in an oscillator consisting of a spring and a block, the amount of kinetic energy reaches maximum when:

These forces will produce a resultant force with the greatest magnitude when angle between them is 0° .

When an object with mass is pushed or pulled, it changes its velocity, according to the definition of force in physics.

Force is an external agent that has the power to alter a body's resting or moving condition. It has a size and a movement. The direction of the force is referred to as the force's direction, and the application of force is the place at which the force is applied.

Given that: two 20. newton forces act concurrently on an object.

If the angle between the forces is α then resultant force be:

= √(20² + 20² +2.20.20cosα)

Hence, these forces will produce a resultant force with the greatest magnitude when angle between them is 0° and the  the greatest magnitude of resultant force be 40 N.

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The mass of the planet and star is [tex]2.4 *10^{25}[/tex] kg and [tex]1.2 * 10^{31}[/tex] kg respectively.

Acceleration due to gravity is the force experienced per unit mass of an object due to gravitational force and it is given by:

[tex]a = \frac{GM_{planet} }{r^{2} }[/tex]

[tex]19.5 =\frac{6.67 * 10^{-11} * M_{planet} }{(0.9 * 10^{7}) ^{2} }[/tex]

[tex]M_{planet} = 2.4 * 10^{25}[/tex] kg

Now this planet orbits a star and so we can use Kepler's Third Law to find the mass of the star.

[tex]T^{2} = \frac{4\pi ^{2} }{GM_{star} } r^{3}[/tex]

T = 402 earth days = 60 x 60 x 24 x 402 = 34732800 seconds

[tex]34732800^{2} = \frac{4\pi ^{2} }{6.67 * 10^{-11} M_{star} } (2.9 * 10^{11}) ^{3}[/tex]

[tex]M_{star} = 1.2 * 10^{31}[/tex] kg

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The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg

g = G M / r

g = Acceleration due to gravity

G = Gravitational constant

M = Mass of star

r = Distance between both bodies

g = 63.6 m / s²

G = 6.67 * 10⁻¹¹ N m² / kg²

r = 8.6 * 10¹¹ m

Ms = 63.6 * 8.6 * 10¹¹ / ( 6.67 * 10⁻¹¹ )

Ms = 82 * 10²² kg

F = G M m / r²

F = m g

Equating,

m g = G M m / r²

Mp = g r² / G

Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹

Mp = 8.58 * 10²⁵ kg

Therefore the mass will be equal to 8.58 * 10²⁵ kg

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The magnetic field in the solenoid is 2.674*10^-3T at 5.90 A of current. The solenoid has a 6.936*10^-5H self-inductance. 1.2072*10^-3J of energy is held in the magnetic field.

The magnetic field has a 2.846 J/m^3 energy density. We obtain 2.846 J/m^3 by dividing your response to part C by the solenoid's volume. An electric charge, an electric current, and magnetic materials are all affected magnetically by a magnetic field, which is a vector field. A solenoid is a particular kind of electromagnet that produces a regulated magnetic field and is made of a helical coil of wire whose length is significantly higher than its diameter.

The magnetic field in the solenoid'

L = Mo*N*I/2*pi*r L = 4*pi*10^-7*340*5.90/28*pi*(0.15m),

where the current is 5.90 A, is equal to 2.674*10^-3T.

a solenoid's internal inductance

The magnetic field's stored energy, L, is given by L = Mo*N2*I/2*pi*r = 6.936*10^-5H.

Ul = 1/2*L*I Ul = 1/2*6.936*10-5*(5.90)2

Ul = 1/2*1.2072*10^-3J.

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Answer: The internal energy within a system associated with the motion of particles and that can be added to a substance is called kinetic energy.

Reason:

Internal energy U of a system or a body with well-defined boundaries is the total of the kinetic energy due to the motion of molecules and the potential energy associated with the vibrational motion and electric energy of atoms within molecules.

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The muscle force on the calcaneus is -14.41 N

Forces are external factors that change the state of the body at rest or in motion. It has size and direction. The direction in which the force acts is called the direction of the force, and the point at which the force acts is called the point of action of the force. It's SI unit is the Newton (N). A force vector F has magnitude, direction, and orientation.

