photons in a beam of light with wavelength l have momentum p. if the wavelength is doubled, the momentum is:

The undamped horizontal spring oscillator has an amplitude of 1.61 m when passing through its equilibrium position during oscillation.

It is given to us that -

Mass of the undamped spring oscillator, m = 2.52 kg

Spring constant during oscillation, k = 21.6 n/m

Speed of the spring oscillator, v = 3.34 m/s

We have to find out the amplitude of oscillation, say A.

According to the concept of Conservation of Energy, we can say that -

[tex]\frac{1}{2} mv^{2} = \frac{1}{2} kA^{2}[/tex] ------ (1)

where,

m = mass of the oscillator

v = speed of oscillation

k = Spring constant

A = Amplitude of oscillation

Now, substituting the given values in equation (1), we have

[tex]\frac{1}{2} mv^{2} = \frac{1}{2} kA^{2}\\= > \frac{1}{2} *2.52*(3.34)^{2} = \frac{1}{2} *21.6*A^{2}\\= > 28.11211 = 10.8A^{2}\\= > A^{2}=2.60\\= > A = 1.61m[/tex]

Therefore, the undamped horizontal spring oscillator has an amplitude of 1.61 m when passing through its equilibrium position during oscillation.

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Yes, It's True.

Voltage is the pressure from an electrical circuit's source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating light.

Voltage is the essential parameter in the circuit for the flow of current. If there is no voltage, no current flow. Voltage is broadly classified into two basic types: direct voltage and alternating voltage. In an electrical or electronic circuit, we can measure the voltage by using either a voltmeter or a multimeter.

The electric generators move magnets near coils of wires to create the voltages on the electrical grid.

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Let L be the natural length,

Since 20J of work is needed to stretch the spring from a₀ cm to 2a₀ cm,

We have,

20 = k/2 [ (2a₀-L)² - (a₀-L)²] --------- eq 1

Again,

80 J of work is needed to stretch the spring from a₁ cm to 2a₁ cm,

80 = k/2 [ (2a₁-L)² - (a₁-L)²] ---------- eq 2

Now,

eq 2 / eq 1

k/2 [ (2a₀-L)² - (a₀-L)²] / k/2 [ (2a₁-L)² - (a₁-L)²] = (80/20)

a₁(3a₁ - 2L) / a₀(3a₀ - 2L) = 4

3a₁² - 2La₁ / 3a₀² - 2La₀ = 4

3a₁² - 2La₁ = 12a₀² - 8La₀

L(8a₀ - 2a₁) = 12a₀² - 3a₁²

L = (12a₀² - 3a₁²) / (8a₀ - 2a₁)

Therefore the required length of spring or the natural length is (12a₀² - 3a₁²) / (8a₀ - 2a₁).

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The light ray will bend downwards.

What is light ray?
A ray, in the field of optics, is a geometrical model of idealised light that is chosen to be perpendicular to a wavefronts of the real light and to point in the direction of energy flow. By segmenting the actual light field into discrete rays that are computationally perpetuated through the system using ray tracing techniques, rays are employed to model this same propagation of light thru an optical system. As a result, even extremely complex optical systems can be mathematically or computationally analysed. For as long as light ray travel through and around objects for whom the dimensions are significantly larger than the light's wavelength, approximate remedies to Maxwell's equations are appropriate for use in ray tracing.

The light will most likely follow the path that curves downward. This is because light rays bend towards the normal when entering a denser medium, such as water from air. The normal is an imaginary line perpendicular to the surface of the water. Therefore, the light ray will bend downwards.

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Given details :

1.Force equilibrium in x direction

∑ [tex]F{x}[/tex] = 0

F - 39 cos Ф = 0

As Ф = 38°

F = 39 cos38°

F = 30.73 N

Force equilibrium in y direction

∑ [tex]F{y}[/tex] = 0

N = W + P sin38°

   =  70 + 39 sin38°

N = 93.79 N

Thus the normal force on chair = 93.79 N

From the free body diagram

F = μN

30.73 = μ x 93.79

μ = 30.73 / 93.79 = 0.32

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The speed of the spaceship is 0.099c.

