__is the energy of a macroscopic system

a) 2.0 represents the initial position of the ball,  -3.6 represents the initial velocity of the ball  and 1.7 represents the acceleration of the ball.

b)The unit of 2.0 is meters, the unit of -3.6 is meters per second, and the unit of 1.7 is meters per second squared.

c) Position of of ball at t=1, 2, 3 are -1.9, 5.4 and 9.1 meters respectively

d) Average velocity is 5.5 meter per second

Part a

In the equation x = 2.0 - 3.6t + 1.7t2, the number 2.0 represents the initial position of the ball (i.e., the position of the ball at t = 0 seconds), -3.6 represents the initial velocity of the ball (i.e., the velocity of the ball at t = 0 seconds), and 1.7 represents the acceleration of the ball.

Part b

The unit of 2.0 is meters, the unit of -3.6 is meters per second, and the unit of 1.7 is meters per second squared.

Part c

To determine the position of the ball at t = 1.0 s, 2.0 s, and 3.0 s, we simply substitute these values into the equation:

When t = 1.0 s: x = 2.0 - 3.6(1.0) + 1.7(1.0)^2 = -1.9 meters

When t = 2.0 s: x = 2.0 - 3.6(2.0) + 1.7(2.0)^2 = 5.4 meters

When t = 3.0 s: x = 2.0 - 3.6(3.0) + 1.7(3.0)^2 = 9.1 meters

Part d

The average velocity over the interval t = 1.0 s to t = 3.0 s can be calculated by taking the displacement of the ball during this time interval and dividing it by the time interval:

Displacement = x(3.0) - x(1.0) = 9.1 - (-1.9) = 11.0 meters

Time interval = 3.0 s - 1.0 s = 2.0 s

Average velocity = Displacement / Time interval = 11.0 meters / 2.0 seconds = 5.5 meters per second.

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The velocity of the canoe is  1.7 m/s.

Momentum in physics is the products of mass and velocity. Now we have to find momentum with the formula; p = mv

a) Initial momentum = (15)8 m/s + 135 = 255 Kgms-1

b) Since momentum is conserved, the total momentum after throwing the anchor is still 255 Kgms-1

c) The final velocity of the boat is obtained from;

255 Kgms-1 = (15Kg + 135 Kg) v

v = 255 Kgms-1/(15Kg + 135 Kg)

v = 1.7 m/s

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Answer:

too much :(

Explanation:

\overline{a} = \frac{v - v_0}{t} = \frac{\Delta v}{\Delta t}

\overline{a} = average acceleration

v = final velocity

v_0 = starting velocity

t = elapsed time

Answer:

a = Δv⁄t.

Explanation:

The molar solubility of cobalt(III)hydroxide in a solution containing 0.068 M KOH at 25°C is approximately 1.22e-40 M.  

To determine the molar solubility of cobalt(III) hydroxide, Co(OH)3, in a solution containing 0.068 M KOH at 25°C, given that the solubility product, Ksp, is 1.6e-44.
Step 1: Write the balanced dissolution equation:
Co(OH)3(s) ⇌ Co3+(aq) + 3OH-(aq)
Step 2: Express Ksp in terms of molar solubility:
Ksp = [Co3+][OH-]^3
Step 3: Since the solution already contains 0.068 M OH-, let x be the molar solubility of Co(OH)3. Then,
[Co3+] = x
[OH-] = 0.068 + 3x

Step 4: Substitute the molar concentrations into the Ksp expression:
1.6e-44 = (x)(0.068 + 3x)^3
Step 5: Solve the equation for x (molar solubility of Co(OH)3):
As 1.6e-44 is a very small value, we can assume that 3x is much smaller than 0.068. Hence, we can approximate the equation as follows:
1.6e-44 = (x)(0.068)^3
Now, solve for x:
x = 1.6e-44 / (0.068)^3
x = 1.22e-40, Therefore, the molar solubility of cobalt(III) hydroxide is approximately 1.22e-40 M.

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A student drops a ball and it falls downward. Types of energy are involved in this energy transformation are kinetic and gravity potential.