As the foot is in equilibrium it means that the net force is zero, the equation for this system is as follows:

N + F + W = 0

-N -F = W

Where,

N = Normal (10 N)

F = Muscle force

W = Weight

W = m × g

W = 0.45 × 9.8

W = 4.41 N

Now substitute the values in following equation:

-N -F = W

-10 -F = 4.41

-F = 4.41 + 10

-F = 14.41

F = -14.41 N

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Travel seems to be the movement of individuals between far-off geographic sites, therefore if a suv could drive 296 miles in 8 hours, he would travel around 370 miles in 10 hours.

The physics of time travel. According to some concepts, most notably special and general relativity, certain geometries of spacetime or particular motions in space might permit time travel into the possible futures if they were real.

The simplest explanation is that time travel is not feasible because if it were, we'd be doing it by now. The laws of thermodynamics or relativity, for example, could be used to support the claim that it is against the laws of physics.

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The primary coil of a transformer, which has 59 turns, receives 80 v from a generator. The secondary voltage will be 530 if the secondary coil has 530 turns IS 718.644 V

For an ideal transformer

Vs/Vp=Ns/Np

Given that primary voltage V =80 V

Number of turns in primary N = 59 turns

Number of turns in srcondary Ng = 530 turns

Therefore

Vs/80=530/59

Hence voltage across secondary V = 8.98*80 V

=718.644 V.

Voltage is the quantity of potential charge that exists between two points on a circuit. One idea is charge more strongly than another. Voltage refers to the difference in charge between the two points. Volt, denoted by the symbol "V," is the accepted unit of measurement for the voltage expression.

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Yes,Sometimes friction does positive work

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact.

Friction is a type of contact force and one of it's best advantage is that it enables walking and enables the application of brake in vehicles and other automobile.

Though friction has many disadvantags like wear and tear of material, loss of heat energy and reducing efficiency but it also have some positive effect in daily life as mentioned above.

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Capacity factor = actual output / maximum feasible output is the formula. The maximum output for a wind turbine would be equal to the capacity times 8760 hours (there are 8760 hrs in a year).

Consequently, the Northwind 100C's maximum output is 95 kW x 8760 hours per year, or 832,200 kWh per year (or 832.2 MWh). The quantity produced is a function of the total input amounts of each ingredient, and the production function is represented as Q = f(K, L, P, H). Of course, not every firm needs the same number of inputs or production components.

The total product for every input degree is equal to the sum of the marginal products of all previous units of that input. The sum of marginal products is therefore the total product.

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The total resistance of the four resistors connected in parallel is 0.762 ohms.

To calculate the total resistance of the four resistors connected in parallel, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation equation 1

Hence, the total resistance is 0.762 ohms.

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The moving plane is visible for 0.8 second.

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity. SI unit of speed be meter/second and CGS unit of speed be cm/s.

Given that:

Another plane lands and passes the stationary plane at a speed: v =  45 m/s.

length of the arriving plane be : L = 36 m.

So, Time the moving plane remains visible be: t = L/v = 36/45 s = 0.8 second.

Hence, the moving plane is visible for 0.8 second.

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Intensity of light is a measurement of the amount of power either emitted or reflected by a source, and it can be calculated using either the total wave output, luminosity, or brightness. passing through polarized sheets

How to calculate intensity of light passing through polarized sheet ?

The intensity of unpolarized light , Iⁿ = 28 W/m²

The intensity of light passing through, I¹= 0.5 × Iⁿ

I¹ = 14 W/m²

The intensity of light passing through the second polarizer , I² = I¹ × (cos(theta1 + 90 - theta2) )²

I² = 14 × cos^2(40 + 90 - 20) W/m²

I² = 1.64 W/m²

The intensity of light passing through the third polarizer , I³ = I²× (cos(180 - theta2 - theta1) )²

I³ = 1.64 × cos^2(180 - 20 - 20) W/m²

I³= 0.962 W/m²

The intensity of light passing through the fourth polarizer , I⁴= I³ ×(cos(theta3 + 90 + theta4) )²

I⁴ = 0.962 * cos^2(28 + 90 + 20) W/m²

I⁴ = 0.53 W/m²

The intensity of the light that emerges from the system is 0.53 W/m²

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The supplied statement states that perhaps the system's light output has a 0.53 W/m² intensity.

The rate at which a wave moves over just a substrate in a given amount of time and space is referred to as its intensity. It is additionally equal to the wave speed times the power density. It is commonly evaluated in Watts per square meter. The intensity of a beam depends on its height and power.

