How is the work energy theorem represented as an equation?

kepler's third law,

Semi-major cross (r) r³=t² =[tex]T^{\frac{2}{3} }[/tex]

The semi-major axis of short-period comet = [tex](111)\frac{2}{3} ^{}[/tex] = 23.10AU

The semi-major axis of short-period comet = [tex](701)^\frac{2}{3}[/tex] = 78.91AU.

Kepler's third regulation is valid due to the fact the sun is tons more huge than any of the planets and therefore Newton's correction is small. The information Kepler had gotten admission to were now not top-sufficient to reveal this small impact. Kepler posted his first two legal guidelines approximately planetary movement in 1609, having located them via reading the astronomical observations of Tycho Brahe. Kepler's 0.33 law become posted in 1619.

It turns out that the steady in Kepler's 0.33 regulation relies upon on the entire mass of the two our bodies worried. Kepler himself, analyzing the motion of the planets across the sun, always treated the 2-frame device of sun-plus-planet. Kepler's third law: the squares of the orbital intervals of the planets are directly proportional to the cubes of the semi-main axes of their orbits. Kepler's 0.33 regulation implies that the period for a planet to orbit the sun increases rapidly with the radius of its orbit.

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The Short-period comet's using kepler's Third law semi-major axis for 111 years is 23.10AU and for 701 years is 78.91 AU is the short-period comet's semi-major axis.

Cross (r) semi-major [tex]r^3[/tex]=[tex]t^2[/tex]

=> r = [tex]t^\frac{2}{3}[/tex]

so for 111 years is( [tex]111^\frac{2}{3}[/tex]) = 23.10 AU

for 701 years is ([tex]701^\frac{2}{3}[/tex]) = 78.91 AU

According to Kepler's Third Law, the planets' squared orbital periods and cubes of their semi-major axes are directly inversely related. According to Kepler's Third Law, a planet's period of orbiting the Sun grows exponentially with its orbital radius. It turns out that the constant of Kepler's Third Law is a function of the combined masses of the two bodies. When analysing the motion of the planets around the Sun, Kepler himself dealt exclusively with the Sun-plus-planet 2-body system.

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Answer:

At 100m, water pressure is 10bar, relative to the surface. But the absolute pressure is 11bar (1bar is the atmospheric pressure on the water surface, plus 10bar water pressure).

Answer:

pressure = 981000 N/m²

Explanation:

To calculate the pressure in liquids, we have to use the following formula:

[tex]\boxed{p = h \rho g}[/tex],

where:
• p = pressure in N/m² (or Pa)

• h = height in m

• ρ = density in kg/m³

• g = gravitational acceleration (9.81 m/s²)

From the question, we know that the height is 100 m, therefore h = 100. The density of water is 1000 kg/m³, therefore, ρ = 1000.

Using this information along with the formula above, we can calculate the pressure:

p = hρg

⇒ p  = 100 × 1000 × 9.81

⇒ p = 981000 N/m²

Therefore, the pressure at a depth of 100 m is 981000 N/m².

Without glasses, the far point is 20.3 cm from the eye. With glasses with a 5.5-D lens, the distance is 2.2 cm. A nearsighted eye exists. A measurement is the optical system's focal length.

It is the inverse of the system's optical power how strongly the system converges or diverges light. A system's light converges when the focal length is positive, while it diverges when the focal length is negative. There isn't a current entry in Britannica on this subject.

f = -1/5.5\s= -0.182m

1/(d1+1/d2) = 1/(d1=f) = -0.182 = -18.2m

Since the diverging lens is 2.1 cm away from the eye.

Therefore, -18.2-2.1=20.3 cm

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At every stage of the formation process, astronomers have seen a wide variety of stars.

An buildup of gas and dust falls under the influence of gravity to generate stars. From the moment the first gas cloud begins to compress to the time the star is formed and begins to shine like the Sun, the process of star creation takes roughly one million years. Large (molecular) clouds of gas and dust with a lot of dust particles are ideal for star formation. Visible light cannot pass through the dust, but infrared radiation may. The mass of the material that originates at a star essentially affects its life and fate because gravity is the factor that causes stellar formation.

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The objective of a heat engine is to transform heat into work. So, correct option is A.

A heat engine is a device that converts thermal energy (heat) into mechanical work. It operates by absorbing heat from a hot source, such as a furnace, and converting it into useful mechanical energy, such as rotating a shaft or driving a machine. The efficiency of a heat engine is determined by the difference between the temperature of the hot source and the temperature of the cooled working fluid (usually air or water). Examples of heat engines include internal combustion engines in cars, steam turbines in power plants, and Stirling engines in heat pumps and refrigeration systems.