Speed is the fastest movement of something.

Given:

L = 30 m is the proper length of the ship

• Delta*L = 13.8cm = 0.13m is the change in length

Let us first determine our contracted length. We can do this by subtraction:

L = 30m - 0.13m

We get:

L = 29.87

Now to determine the speed of the ship, we use the length contraction equation:

L = L_{0} * √(1 - (v ^ 2)/(c ^ 2))

We isolate the square root term:

√(1 - (v ^ 2)/(c ^ 2)) = L/L_{0} To simplify calculations, let us first substitute our lengths:

√(1 - (v ^ 2)/(c ^ 2)) = (29.87/(30) =

= 0.995

After calculation

V/C = 0.099874

Or V= 0.099c

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The projectile hit the ground 3,992.97 m in front of the release point.  The projectile speed when it hits the ground is 438.5 m/s

When an airplane flying horizontally fires a projectile horizontally in its direction of motion it means

The projectile moves in horizontally but it has projectile motion that move horizontally and vertically according to the parabolic curve.

In vertical, the projectile moves in a non-uniform motion.

Horizontal, the projectile moves in uniform motion.

When the projectile almost hits the ground

Final speed for the projectile

v² = vx² + vy²

v² = 428.89² + 91.24²

v² = 183,946.63 + 8,324.37

v² = 192,271.004

[tex]v = \sqrt{192,271.004}[/tex]

v = 438.5 m/s

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The average power being emitted by the source is 12.56* 10⁻⁴°⁵ W.

Given that,

Sound level L = 35 db

Distance d = 100 m

We know the formula for L as, ( take I₀ as 10⁻¹²)

L = 10 log(I / I₀) = 35

log(I / I₀) = 3.5

log(10¹²×I ) = 3.5

12 + log I =3.5

log I = 3.5 - 12 = -8.5

I = 10⁻⁸°⁵ W/m²

We know the formula for intensity of sound as I = P/(4πd²)

I = P/(4πd²)

To find out power, make P as the subject,

P = I * 4πd² =  10⁻⁸°⁵ * 4* 3.14* (100)² = 10⁻⁸°⁵ * 10⁴ * 12.56 = 12.56* 10⁻⁴°⁵ W

Thus, the average power being emitted by the source is 12.56* 10⁻⁴°⁵ W.

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We have seasons primarily because of how tilted the Earth is on its axis.

SUMMER: The Earth revolves around the sun, and the hemisphere that is tilted toward the sun receives the most sunlight. This is summer, when there is more sunlight.

WINTER: Because of the tilt of the earth's axis, days are shorter and less bright in the hemisphere that faces away from the sun. Winter is the result of the weather getting colder.

24-HOUR DARKNESS: Due to the tilt of the Earth, it is possible for darkness to last 24 hours a day at the North Pole of earth.

It is more frequently exposed to sunlight near the equator. Because of this, it is always much hotter at the equator. There is less variation between seasons because it is hotter for longer periods of time.

Direct sunlight strikes the Earth at the equator. In contrast, the sun's rays barely reach the poles where it is located.

More specifically, it's not because the equator is nearer the sun. But the reason is that the equator is being directly illuminated by the sun.

Because of this, the equator is home to some of the planet's warmest ecosystems, including tropical rainforests and deserts.

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As the charge, ( Q ) is equal and constant, the voltage drop across the capacitor is determined by the value of the capacitor only as V = Q ÷ C.

What is charge?

Charged material experiences a force when it is exposed to an electromagnetic field due to the physical characteristic of electric charge. You might have a positive or negative electric charge. Unlike charges attract one another while like charges repel one another.

As the charge, ( Q ) is equal and constant, the voltage drop across the capacitor is determined by the value of the capacitor only as V = Q ÷ C. A small capacitance value will result in a larger voltage while a large value of capacitance will result in a smaller voltage drop.

While the voltage drop across a resistor is proportional to the current and there is a current at the beginning, the voltage drop across a capacitor is related to its charge and is uncharged at the beginning. However, when charge on the capacitor begins to accumulate, some voltage is now lost across the capacitor.