Here,

The intensity of unpolarized light , I0 = 28 W/m²

The brightness of the light that comes through I1 = 0.5 * I0

I1 = 14 W/m²

Light output through to the second polarizer, measured in intensity,

I2 = I1 * (cos(∅1 + 90 - ∅2) )²

I2 = 14 * cos²(40 + 90 - 20) W/m²

I2 = 1.64 W/m²

Light output through the third polarizer, in terms of intensity I3 = I2 * (cos(180 - ∅2 - ∅1) )²

I3 = 1.64 * cos²(180 - 20 - 20) W/m²

I3 = 0.962 W/m²

The fourth polarizer's ability to intensify light,

I4 = I3 * (cos(∅3 + 90 + ∅4) )²

I4 = 0.962 * cos²(28 + 90 + 20) W/m²

I4 = 0.53 W/m²

The process delivers sunlight that has a 0.53 W/m² intensity.

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The complete question is-

In the figure, unpolarized light with an intensity of 28.0 W/m2 is sent into a system of four polarizing sheets with polarizing directions at angles θ1 = 40.0˚, θ2 = 20.0˚, θ3 = 20.0˚, and θ4 = 28.0˚, What is the intensity of the light that emerges from the system?

The tangential velocity of the object if it is moving in a circle of radius 2 m is

6.28 m/s

It is given that

time taken to move in circle = 2 seconds

radius of circle = 2m

Tangential velocity is equal to the circumference of the circle divided by the time it takes to make one full rotation: 2*pi*r/t

Tangential velocity = 2πr/t

= 2 x 3.14 x 2/2 = 6.28 m/s

Hence, tangential velocity of the object if it is moving in a circle of radius 2 m is 6.28 m/s

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Your body is pulling on the Earth with the same reaction force that the Earth is pulling on you.

The gravitational force, which is what pushes mass-containing objects toward one another. We frequently consider the pull of gravity from the Earth. Your body is kept on the ground by this force. However, all mass-bearing objects are pulled toward one another by gravity.

An action force with an opposite direction has an effect called a reaction force. These two forces—also referred to as action and reaction forces—are covered by Newton's third law of motion. According to Newton's third law, there is an equal and opposite reaction to every action.

The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass times the acceleration due to local gravity.

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The power rating of the engine of a 1000 kg car that can accelerate the car from 0 to 27m/s in 4.3 seconds in watts is 84767 W and kilowatts is 84.767 KW

a = ( v - u ) / t

a = Acceleration

v = Final velocity

u = Initial velocity

t = Time

v = 27 m / s

u = 0

t = 4.3 s

a = ( 27 - 0 ) / 4.3

a = 6.279 m / s²

F = m a

F = Force

m = Mass

m = 1000 kg

F = 1000 * 6.279

F = 6279 N

s = u t + 1 / 2 a t²

s = 0 + ( 1 / 2 * 6.279 * 4.3² )

s = 58.1 m

W = F s

W = Work one

s = Displacement

W = 6279 * 58.1

W = 364496 J

P = W / t

P = Power

P = 364496 / 4.3

P = 84767 W

P = 84.767 KW

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The curve that most accurately depicts how the average heat transfer coefficient decreases with the length of the plate is increasing for a laminar flow of air over flat plates with uniform surface temperature.

Laminar flow in fluid dynamics is characterized by fluid particles travelling in layers along clean routes, passing each other without much or any mixing between them. Adjacent layers slide past one another like playing cards when the fluid is moving at low speeds because it tends to Laminar flow without lateral mixing. Convective heat transfer between a fluid medium (a fluid) and the surface (a wall) it flows over is quantified by the heat transfer coefficient. heat transfer coefficient can be seen in the Newton-Richmann relation as a proportionality factor.

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There are plenty billions of galaxies in the universe, and each galaxy has many thousands of stars. The best choice is A.

Countless stars, solar, gas, and dust make up a galaxy. Gravity holds a galaxy together. A supermassive black holes also resides in the center of our galaxy, namely Milky Way. You see additional stars in the Cosmos as you look up there at night sky for the stars.

Galaxies are enormous islands in space made up of stars, plasma, dust, and gravitational waves that are bound together by gravity. Whether galaxies are found alone, in small groupings, or as part of enormous clusters, Hubble's acute vision has uncovered precise details about their shapes, structures, and histories.

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The inductance is 680µH if the induced emf is 17 v and the rate of change of the current is 25 ka/s.