The objective of a heat engine is to transform heat into work. A heat engine is a device that uses heat energy from a high-temperature source to perform mechanical work by using a thermodynamic cycle. The basic idea behind a heat engine is to extract thermal energy from a high-temperature source, convert some of this energy into useful mechanical work, and then reject the remaining heat to a lower-temperature sink. The efficiency of a heat engine is determined by the amount of thermal energy that is converted into useful work and the amount of heat that is rejected to the lower-temperature sink.

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The total mass of outputs is less than the corresponding inputs, is the statement about the inputs to and outputs from nuclear fusion in the Sun is true.

What is nuclear fusion ?

The Sun and other stars are propelled by nuclear fusion processes. In a fusion reaction, two light nuclei combine to create one heavy nucleus. Because the mass of the resulting single nucleus is smaller than the combined mass of the two initial nuclei, the process releases energy.

What is fission ?

Splitting or breaking apart, either actively or passively. biology a process in which two or more equal sections divide to generate new cells, used in the reproduction of single-celled animals and plants.

Therefore, the total mass of outputs is less than the corresponding inputs, is the statement about the inputs to and outputs from nuclear fusion in the Sun is true.

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The maximum energy of a photoelectron cannot be greater than the energy of the incident photon minus the minimum energy needed to escape from the surface of the metal.(5.30*10^-19)

How much energy does a photoelectron have?

The photoelectrons' highest recorded kinetic energy is 6.63 1019 J. The metal's threshold frequency is when it is exposed to radiation with a frequency of 2 1015 Hz.

What is the photoelectron equation?

E = h c W, m an x, where h seems to be the Planck constant, c is the speed of the light, is the wavelength of a incident photon, & W is the activity function of a metal surface, is the formula for a photoelectron's maximal kinetic energy.

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you would measure it ur and 6th form as well and actively open to you by the

The area of the lens is 7903 mm2. It takes technician 45s to clean 135 mm2 then he will take 73.43  hours to complete whole lens.

So first we have to divide the area by 135 mm2

7903 mm2 / 135 mm2 = 58,741

Next up, we have to multiply the calculated ratio by 45 s to get the amount of time that is needed to polish the entire lens.

Total time needed = 58,741 x 45 s

                               = 2643,33 s

time in hours = ?

1 hour = 60x60 sec

1 sec = 1/3600 hours

therefore, time in hours =  2643,33 x 1/3600

                                       = 73.43 hours.

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The horizontal distance the fish travels before hitting the water is independent of the height the fish is dropped from, and the speed at which the pelican is traveling. The horizontal distance is determined only by the time the fish is in the air, which can be found using the equation:

Distance = Speed * Time

To find the time, we use the equation:

Time = sqrt(2 * Distance / Acceleration due to gravity)

Where distance is the height the fish is dropped from (5.4m) and the acceleration due to gravity is 9.8 m/s^2

Time = sqrt(2 * 5.4 / 9.8) = sqrt(2 * 5.4 / 9.8) = sqrt(1.08) = 1.03s

So the fish is in the air for 1.03s and the horizontal distance it travels is given by:

Distance = Speed * Time = 5.0m/s * 1.03s = 5.15m

So the fish will travel horizontally 5.15m before hitting the water.

Rounded to 2 decimal places, E = 0.64

The formula for margin of error (E) is E = s * c / sqrt(n), where c is the confidence level (as a decimal), n is the sample size, and s is the standard deviation.

So in this case, E = 2.6 * 0.99 / sqrt(16) = 2.6 * 0.99 / 4 = 0.6435

Margin of error (ME) is a measure of the uncertainty associated with a sample estimate of a population parameter. It is commonly used in opinion polls and other surveys to indicate the degree of accuracy of the results. ME is usually expressed as a percentage of the estimate and is calculated by dividing the standard error of the estimate by the sample estimate, and then multiplying by 100. It can be used along with a confidence interval to indicate the level of precision desired in the estimate. The smaller the margin of error, the more confident one can be that the sample estimate is close to the true population parameter.

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The net force acting on a moving object is calculated with the equation   F= ma, m is the mass and a is the acceleration. In this case we have to calculate acceleration at each stage.

Here we have a velocity-time graph. The acceleration is the slope of the velocity time graph. As there are three different slopes, we could calculate each accelerations differently.