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a box starts from rest and slides down an incline that is 10m long. At the bottom it is travelling at a speed of 5.0m/s. If the incline makes an angle of 20 degrees with respect to the horizontal, then the coefficient of friction between box and incline is 0.23.

Coefficient of friction is a measure of the amount of friction existing between two surfaces. When you find a coefficient of friction, you’re calculating the resistance to motion at the interface of two surfaces of similar or dissimilar materials. To find the coefficient of friction between box and incline, first we need to under the free body diagram of box, so the box is sliding downward and the friction is acting opposite to the motion. From this we conclude that-

mgsinθ - fN = ma

where f= frictional force acting between the box and the incline

N= normal force action on the box

a= acceleration

To find acceleration of the box, we know

v² - u² = 2as

(5m/s)² - 0² = 2xax10m

as u= initial velocity i.e. box is at rest

25 = 20xa

a = 1.25m/s²

as we know -

f = uN

where u = coefficient of friction between box and the incline

u = (mgsinθ - ma) / mgcosθ

u = tanθ - a/gcosθ

u = tan(20°) - 1.25/gcos(20°)

u = 0.36 - 1.25/9.81*0.939

u = 0.225 or 0.23

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The relationship between the absolute temperature and the average kinetic energy of the gas particles is inverse. Gas particle collisions are thought to be elastic.

When compared to the volume that the gas occupies, the volume of the gas particles is insignificant. There are no forces of attraction or repulsion between the gas particle. Although they travel in straight lines, the gas particles are constantly in a random motion.

What is particle collision?

There may be collisions between the particles and the wall during particle flows. The kinetic energy lost upon particle collision can cause frictional heat to be produced, walls to erode, particles to shatter or deform, be aggregated, or substances to become electrified.

What occurs when gases come together?

Gas molecules exclusively interact with one another through collisions; they do not apply any other forces. They don't adhere to one another.  All gas molecule collisions are flawlessly elastic, and all kinetic energy is preserved.

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In Kohlberg's terms, Michael's father is demonstrating Conventional reasoning.

According to Kohlberg's Structural Theory of Moral Development, conventional moral reasoning is the second of three levels of moral reasoning. At this level, people have internalized the moral standards and expectations of those closest to them and typically base their moral decisions on these standards and expectations.

In the given question, Michael is unaware that marijuana is prohibited, but his grandfather has instructed him to take it out because it is forbidden. It is unlawful, according to his father. It demonstrates that his father is aware of the laws. He believes that they must follow it since it is their responsibility, or else his son would be punished for breaking the law.

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The appearance of comets, meteors, and meteor showers was seen by the Greeks and Romans as portentous. They indicated either positive or negative events that had occurred or were about to occur.

Define greek mythology

Greek mythology is a significant area of classical mythology and a category of Ancient Greek folklore. It is a collection of myths that were first narrated by the Ancient Greeks. These tales discuss the beginning and nature of the world, the lives and exploits of gods, heroes, and other mythical beings, as well as the genesis and import of the ancient Greeks' own cult and ritual traditions.

Around the world and throughout time, comets have caused dread, anxiety, and awe in a variety of cultures and societies. They have been dubbed "the Menace of the Universe" and "the Harbinger of Doom," among other names.

A meteor sighting implied that heaven had bestowed a gift. It frequently symbolized a mystery originating from the cosmos, a phenomenal force far greater than ourselves. A meteor stood for knowledge of understanding that there is more to life than what we currently know. Many believe it to be a soul or spirit.

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The total width of the central maximum be 1.266 cm.

The act of bending light around corners such that it spreads out and illuminates regions where a shadow is anticipated is known as diffraction of light.

In general, since both occur simultaneously, it is challenging to distinguish between diffraction and interference. The diffraction of light is what causes the silver lining we see in the sky. A silver lining appears in the sky when the sunlight penetrates or strikes the cloud.