The magnetic field will change as a result of growing current, so the inductor will resist the flow of current through it, resulting in a decrease in current.

e=induced emf=17V

e=Ldi/dt [di/dt=25000a/s]

17=L×25000

17/25000=L

0.00068=L

680×10⁻⁶Henry

=680µH

Inductance=680µH

The amount of energy delivered per unit of electric charge by a power source, such as a generator or a battery, is known as electromotive force (abbreviated E or EMF).

Energy is converted from one form to another as the generator or battery operates on the electric charge that is carried inside itself. Positive charge is applied to the device's positive terminal, whereas negative charge is applied to the device's negative terminal. The work done on an electrical charge unit, or the energy acquired per electrical charge unit, is known as the electromotive force. It is also referred to as EMF and is denoted by the international metric system's letter E.

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The gauge pressure at the oil-water interface and at the bottom of the barrel is 705.6 Pa and 3155.6 Pa.

The barrel contains 0.10m of oil and floating on water that is 0.250mm deep.

The density of the oil is given to be 600 kg/m³.

a) The gauge pressure at the oil water interface is given by,

P = pgh

Where,

p is density of oil and h is the hieght of the oil,

Putting values,

P = 0.120 x 600 x 9.8

P = 705.6 Pa.

So, thr pressure at oil-water interface is 705.6 Pa.

(b) The pressure at the bottom of the barrel can be found as,

P = pgh + pxH

Where,

H is the height of the water and x is the density of water,

Assigning value,

P = 705.6 + 1000 x 9.8 x 0.250

P = 705.6 + 2450

P = 3155.6 Pa.

So, the pressure at the bottom of the barrel is 3155.6 Pa.

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Angle of axis of a polarizing filter would be 0.22°.

Malus law explains, "whenever a light beam is passing through any polarizer, the intensity of the resultant beam is less than that of the incident beam." Let I and I₀ be the resultant and incident beam, and ∅ be the angle of the polarizer. So, the resultant intensity is given by:

I = I₀cos²∅

cos²∅ = [tex]\frac{I}{I_{0} }[/tex]

          = [tex]\frac{50W/m^{2} }{1.0 kW/m^{2} }[/tex]

          = 0.05

cos∅ = [tex]\sqrt{0.05}[/tex]

    ∅ = 0.22°

What's the process of a polarizing filter?

Light that vibrates in one way can pass through polarizing filters, while light that vibrates in the opposite direction is absorbed. Scientific tools make considerable use of these filters.

Why, in physics, is a polarizing filter useful to a photographer?

Circular polarizing filters decrease reflections coming from the objects you are photographing and screw into the thread of your lens. This may result in a darker, richer sky color and the ability to see through water and windows that would otherwise just reflect surface reflections.

What impact does polarization have?

Polarization is a phenomenon that makes batteries function worse. The electrode potential is displaced from equilibrium by this impact. Activation and concentration are the two different kinds of polarization.

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Mechanical waves and electromagnetic waves are the two major modes of energy transportation on Earth. Air and water waves produced by sound are examples of seismic wave.

Electromagnetic waves, as opposed to physical phenomena, may move across empty space. This suggests that pulses may travel through void spaces as well as through solid substances like air and rock.
Since their wavelengths are measured in millimeters, microwaves are shorter than radio waves. Microwaves are used in radar that aids in weather forecasting, food preparation, and information transmission. Because they can pass through smoke, clouds, and light rain, microwaves are useful for communication.

Infrared waves lie between microwaves and visible light. There are two subcategories of infrared waves: near infrared and far infrared. The waves with wavelengths closest to visible light are known as near infrared waves. Your television remote uses these infrared radiation to change channels.

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The resulting acceleration of proton, compared to the electron's acceleration is in the opposite direction and at a similar rate.

Acceleration is a vector quantity that has elements in both the x- and y-axes. The final acceleration of the item can be calculated by calculating the vector's magnitude and direction.

The proton will accelerate in the opposite direction and at a similar rate because its mass is greater than that of the electron. The acceleration of the proton, however, is less than that of the electron.

In conclusion, the proton's subsequent acceleration would be smaller in amplitude and in the opposite direction from the electron's.

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The calculated value is 5.6 m. Much more frequently than sound intensities in watts per square meter, sound intensity levels are expressed in decibels (dB).