Energy is defined as the capacity of a physical system to perform work.

Types of energy are Kinetic energy and potential energy.

The energy an object has as a result of motion is known as kinetic energy. Applying force to an object will cause it to accelerate.

Potential energy is the energy that is stored in any object or system as a result of its position or component arrangement.

A student drops a ball and it falls downward then there is kinetic energy due to motion and potential energy due to height.

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The output response v(t) to a unit step input, we first express the transfer function H(s) in partial fraction form. After solving for constants A and B, we take the inverse Laplace transform of each term to get h(t). For the sinusoidal steady-state response to input vi(t) = 10 cos(40t + 60°) V, we multiply Vi(s) by H(s) and simplify V(s). Then, we use inverse Laplace transform properties to find the steady-state response v(t). The sinusoidal steady-state response to the input voltage vi(t) = 10 cos(40t + 60°) V is given by v(t) = (10 / ((s + 1)(s + 11))) * (s + 10) * (10 \(e^{(-20t)}\) + 200t \(e^{(-20t)}\)).

To find the output response v(t) to a unit step input, we need to take the inverse Laplace transform of the transfer function H(s) =\((s + 10) / (s^2 + 18s + 11).\)
Step 1: Write the transfer function in partial fraction form:
H(s) = A / (s + 1) + B / (s + 11)
Step 2: Multiply both sides of the equation by the denominator:
(s + 1)(s + 11) H(s) = A(s + 11) + B(s + 1)
Step 3: Set s = -1 and solve for A:
(-1 + 11) H(-1) = A(-1 + 11) + B(-1 + 1)
10 H(-1) = 10A
A = H(-1)
Step 4: Set s = -11 and solve for B:
(-11 + 1) H(-11) = A(-11 + 11) + B(-11 + 1)
-10 H(-11) = -10B
B = H(-11)
Step 5: Substitute the values of A and B back into the partial fraction form:
H(s) = H(-1) / (s + 1) + H(-11) / (s + 11)
Step 6: Take the inverse Laplace transform of each term:
h(t) = \(H(-1) e^{(-t)} + H{(-11)} e^{(-11t)}\)
Since we have a unit step input, the Laplace transform of a unit step function is 1/s. Therefore, the Laplace transform of the unit step input is U(s) = 1/s.
Step 7: Multiply the transfer function H(s) by the Laplace transform of the unit step input:
V(s) = H(s) U(s)
V(s) = (H(-1) / (s + 1) + H(-11) / (s + 11)) * (1/s)
Step 8: Take the inverse Laplace transform of V(s) to find the output response v(t):
h(t) = \(H(-1) e^{(-t)} + H{(-11)} e^{(-11t)}\)
Now, let's find the sinusoidal steady-state response to an input voltage vi(t) = 10 cos(40t + 60°) V.
Step 1: Write the input voltage in phasor form:
Vi(s) = 10 / (\(s^2\) + 40s + 1600)
Step 2: Multiply Vi(s) by the transfer function H(s):
V(s) = H(s) Vi(s)
V(s) = (s + 10) / (s^2 + 18s + 11) * (10 / (s^2 + 40s + 1600))
Step 3: Simplify V(s) by canceling out common factors and combining terms:
V(s) = (s + 10) / ((s + 1)(s + 11)) * (10 /\((s + 20)^2\))

Step 4: Take the inverse Laplace transform of V(s) to find the steady-state response v(t):
\(v(t) = (10 / ((s + 1)(s + 11))) * (s + 10) * (10 e^{(-20t)} + 200t e^{(-20t)})\)
Note: In this step, we use the inverse Laplace transform properties to simplify the expression.

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Therefore, the sensitivity of the Bourden gauge in terms of scale length per bar (i.e., mm/bar) is 1.6 mm/bar.