Given that:

wavelength of light = 633 nm

wide of the slit = 0.200 mm.

distance of the central maximum = 2.00 m

So,  the total width of the central maximum = 2λD/a

= ( 2 × 633 nm × 2.00 m)/ 0.200 mm.

= 0.01266 m = 1.266 cm.

Hence,   the total width of the central maximum be  1.266 cm.

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The magnitude of the force exerted by the sled on the student is 20N

Concept:

Every action on one body causes an equal and opposite response on the other, according to Newton's third rule of motion. It implies that if a body is pulled toward itself by a human, the body will also draw the person toward itself with the same force.

The direction of the body's response to the person will be in opposition to the direction of the person's response to the body.

The sled will similarly exert the same amount of effort on the student to drag him backward in the opposite direction as the student exerts on the sled to pull it forward.

The sled's weight moves in a vertically downward direction, therefore it has no bearing on the reaction force the sled exerts on the learner.

Consequently, the sled's force on the student was of the following magnitude: 20N

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False. Current will travel along the path with the lowest resistance. This is because electrons will take the path of least resistance in order to reach the point of lowest potential energy.

The concept of electrons traveling along paths of least resistance is a fundamental principle of electrical engineering. This principle, known as the principle of lowest resistance, states that electrons will take the path of least resistance in order to reach the point of lowest potential energy. This phenomenon has implications in various areas of electrical engineering, from circuit design to power distribution.

The basic principle of lowest resistance can be demonstrated with a simple circuit. Imagine a circuit with two parallel paths, one with a higher resistance and one with a lower resistance. When a voltage is applied to the circuit, electrons will flow along the path of least resistance, which in this case is the one with the lower resistance.

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What amount of power, measured in watts, is provided by the force pushing up on the man? (Ignore gains or losses in kinetic energy). His body uses up a total of 2828.74 W h of energy.

An object's kinetic energy is the energy it has as a result of motion. Is called as kinetic energy.  Applying force is necessary if we wish to accelerate an object. We have to put forth work to apply a force. An influence that can alter an object's motion is called a force. A force can cause an object with mass to change its velocity, or accelerate (for example, moving from a condition of rest).

Power P is the product of work done (W) and time spent (t), or (74.7)(9.8)(19.9)/12.5) = 1165.44 W

Let his body's power consumption be P' We have (0.412)

P' = P

P' = P/0.412 = (1165.44/0.412) = 2828.74 W

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Generally speaking, the object distance indicates that the light rays emanating from the object are parallel to one another, resulting in f=-4.221.

A ray is defined as a small, usually straight-traveling beam of light. The laser or laser pointer's light beam is an illustration of a ray. According to the ray model of light, a ray moves in a straight line until it encounters an object, such as a mirror or the boundary between two materials.

image distance is v = 4.7 + (2.1 * 10-2) = -4.721 m the negative

means image is formed behind the lens

Generally the object distance is u = ∞ this mean the light ray coming from the object are parallel to each other.

So from lens equation

=-고=수

=> f = -4.721 m

As an electromagnetic wave, light travels in straight lines along narrow beams of light, which are referred to as rays. Despite the fact that reflection or refraction can alter its direction, light always moves in a straight line.

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By increasing the time of impact a smaller amount of force would be required to stop the cart. The force of the impact decreases as the impact of time increases. Therefore, the force on the body decreases as time increases with a constant change in momentum.

The push or pull on a massed object changes its velocity is defined as force. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Force = Mass × Acceleration

The change in momentum over time is measured by force. In real life, when a force is applied to an object, it accelerates and rises in velocity, which increases the momentum of the object.

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15000000 Joule work is done on the ship if it moves a distance of 3000m.

The amount of force multiplied by the distance moved in the force's direction is known as the work done by a force acting on an item. Work has no direction and only magnitude. Work is a scalar quantity as a result. SI unit of work is joule.

Given parameters:

horizontal force applied on the tugboat is: F = 5000N.

The tugboat moves a distance: d =3000m.

Hence, The work done on the ship is  = Fd =  5000N ×​ 3000m = 15000000 Joule.

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Bond order for the diatomic element is 2

A bond order is something that pairs two atoms with their atoms.