Both the scientific literature and the public media use decibels as their preferred measurement unit. The rationale behind this decision of units has to do with how we hear. Noise exposure is harmful to the hearing, and it is normal for musicians to suffer from hearing loss that is so severe that it affects their ability to play. Sound intensity, a term that applies to all noises, whether or not they are heard, is the pertinent physical quantity.

We are given Δp, so we can calculate I using the equation I=(Δp)22ρv . Using I , we can calculate β straight from its definition in β (dB)=10 log10(II0) β (dB)=10 log10(II0) .

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The final velocity of the object are Vaf = 0 and Vbf = 6 m/s as a result of an elastic collision between a 10 kilogram mass traveling at 2 m/s and a 2 kg mass moving at 4 m/s.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

Briefing :  Let the  Vₐ= velocity of a, and Vb= velocity of b

Initial speed of object a with mass 10 kg = 2m/s , and initial speed of object with mass 2 kg = 4m/s

therefore , initial momentum (Pi = 10×2 - 2 × 4) = 12kgm/s  is initial momentum . Pi = 12 kgm/s

then we have final momentum (Pf = 10 Va + 2 Vb), therefore  Pi=Pf ,

12 = 10 Va + 2 Vb    

=  5 Va + Vb = 6 ------------equation (1)

according to newton equation we have , e = vel of seperation /vel of approach

e = (Vb - Va)   =1           =   Vb -Va = 6   -------------equation (2 )

         6                    

hence solving both equation (1)&(2), we get Vaf=0 final velocity of a  and Vbf= 6m/s final velocity of b.

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The correct option is (c) andromeda galaxy as it was originally classified as nebula.

A nebula is a distinctively luminous region of the interstellar medium, which is mainly made up of of cosmic dust, neutral, neutrally ionised, or molecular hydrogen. Nebulae are usually areas where stars develop.

Initially, any diffused astronomical object, including galaxies outside the Milky Way, was referred to as a "nebula."

Before Vesto Slipher and Edwin Hubble revealed the real nature of galaxies in the early 20th century, the Andromeda Galaxy, for instance, was originally known as the Andromeda Nebula.

So, Andromeda Galaxy was originally classified as nebula.

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Two forces produce the same torque but this will not ensure that they have the same magnitude of torque because torque is the product of force times distance.

T = F * d

where:

T = torque [N*m]

F = force [N]

d = distance [m]

We can see in the above equation, that increasing the distance increases torque proportionally.

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1)Now as we increase more bulb in series n increase to (n+1),so the total resistance of the circuit increases.

2)Current increases if number of bulb in series decreases.

Equivalent of the circutes

R=∑P=nn

so resistence increases

i=V/R=V/nn

current i'=V/n'R

i'/i=n/n'

since n'>n

i'<i

so current increases

Resistance is the degree to which a substance obstructs or opposes an electric current. Electron flow is referred to as electric current. To better understand resistance, imagine how difficult it would be for a person to move from one shop to another in a crowded market. The opposition a substance provides to the flow of electrical current is referred to as resistance. The capital letter R is used to symbolize it. The ohm, sometimes written as a word and sometimes represented by the uppercase Greek letter omega, is the commonly used unit of resistance.

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The flow rate is 3.1175×10⁻³ m³/s.

Explanation:

By using Bernoulli's principle:

where the pipe is horizontal,

x₁ = x₂ hence the above equation becomes

since the flow rate is constant then

Q = v₁A₁ = v₂A₂

Where is the area of the two sections given by A₁ = π·D₁²÷4 and

A₂ = π·D₂²÷4

Therefore, A₁ = π·0.08²÷4 = 5.02×10⁻³ m²

and, A₂ = π·0.05²÷4 = 1.96×10⁻³ m²

v₁ = v₂A₂/A₁ =0.391×v₂

The given pressures are P₁ = 33.0 kPa and P₂ = 25.0 pKa and

ρ = 1000 kg/m³

By putting the values into the above equation we get,

33.0 kPa +0.5× 1000 kg/m³× (0.391×v₂)² = 25.0 pKa +0.5×1000 kg/m³×v₂²

= 33000+76.3·v₂² =25000+500·v₂²

=33000-25000

or 423.706·v₂² = 8000

v₂² = 8000/423.706 = 18.88 or  v₂ = 4.065 m/s and  v₁ 0.391×4.065 = 1.59 m/s

The flow rate = v₂A₂ = 1.59×1.96×10⁻³ = 3.1175×10⁻³ m³/s

Hence, Q= 3.1175×10⁻³ m³/s

The volume rate of flow is Q= 3.1175×10⁻³ m³/s.