From 0s to 3s the object is in constant acceleration.

 Acceleration, a = (v-u)/(t₂-t₁)

                           = (12-0)/(3-0) = 4m/s²

Force, F = ma = 2.7 × 4 = 10.8 N

        2.  At t = 4s

From the graph, we could observe that the object is in constant velocity. That means the object is in 0 acceleration. So net force acting will be 0

     3. At t = 7s

From the graph we could observe the object is in constant deceleration. Calculating the slope,

    Acceleration, a = (v-u)/(t₂-t₁)

                               = (0-12)/(8-6)

                               = -6m/s²

force, F = ma = 2.7× -6  = -16.2 N.

So the net force acting at t=1s is 10.8N, at t= 4s is 0N, at t= 7s is 16.2N.

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Potential energy is the energy that is stored in any object or system as a result of its position or component arrangement. The environment outside of the object or system, such as air or height, has no impact on it. In contrast, kinetic energy refers to the energy of moving particles within a system or an object.

Potential energy can take many different forms, including chemical, elastic, electrical (electromagnetic), gravitational, nuclear, and thermal energy, and can be found in systems of objects ranging from atoms to planets.

When an electric charge is infinitely removed from other charges, it is said to have zero potential.

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A reaction will be spontaneous if the change in Gibbs free energy is less than 0. So, the correct option is A.

The Gibbs free energy, sometimes referred to as the Gibbs function, Gibbs energy, or free enthalpy, is a thermodynamic potential that is used to determine the greatest amount of work that can be done in a particular thermodynamic system when the system's temperature and pressure are held constant. An abbreviation for Gibbs free energy is G.

Since it is a kind of energy as well, its value is frequently stated in Joules or Kilojoules. Gibbs free energy is outlined as the most work that can be accomplished using a closed thermodynamic system.

The equation is given as:

G = H - TS

Where,

G = Gibbs free energy

H = enthalpy

T = temperature

S = entropy

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The average speed he needs to reach in his second round is 54.55km/hr

When two speeds of x and y km/h are used to travel a distance, the average speed is determined as

The distance traveled divided by the time taken is the most popular formula for calculating average speed. The alternative formula is to add the initial and final speeds together, then divide by 2.

average speed= 2xy/(x+y)

He needs to reach his second round in order to attain the overall average speed of 60 mph required for the test will be-

Required average speed= (2x60x50)/60+50

= 6000/110

=54.55km/hr

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According to the question, the magnitude of the net force required to stop the car is 8400 N.

What is magnitude?
Magnitude is a term used to describe the size or intensity of something. It is typically used in physics and mathematics to describe the size of a physical quantity, such as a force or an angle. Magnitude can also be used to describe the magnitude of an event, such as an earthquake. In astronomy, magnitude is used to describe the brightness of a star or other celestial object. The magnitude of intensity is usually expressed in terms of the Richter scale or logarithmic scale. Magnitude can also be used to describe the power of an earthquake or the size of a storm. Magnitude is also used to describe the size or importance of a person, place, or event.

The magnitude of the net force required to stop the car is:

F = m × a

F = 1050 kg × (2 × (40.0 km/h) / (25.0 m))

F = 8400 N

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The mass of Saturn is approximately 1.35 x 10^26 kg.

The mass of Saturn can be calculated using the formula for Kepler's third law, which states that the square of the orbital period of a satellite is proportional to the cube of the semi-major axis of its orbit.

Kepler's third law states that the square of the orbital period of a planet or a satellite (T^2) is proportional to the cube of the semi-major axis of its orbit (a^3). Mathematically, it can be represented as:

T^2 = \frac{4 * \pi^2 * a^3}{G * M}

Where T is the orbital period, a is the semi-major axis, G is the gravitational constant and M is the mass of the central body (in this case, it's Saturn).

Given that we know the orbital period and radius of Titan, we can rearrange the above equation to find the mass of Saturn.

M = \frac{4 * \pi^2 * a^3}{G * T^2}

By plugging in the values for Titan's orbit, we get:

M = \frac{4 * \pi^2 * (1.22 * 10^9 m)^3}{G * (15.9 days)^2}

Keplers third law: T^2 = \frac{4 * \pi^2 * a^3}{G * M}

Saturn mass: M = \frac{4 * \pi^2 * a^3}{G * T^2}

The mass of Saturn is around 1.35 x 10^26 kg.