According to molecular orbital theory, the bond order is half the difference between the bonding and antibonding electrons.

Bonding electrons of the element = 6

Anti-bonding electrons of the element = 2

Difference = bonding electrons - anti-bonding electrons

= 6 - 2

= 4

Bond order = (0.5)*(difference)

Bond order = (0.5)*(4)
Bond order = 2

Bond order for the diatomic element has six bonding electrons, six non-bonding electrons, and 2 anti-bonding electrons is 2.

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Capacitance is C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]

A material thing or device's capacitance is its ability to hold electric charge. The ratio of those two values is used to calculate the change in charge in response to an alteration in electric potential.

According to the given information

The RLC circuit's resonant frequency is determined by

f = [tex]\frac{1}{2\pi \sqrt{LC} }[/tex]

L is the circuit's inductance, and C is its capacitance.

By rearranging the equation, we get

C = [tex]\frac{1}{(2\pi) ^{2}f^{2} L }[/tex]

and by substituting the inductance of the circuit L = 30mH = 0.030mH

The resonant frequency f = 1040 Hz

We need to find the value of the capacitance

By substituting the values in C

C = [tex]\frac{1}{(2\pi) ^{2}(1040)^{2}(0.03) }[/tex]

C = 0.0008126 [tex]u[/tex]C

C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]

Capacitance is C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]

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The frame size for these settings is the inverse of the frequency resolution and is 2 seconds. 2048 samples are taken each second is the sampling frequency.

The capacity to distinguish between two signals called resolution in general. This pertains to the capacity to distinguish between two peaks in chromatography. Provided by where tr1 & tr2 and w1 but also w2 are the resolutions, R. A vector is resolved when it is divided into a number of vectors that point in distinct directions.

How many pictures are displayed each inch of a screen is sometimes referred to as PPI, or pixels per inch. Higher resolutions have more pixels per square inch (PPI), which means more digital signal and a better, more precise image.

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The number of conducting electrons per cubic meter for copper, given that its electron mobility is 3 × 10-3 m2/v-s is 1.20 × 10⁷ electrons/ m³.

Electron mobility characterizes how fast an electron (or charged carrier) can pass through a stable fabric (e.g. metals or semiconductors), whilst pulled by means of an electric subject.

Calculation:-

resistivity of the copper (p) = 1.73 × 10⁸ Ωm

η = σ/μe

Here, σ = electrical conductivity

σ = 1/ρ

e  = charge on electrons = 1.6 × 10⁻¹⁹

μ = mobilty of electrons

n = σ/μe

n = 1/ρμe

n = 1/8.304 × 10⁻⁸

n = 10⁸/8.304

n = 1.20 × 10⁷ electrons/ m³

Mobility is described as the potential for motion and the potential to get from one region to another using one or extra modes of delivery to satisfy every day needs. As such, it differs from accessibility, which refers back to the ability to get entry to or attain a desired provider or activity.

Mobility is officially described as the fee of the glide pace in keeping with unit of electric field strength; for that reason, the faster the particle actions at a given electric field strength, the larger the mobility. The mobility of a particular sort of particle in a given stable can also vary with temperature.

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Frequencies in both cases are [tex]& f_2=1.225 \mathrm{H}_z[/tex] and [tex]}} \\& f_2=1.522 \mathrm{H}_z[/tex]

The frequency of a repeated event is its number of instances per unit of time. It differs from angular frequency and is sometimes referred to as temporal frequency for clarification. One event occurs per second when measuring frequency in hertz.

The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 times per hour if it takes 1/100 of an hour.