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The flow rate is 3.1175×10⁻³ m³/s.

Bernoulli's principle states that an increase in the speed of a fluid (such as air or water) results in a decrease in pressure. This is due to the fact that faster-moving fluids have lower pressure, while slower-moving fluids have higher pressure. This principle is also applicable to the behavior of objects moving through a fluid. The faster the object moves, the lower the pressure around it. This is why objects like planes and boats are able to "fly" or "float" because the decrease in pressure around them causes a lift. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who first described it in 1738.

By using Bernoulli's principle:

where the pipe is horizontal,

x₁ = x₂ hence the above equation becomes

since the flow rate is constant then

Q = v₁A₁ = v₂A₂

Where is the area of the two sections given by A₁ = π·D₁²÷4 and

A₂ = π·D₂²÷4

Therefore, A₁ = π·0.08²÷4 = 5.02×10⁻³ m²

and, A₂ = π·0.05²÷4 = 1.96×10⁻³ m²

v₁ = v₂A₂/A₁ =0.391×v₂

The given pressures are P₁ = 33.0 kPa and P₂ = 25.0 pKa and

ρ = 1000 kg/m³

By putting the values into the above equation we get,

33.0 kPa +0.5× 1000 kg/m³× (0.391×v₂)² = 25.0 pKa +0.5×1000 kg/m³×v₂²

= 33000+76.3·v₂² =25000+500·v₂²

=33000-25000

or 423.706·v₂² = 8000

v₂² = 8000/423.706 = 18.88 or  v₂ = 4.065 m/s and  v₁ 0.391×4.065 = 1.59 m/s

The flow rate = v₂A₂ = 1.59×1.96×10⁻³ = 3.1175×10⁻³ m³/s

Hence, Q= 3.1175×10⁻³ m³/s

The volume rate of flow is Q= 3.1175×10⁻³ m³/s.

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The difference between the pressure on a pool's bottom and the pressure on the water's surface is approximately 14 feet or 168 inches deep. Fresh water has a density of 1 psi per 27.7 inches of depth.

Holding a knife against a piece of fruit will demonstrate pressure in an easy way. It won't cut the surface of the fruit if you press the flat part of the knife against it. A sizable area is affected by the force (low pressure).

The force applied physically to an object is referred to as pressure. Per unit area, the force is applied perpendicularly to the surfaces of the objects. The fundamental pressure formula is F/A. (Force per unit area). The Pascal unit of pressure (Pa). The four different types of pressure are gauge, absolute, atmospheric, and differential.

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Ra = 32.1 m far is the speaker from each observe .

In physics, the power supplied per unit area is known as the intensities or flux of cosmic rays, where the area is expressed on a plane plane perpendicular of the energy's propagation.

Briefing :

Let's solve this problem in parts, let's start by finding the intensity of the sound in each observer

observer A β = 64 db

            β = 10 log Iₐ / I₀

where I₀ = 1 10⁻¹² W / m²

             Iₐ = I₀ 10 (β/ 10)

let's calculate

             Iₐ = 1 10⁻¹² (64/10)

             Iₐ = 2.51 10⁻⁶ W / m²

Observer B β = 85 db

            I_b = 1 10-12 10 (85/10)

            I_b = 3.16 10⁻⁴ W / m²

now we use that the emitted power that is constant is the intensity over the area of ​​the sphere where the sound is distributed

             P = I A

therefore for the two observers

            P = Ia Aa = Ib Ab

the area of ​​a sphere is

              A = 4π R²

we substitute

              Ia 4pi Ra2 = Ib 4pi Rb2

              Ia Ra2 = Ib Rb2

Let us call the distance from the observer be to the haughty R = ax, so the distance from the observer A to the haughty is R = 35 ax; we substitute

           Ia (35 -x) 2 = Ib x2

we develop and solve

         35-x = Ra (Ib / Ia) x

          35 = [Ra (Ib / Ia) +1] x

          x (11.22 +1) = 35

          x = 35 / 12.22

           x = 2,864 m

This is the distance of observer B

The distance from observer A

Ra = 35 - x

Ra = 35 - 2,864

Ra = 32.1 m

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