The sensitivity of a bourdon gauge in terms of scale length per bar is the rate of change of the bourdon gauge's reading for a unit change in the applied pressure. The formula to calculate the sensitivity of bourdon gauge is:Sensitivity = Total length of scale / Pressure range Sensitivity = (270/360) × π × D / PWhere D = diameter of the dial and P = Pressure rangeThe diameter of the circular dial can be calculated as follows:D = Length of pointer + Length of pivot + 2 × OverrunD = 50 + 10 + 2 × 5D = 70 mmThe pressure range of the gauge is given as 0 to 15 bar. Thus, P = 15 bar.Substituting these values in the above formula, we get: Sensitivity = (270/360) × π × 70 / 15Sensitivity = 1.6 mm/bar. Therefore, the sensitivity of the Bourden gauge in terms of scale length per bar (i.e., mm/bar) is 1.6 mm/bar.

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The longest wavelength of light that can remove an electron from magnesium will be obtained.

To determine the longest wavelength of light that can remove an electron from magnesium (Mg) metal, we can use the equation relating the energy of a photon (E) to its wavelength (λ):

E = hc/λ

Where:

E is the energy of the photon

h is the Planck's constant (6.62607015 x 10^(-34) J·s)

c is the speed of light in a vacuum (2.998 x 10^8 m/s)

λ is the wavelength of light

In this case, the energy required to remove an electron from magnesium (Mg) metal, also known as the work function (Φ), is given as 3.68 eV. We need to convert this energy from electron volts (eV) to joules (J) before we can proceed with the calculation.

1 eV = 1.602176634 x 10^(-19) J

Therefore, the work function Φ for magnesium can be converted to joules as:

Φ = 3.68 eV * (1.602176634 x 10^(-19) J/eV)

Now, we can rearrange the equation to solve for the wavelength (λ):

λ = hc/E

Substituting the values:

λ = (6.62607015 x 10^(-34) J·s * 2.998 x 10^8 m/s) / Φ

Calculating Φ:

Φ = 3.68 eV * (1.602176634 x 10^(-19) J/eV) = 5.8988621312 x 10^(-19) J

Now, we can calculate the wavelength:

λ = (6.62607015 x 10^(-34) J·s * 2.998 x 10^8 m/s) / (5.8988621312 x 10^(-19) J)

After performing the calculation, the longest wavelength of light that can remove an electron from magnesium will be obtained.

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My understanding of the concept of when a baby is considered alive is based on the medical, legal, and ethical standards provided by the scientific and medical communities, and it is not based on personal beliefs or opinions.

The determination of when a baby is considered alive is a complex and nuanced issue that is influenced by a variety of factors, including medical, legal, religious, and ethical considerations.

Therefore, it is important to consult with qualified professionals in each area to gain a better understanding of this topic.

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Complete Question:

What I your view on when the baby I alive? What standard or standard are you using to form your opinion?

The phase constant, denoted as φ0, is a fundamental concept in wave analysis that describes the starting position of a wave at a given point in time. It is particularly relevant when studying sinusoidal waves like sine or cosine waves.

The phase constant is a term used in wave analysis to represent the initial phase or starting position of a wave.                                                                                                                                                                                                     It indicates the value of the phase at a particular reference point in time.                                                                                                        In simple terms, it determines where the wave begins within its oscillation pattern.                                                                                                                                                                          These waves create a repeating pattern of oscillation, and the phase constant determines where this pattern begins.   To visualize it, imagine a graph with time on the horizontal axis and wave amplitude on the vertical axis.                                            The phase constant φ0 determines the horizontal shift of the wave, indicating the position at which the wave starts.                 For instance, if the phase constant is zero, the wave starts at its highest positive amplitude.                                                                                 If the phase constant is π/2 (pi/2), the wave starts at the point where it crosses zero.                                                                                                                  And if the phase constant is π (pi), the wave starts at its highest negative amplitude.                                                                                                                                                                                                          The phase constant is typically expressed in radians or degrees, depending on the context.                                                                      It plays a crucial role in wave analysis as it influences the behavior, interference, and superposition of waves.                                                                              In conclusion, the phase constant φ0 signifies the initial phase or starting position of a wave.                                                                         It determines where the wave begins within its oscillation pattern and is a vital parameter in wave analysis.