According to the given information

We got to know

A) the frequency of two spring

[tex]f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}[/tex]

for Same spring

[tex]f \propto \frac{1}{\sqrt{m}}[/tex]

So

[tex]& \frac{f_2}{f_1}=\sqrt{\frac{m_1}{m_2}} \Rightarrow f_2=f_1 \sqrt{\frac{m_1}{m_2}} \\[/tex]

[tex]& f_2=1.35 \times \sqrt{\frac{0.75}{(0.16+0.75)}} 2=222=1 \frac{1}{2} \\[/tex]

[tex]& f_2=1.225 \mathrm{H}_z[/tex]

B)

[tex]& f_2=f_1 \sqrt{\frac{m_1}{m_2}} \\& f_2=1.35 \times \sqrt{\frac{0.75}{(0.75-0.16)}} \\& f_2=1.522 \mathrm{H}_z[/tex]

Frequencies in both cases are [tex]& f_2=1.225 \mathrm{H}_z[/tex] and [tex]}} \\& f_2=1.522 \mathrm{H}_z[/tex]

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The concentration of an chemical in an oil spill in ppb is 0.013 ppb (approx).

concentration is the abundance of a constituent divided by the total volume to the  mixture. Several by the  types of mathematical description can be the  distinguished: mass of the  concentration, molar concentration, number and  concentration, and volume concentration.

Calculate the concentration in ppb by multiplying to the  ratio of the mass of solute to  mass of solution by 1 billion or 10 ^9

So here the answer can be calculated by

(10^ 9)(6×10 ^-8)/4600

(Here 0.060 mg = 6 × 10 ^-8 kh)

=  6/460

= 0.013 ppb (approx)

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16.77m is the lemming's change in height when it reaches the water.

A thing is said to be in projectile motion when it has been fired into the air. After the initial force that launches the object, it only experiences the force of gravity. It is what it is—a projectile—and the path it took to get there is what it was.

You can tell from the situation that this projectile is a Type 1 projectile, or a horizontal projectile. Before you can resolve this issue, you will need a few things.

You must first examine the information you were given:

Vix = 2.87 m/s

dx = 5.32m

Your height or vertical distance are what you need. The following is the usual formula for projectile displacement:

d = Vit +1/2gt²

Specifically, you only need to enter the y-components to obtain the vertical distance. Now keep in mind that a horizontal projectile initially moves only forward and not vertically. Your vi = om/s, leaving you with the following equation:

dy = Viyt + 1/2 gt²

dy = (0m/s)t + 1/2 gt²

dy = 1/2 gt²

However, if you examine your issue, you will discover that no time has been allotted. You can resolve it using the information provided by deriving it from the x component formula:

dx = Vixt

Plug in your knowledge and find a solution for your ignorance.

dx = Vixt

5.32m = (2.87m/s)t

5.32/2.87= t

t = 1.85s

You can solve for your vertical distance/displacement now that you know the time:

dy = 1/2 gt²

dy = 1/2 (9.8 × 1.85²)

dy = 16.77m.

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Answer:

the answer is -16.8

Explanation:

it’s negative because your going down and you have to round off to match the significant digits.

A. The average kinetic energy for each atom of argon gas in the cylinder is 6.04 × 10⁻²¹ Joule.

B. The number of moles of argon inside the cylinder is 1.38 × 10² mol.

The formula to calculate the average kinetic energy for monoatomic gas is

KE = 3/2 kT

KE = 1.5 kT

KE = 1.5 × 1.38 × 10⁻²³ × 292

KE = 6.04 × 10⁻²¹ J

For every ideal gas applies the ideal gas equation

PV = nRT

PV = nRT

1.7 × 10⁶ × 1.97 × 10⁻¹ = n × 8.314 × 292

3.35 × 10⁵ = n × 2.43 × 10³

n = 1.38 × 10² mol

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Under cold air standard conditions, Then the thermal efficiency of this cycle is 61.38%.

n= 1- ((a^x)-1)/(x*e^(x-1) *(a-1)

n=thermal efficiency

e=compression ratio= v1/v2

a=cut off ratio=V3/V2

x=Cp/Cv=1.4 for air

v1=4L

v2=0.25L

v3=0.5 L

e= 4/0.25=16

a= 0.5/0.25 =2

n= 1- ((2^1.4)-1)/(1.4*16^(1.4-1) *(2-1) = .6138 = 61.38%

A system's thermal efficiency is determined by how much work is produced for every unit of heat input. Work is produced by heat engines. The percentage of heat that is converted into usable work is expressed as thermal efficiency.

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