This is an indirect method, Kepler's third law can only be used to find the relative masses of the central body if we know the relative masses and radii of the orbiting bodies.

we can use this method, but it is not very precise and it relies on the accuracy of the measurements of the orbital data.

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The Rank of the vectors is D A C B.

What is Vectors?

In contrast to a scalar number, a vector quantity also includes a direction component that aids in locating one point in relation to another. Here is more information on vectors. A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

A vector primarily consists of two elements, the horizontal component and the vertical component. The horizontal component's value is cos, and the vertical component's value is sin. Here is further information about vector components.

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This force is equal to 1.18 x [tex]10^{-10}[/tex] after comparing it to the weight of a 0.200-mg flea owing to gravity.

Force is a factor that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to define force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

As per the data given in the above question are as bellow,

The data share are as follow,

The weight of a flea is 0.200 mg.

We have to compare the weight with earths gravity.

Thus by using the formula is equal to force upon mass into gravitational force.

i.e F/mg

substitute the value in above equation we get,

[tex]\frac{2.304 \times 10^{-16} \mathrm{~N}}{\left(0.2 \times 10^{-6} \mathrm{~kg}\right)\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)}[/tex]

Further solving we get,

1.18 x [tex]10^{-10}[/tex]

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Binding energy per nucleon is 7.48 MeV.

What is Binding Energy?

The minimal amount of energy needed to remove a particle from a system of particles is often referred to as binding energy. Or to put it another way, it's the energy that divides a system of particles into single units. In atomic physics, chemistry, condensed matter physics, and other fields, we primarily research binding energy. The separation energy is referred to as binding energy in nuclear physics.

Binding energy is required to separate the neutrons and protons, collectively known as the nucleons, from the other subatomic particles that make up atomic nuclei or the nucleus of an atom. Because each nucleus need net energy to be separated into each neutron and proton, the binding energy of nuclei has a positive value.

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Answer:

The car's final speed will be 28 m/s

Explanation:

We can use the kinematics equation

[tex]v_f=v_0+at[/tex]

Note

[tex]v_f[/tex] is the final velocity

[tex]v_0[/tex] is the initial velocity

[tex]a[/tex] is the acceleration

[tex]t[/tex] is the time

We are given

[tex]v_0=0\\a=7\\t=4[/tex]

Lets evaluate [tex]v_f[/tex].

Substituting our values into the equation gives us

[tex]v_f=0+7*4[/tex]

Lets simplify

[tex]v_f=7*4[/tex]

[tex]v_f=28[/tex]

The impulses that colliding objects exert on each other are equal and opposite because the time for which they interact is equal for both objects.

When two bodies collide, Newton's Third Law ensures that the normal forces from the collision will always be equal and opposite.

This means that the impulses will be equal and opposite and will cancel out in our impulse-momentum equation when examining the system of equations.

The impulses that colliding objects exert on each other are equal and opposite Where Newton's third law of motion states that every action has its equal and opposite reaction.

This also describes that when an object applies force on a second object, the second object applies an equal and opposite force onto the first object

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Greater than is the correct answer .

What is resistance ?

Resistance is measured in ohms and represented by the Greek letter omega (Ω). Ohm is named after German physicist Georg Simon Ohm (1784-1854), who studied the relationship between voltage, current and resistance. He has been credited with formulating Ohm's law.

All substances resist the flow of electricity to some degree. They fall into one of two broad categories:

conductor: A material that offers very little resistance through which electrons can easily move. example:

silver, copper, gold, aluminium.

Insulator:

A substance that has a high resistance and restricts the flow of electrons. example: Rubber, paper, glass, wood, plastic.

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Answer:

To find the frequency of the microwaves, we can use the equation f = c / λ, where f is the frequency, c is the speed of light (approximately 3 x 10^8 m/s), and λ is the wavelength of the wave. For example, if the wavelength of a microwave is 14 cm, we can convert this to meters and use it in the equation to calculate its frequency which will be 0.14m.

Plugging in the numbers and solving we have:

f = 3 x 10^8 m/s / 0.14m = 2.143 x 10^9 Hz

So, the frequency of the microwaves in the oven is approximately 2.143 GHz

The change from ni=6 to nf=3 is represented by spectral lines with letters in the D format. Spectral lines are widely used to identify atoms and compounds.

