeats or its spatial period. It is the separation between neighboring wave points that correspond to the same phase, such as two adjacent crests, troughs, or zero crossings. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. The spatial frequency is the wavelength's reciprocal. The Greek letter lambda (), which represents wavelength, is frequently used. When describing modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids, the term wavelength is also occasionally used.

Wavelength is inversely related to frequency for a sinusoidal wave flowing at a constant speed.

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The reflected rays of light do not produce visible colored interference fringes in a window because the glass structure of a window pane prevent.

In the case of the window pane, it is true that the light is still reflected on the front and rear surface of the glass. the reflecting medium need to have a thickness that the that is comparable to the wavelength of light. windows are simply too thick. Due to the structure of glass, No Interference. In the case of thin film both reflected rays belong to the same waveform. light striking a film is partially reflected and partially refracted at the top surface. the refracted ray is partially reflected at the bottom.

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Jan Baptista van Helmont's famous experiment incorrectly showed that the plants produce most of their mass from:

Answers

Jan Baptista van Helmont's famous experiment incorrectly showed that the plants produce most of their mass from water.

In physics, mass is used to express inertia, a property common to all matter. In essence, it is the resistance of a mass of matter to changing its course or speed in response to the application of a force. The more mass a body has, the less of a change an applied force makes. Using Planck's constant, the kilogram, the ISU's unit of mass, is equivalent to 6.62607015 1034 joule seconds (SI). One kilogram is multiplied by one square meter per second to produce one joule. Since the second and the meter have already been defined in terms of other physical constants, the kilogram is determined by precise measurements of Planck's constant.

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a 31000-kg open railroad car, initially coasting at 0.925 m/s with negligible friction, passes under a hopper that dumps 120000 kg of scrap metal into it.

Answers

The final velocity of the loaded freight car is [tex]$0.182 \mathrm{~m} / \mathrm{s}$[/tex].

What is Velocity?

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

The mass of freight car, m₁ = 31000-kg

Velocity of freight car, u₁ = 0.925 m/s

Mass of hopper, m₂ =  120000 kg

(a) Let[tex]$v$[/tex] is the final velocity of the loaded freight car. Initial momentum of the car before the dump, [tex]$p_i=31000 \mathrm{~kg} \times 0.925 \mathrm{~m} / \mathrm{s}=28,675 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$[/tex]

Final momentum, [tex]$p_f=(31000 \mathrm{~kg}+ 120000 \mathrm{~kg}) v=1,51,000\mathrm{v}$[/tex]

According to the conservation of momentum,

initial momentum = final momentum

[tex]25500 \mathrm{~kg}-\mathrm{m} / \mathrm{s}=140000 \mathrm{v}$$v=0.182 \mathrm{~m} / \mathrm{s}$[/tex]

So, the final velocity of the loaded freight car is [tex]$0.182 \mathrm{~m} / \mathrm{s}$[/tex].

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the current i in a long, straight wire is constant and is directed toward the right as in (figure 1). conducting loops a, b, c, and d are moving, in the directions shown, near the wire.

Answers

Answer: The directions shown, near the wire is moving anticlockwise

Explanation:

When the current in the wire AB decreases, the magnetic flux linked with the loop (which is out of the page) will decrease. Hence, the current induced in the loop must be anticlockwise to oppose the decrease in magnetic flux.

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protons having a kinetic energy of 5.20 mev are moving in the positive x-direction and enter a magnetic field of 0.0550 t in the z-direction, out of the plane of the page, and extending from x. 0→x=1m as shown in Fig.
a. Calculate the y-component of the protons' momentum as they leave the magnetic field.
b. Find the angle ϕ between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Ignore relativistic effects and note that 1eV=1.60×10−19J.

Answers

a)  The y-component of the protons' momentum as they leave the magnetic field is 8.8 x 10-21 kg m/s

b) The angle ϕ between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field is  9.812821°

Since are given with the kinetic energy of  5.20 Mev (8.32X 10^-13J), and  a magnetic field of 0.0550 t in the z-direction.From the diagram we can see  that, p(Y) =mv sin θ

=> sin θ =1/R , where R = mv/eB

=>sin θ = eB/mv

=>eB= mv sin θ

=> Py(the momentum) = eB =1.60×10−19J*0.0550 =  8.8 x 10-21 kg m/s .In the second case, sin θ  =  eB/mv, since the kinetic energy is 5.20 Mev

=>1/2 mv² =  5.20 mev = 8.33132e⁻¹⁹

=> v = √(2* 8.33132e-19 / 1.6 x10⁻²¹) = 32.27 m/s²

Now sin φ = eB/mv

=>sin φ =  8.8 x 10-21/ 1.6 x10^-21* 32.27 = 0.17043

=>φ = sin-1(0.17043)  = 9.812821°

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A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a stationary 10.0 kg penguin. After the collision the 15.0 kg penguin is traveling at a velocity of 4.2 m/s 20.0o S of E.
a. What is the velocity of the 10.0 kg penguin after collision?
b. is this collision elastic or inelastic?

Answers

The velocity of the 10.0kg stationary penguin after collision with a 15.0 kg penguin which has a velocity of 7.0m/s is 4.2m/s and the collision is inelastic.

Whether it is an elastic or nonelastic collision is the momentum of the system will remain the same, which is also known as the law of conservation of momentum

m1v1+m2v2 = m1u1+m2u2

where,

m1 = mass of the first object

m2= mass of the second object

v1= velocity of the first object before the collision

v2=velocity of the second object before the collision

u1=velocity of the first object after collision

u2=velocity of the second object after collision

So,

15×7 +10×0 = 15×4.2 +10×u2

⇒105 = 63 + 10×u2

⇒u2 = 4.2

Since in this whole process the loss of kinetic energy is happening via the form of heat, light, and sound so it is an inelastic collision

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an atomic spectrum contains a line with a wavelength centered at 402 nm . careful measurements show the line is really spread out between 401 and 403 nm . estimate the lifetime of the excited state that produced this line.

Answers

The lifetime of the excited state that produced this line is 416.66sec if a wavelength ranges from 401nm and 403nm.

For solving this problem we use Rydberg equation whose formula is given by

v=[(1 / λ₁) -1 / λ₂)]×(h×c)

where v is the frequency of the photon,

λ is the wavelength of the photon

h is plank's constant

and c is the speed of light in vacuum

Since we are given λ₁ ,λ₂ as 401nm and 403nm respectively.Also we know that value of h is 6.6ˣ10⁻³⁴(J-sec)/m and c=3ˣ10⁸m/sec

So,putting all values on above formula,we get

=>v=[(1/401)-(1/403)]ˣ(6.6ˣ10⁻³⁴) ˣ (3ˣ10⁸)

=>v=[(403-401) ˣ (6.6ˣ10⁻³⁴) ˣ (3ˣ10⁸)] / (401 ˣ 403)ˣ(1/10⁻²⁷)

=>v= [[2 ˣ (6.6ˣ10⁻³⁴) ˣ (3ˣ10⁸)] ₓ(1/10⁻²⁷)] ˣ (1 / 401 ˣ 403)

=>v=(39.6 ˣ 10) / 161603

=>v = 396/161603

=>v = 0.0024/sec

We know time period is reverse of frequency, so  lifetime span is

=>t=1/v

=>t=1/ (0.0024/sec)

=>t=416.66sec

Hence, lifetime of the excited state is 416.66sec.

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