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Answer:

Explanation:

The average pressure at mean sea-level (MSL) in the International Standard Atmosphere (ISA) is 1013.25 hPa, or 1 atmosphere (atm), or 29.92 inches of mercury. Pressure (p), mass (m), and the acceleration due to gravity (g), are related by P = F/A = (m*g)/A, where A is surface area.

We can solve this problem by using the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

ΔU = Q - W

Since the container is well-insulated, Q = 0 and therefore ΔU = -W. The change in internal energy is given by:

ΔU = (3/2)nRΔT

where n is the number of moles of gas, R is the gas constant, and ΔT is the change in temperature. Since the gas is monatomic, we can substitute n = N/NA, where N is the number of atoms and NA is Avogadro's number, and use R = kNA, where k is the Boltzmann constant. Then we have:

ΔU = (3/2)(N/NA)kΔT

The work done by the gas is given by:

W = PextΔV

where Pext is the external pressure and ΔV is the change in volume. Since the pressure is constant, we can substitute Pext = Patm, the atmospheric pressure. Then we have:

W = Patm(V2 - V1)

where V1 and V2 are the initial and final volumes, respectively. Substituting the given values, we have:

W = 5 J

V1 = 16 cc = 16×10^-6 m^3

V2 = 3 cc = 3×10^-6 m^3

ΔV = V2 - V1 = -13×10^-6 m^3 (negative because the gas is compressed)

Substituting into the work equation, we get:

5 J = (101325 Pa)(-13×10^-6 m^3)

P = -5/(101325×13×10^-6) atm

P ≈ 0.003 atm

This result is negative, which means that the gas has done work on the surroundings rather than the other way around. This is because we have compressed the gas by doing work on it, and the gas has then expanded against the walls of the container, doing work on the surroundings. To get the final pressure of the gas, we need to add the atmospheric pressure to the pressure change caused by the compression:

Pf = Patm - ΔP = Patm - W/V2 = 1 - 5/(3×10^6) atm

Pf ≈ 0.9983 atm

Therefore, the final pressure of the gas is 0.9983 atm.

When the focal length (the distance from the lens to either focal point F) of the lens is f, the following is true of the horizontal distance di from the lens to the image. The horizontal distance di from the lens to the image is greater than 2f.

Explanation: When light rays pass through a convex lens, they converge at a point, as shown in the diagram below. A convex lens is a lens that is thicker in the middle than it is at the edges.

The principal focus (F) of a convex lens is the point where parallel rays of light converge. The focal length (f) of a convex lens is the distance between the center of the lens and the principal focus (F).

The image of an object formed by a convex lens is real and inverted. The size and position of the image are determined by the position of the object and the focal length of the lens.

The following is true of the horizontal distance di from the lens to the image when the focal length of the lens is f:The horizontal distance di from the lens to the image is greater than 2f when the image is real and inverted.

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We are asked to determine the net rate of radiation of a roof given its area and its emisivity. To do that we will use the following formula:

Where:

The Stefan-Boltzmann's constant is given by:

Now, we need to convert the temperature to Kelvin. To do that we use the following:

Where:

For the 33°C we have:

For the 14°C:

Now, we substitute the values:

Solving the operation:

Therefore, the net rate of radiation is -27870.84 Watts.

5A current is passing through the copper wire of diameter 2.05 mm.

Current is the rate of flow of electrons in a conductor.

a) 5.00 A of current = 5 Coulombs of charge per second is passing through the wire

Since current = coulombs/second

Number of electrons per second can be calculated by the formula,

\(n_{e} = \frac{I}{e}\)

I = 5.00 A

\(e = 1.60 *10^{-19}\)

\(n_{e} = \frac{5}{1.60*10^{-19} }\)

\(n_{e} =3.125 * 10^{19}\)

\(3.125 * 10^{19}\) electrons pass through the lamp per second.

b) Current density is defined as the amount of electric current passing per unit cross-section area. It is denoted by j.