The spectral lines that correspond to transitions to the same end state are inherently arranged into spectral series in many atoms. These series are known as Lyman, Balmer, Paschen, etc. in hydrogen. The similar behaviour occurs in the model atom under study, where all transitions involving the ultimate state nf=4 are represented by the middle series. The lines that are farthest to the right in any series correspond to the transitions with the lowest energies and longest wavelengths. Within a series, the energy of the transition rises as you move to the left.

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complete question:  The emission spectrum of hypothetical atom shown below in (Figure 1) for three distinct spectral series. The marked spectral line for instance corresponds the transition from the initial state n = 5 to the final state n = 3. Which of the lettered spectral lines corresponds to the transition from n =6 to n = 3.

The velocity of the object is 3 m/s.

The velocity of an object is the change in the position of the object with time.

The slope of position time graph is known as velocity.

Mathematically, the formula for the velocity of an object is given as;

v = Δx / Δt

v = ( x₂ - x₁ ) / ( t₂ - t₁ )

where;

The velocity of the object is calculated as follows;

v = ( 15 - 3 ) / ( 4 - 0 )

v = ( 12 m ) / ( 4 s )

v = 3 m/s

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Answer: The velocity of the object is 0.1 m/s.

Explanation:

i just did it.

The electron would radiate 2.36 x 10⁻⁴ W per second.

What is an Electron?

An electron is a subatomic particle with a negative electrical charge. Electrons are found in atoms and are the primary subatomic particle responsible for chemical bonding and electrical conductivity. They are also the primary constituent of all forms of electricity, including static electricity and current electricity.

Step 1: Calculate the angular velocity of the electron.

The angular velocity, ω, of the electron can be calculated using the equation:

ω = √(2E/mR²)

where E is the kinetic energy of the electron, m is the mass of the electron, and R is the radius of the orbit.

For the given values, we have:

ω = √(2 x 13.6eV/9.109 x 10⁻³¹Kg x 0.0529 x 10⁻⁹m²) = 2.19 x 10⁹ rad/s

Step 2: Calculate the acceleration of the electron.

The acceleration of the electron can be calculated using the equation:

a = ω²R

For the given values, we have:

a = (2.19 x 10⁹ rad/s)² x 0.0529 x 10⁻⁹m = 1.18 x 10⁻⁸ m/s²

Step 3: Calculate the power radiated by the electron.

The power radiated by the electron can be calculated using the equation:

P = (2/3) x q²a²/c³

where q is the charge of the electron, a is the acceleration of the electron, and c is the speed of light.

For the given values, we have:

P = (2/3) x (1.6 x 10⁻¹⁹C)² x (1.18 x 10⁻⁸m/s²)²/ (3 x 10⁸m/s)³ = 2.36 x 10⁻⁴ W

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The final velocity of the other coin will be 10.33 cm/s and the amount of kinetic energy transferred to the 15.0 g will be 0.00088 J.

Momentum is the result of a particle's mass and velocity. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum. Check out Newton's laws of motion.

Mass of first coin, m = 5.5g = 0.0055kg

Mass of second coin, M = 16.5 = 0.0165kg

Initial velocity of first coin, u = 21 cm/s

Final velocity of first coin, v = -10cm/s (because it's in the opposite direction of the initial motion)

Initial velocity of second coin, U = 0 cm/s

Using principle of conservation of momentum:

Total initial momentum = Total final momentum

m*u + M*U = m*v + M*V

U = 0

=> m*u + 0 = m*v + M*V

m*u - m*v = M*V

V = m(u - V) / M

V = 0.0055(21 - (-10)) / 0.0165

V = 0.3333 * 31 = 10.33 cm/s

Kinetic energy is given as:

KE = 0.5 * M * V²

V = 10.33 cm/s = 0.1033 m/s

KE = 0.5 * 0.0165 * 0.1033²

KE = 0.00088 J

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The Phase difference between points A and B is zero of a circular wave.

                    =  5 pi/2-5pi/2=0

b) What is the phase difference between points C and D?

  Phase difference between points C and D will be

                         = 9pi/2- pi/2=4pi

c) What is the phase difference between points E and F?

    Phase difference between E and F will be

                     = 5pi/2 - 2pi/2= pi

The phase difference of a sine wave can be defined as "the time interval by which one wave leads or lags another", and phase difference is not only a property of one wave, but also the relative property of two or more waves. am. This is also called the "phase angle".

The phase difference between two sound waves of the same frequency passing through a fixed position is given by the time difference between the same position within the wave cycle of the two sounds.

Phase difference is the difference in phase angle between two sine waves or phasors. In a three-phase system, the phase difference between conductors is one-third of the period.

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