\(j = \frac{I}{A}\)

I = 5.00 A

A = \(\frac{\pi }{4} * d^{2}\)

A = 0.7854 * 2.05 * 2.05 * \(10 ^{-6} m^{2}\)

A = \(3.300 * 10^{-6} m^{2}\)

\(j = \frac{5}{3.30010^{-6} }\)

j = 1.51 * \(10^{6}\) \(\frac{A}{m^{2} }\)

The current density through the wire is 1.51 * \(10^{6}\) \(\frac{A}{m^{2} }\).

c) Speed of an electron = u = \(\frac{I}{nAe}\)

u = \(\frac{5}{3.125*1.60*3.300}\)

u = 0.303 mm/s

Speed of the electron in the wire is  0.303 mm/s.

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Answer: Macroscoptic Output

Explanation:

Answers to the rest:

1. B) macroscopic outputs.

2.A) a microscopic change creating a macroscopic output

3.B) Because the energy levels of the electrons in different metals are usually not the same, different metals usually emit different colors of visible light.

4.A) Heat is applied to a solid, causing its molecules to move quickly.

5.A) strontium, sodium, copper, potassium

When fireworks explode, sound and light are produced, these are examples of macroscopic outputs.

In conclusion, when fireworks explode, sound and light are produced, these are examples of macroscopic outputs.

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a ) When they reach the ground, rock B has greater velocity.

b ) Both rocks have the same acceleration

c ) Rock A and Rock B arrives at the same time

According to law of conservation of energy,

1 / 2 m u² + m g hi = 1 / 2 m v² + m g hf

u = 0

hf = 0

m g hi = 1 / 2 m v²

v = √ ( 2 g / m ) √ hi

v ∝ √ hi

a ) hi of rock A will be higher because it reaches a certain height above the ground which will be considered as initial height for rock A. So, the final velocity of rock A is higher.

b ) Both the rock are affected by only the force of gravity. So they will have the same acceleration of 9.8 m / s²

c ) If air resistance is ignored,

s = u t + 1 / 2 at²

For an object that is dropped,

u = 0

a = g

s = at² / 2

t = √ ( 2 s / g )

It can clearly be seen that no matter what height an object might be dropped from, if air resistance is ignore they will fall at the same time.

Therefore,

a ) When they reach the ground, rock B has greater velocity.

b ) Both rocks have the same acceleration

c ) Rock A and Rock B arrives at the same time

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The electric field exerted by a point charge is given by:

where q is the charge and r is the distance to the point where we want to calculate the electric field.

In this case we have three charges with the following properties:

Now, the total electric field on a point is the addition of all the charges; in this case we want the net field to be zero. Then we have:

Now, since the last equation does not have a real solution this means that this distribution of charges will not exert a zero electric field on the origin.

Therefore, there's no possible distance for the field to be zero in this charge configuration

The right response is d.) 1.96 X 10 5 J.

We may apply the calculation for work performed by a constant pressure system to get the quantity of heat extracted from within the refrigerator:

/W = PΔV
Where W is the work done, P is the pressure, and ΔV is the change in volume.
Given the pressure (P) of 4.13 x 10^5 Pa, the radius (r) of the piston of 0.019 m, and the distance (d) the piston is compressed of 25.0 m, we can find the change in volume (ΔV) using the formula for the volume of a cylinder:
/ΔV = πr^2d
Plugging in the given values, we get:
/ΔV = \π(0.019 m)^2(25.0 m) = 0.02267 m^3
Now, we can plug this value back into the formula for work done:
W = \PΔV = (4.13 x 10^5 Pa)(0.02267 m^3) = 1.96 X 10 ^ 5 J
Therefore, the amount of heat removed from within the refrigerator is 1.96 X 10 ^ 5 J.  where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

In this case, we know that the change in the refrigerant's internal energy is 0 J after each cycle, so ΔU = 0 J. We also know that the compressor does work on the refrigerant, which is equivalent to a constant pressure of 4.13 x 10^5 Pa compressing a circular piston with a radius of 0.019 m a distance of 25.0 m. Therefore, the work done by the compressor is:

W = PΔV

where P is the constant pressure, and ΔV is the change in volume of the refrigerant.

Since the refrigerant is compressed by a piston with a radius of 0.019 m, the change in volume is:

/ΔV = πr^2Δx

where r is the radius of the piston and Δx is the distance the piston moves. Substituting the given values, we get:

/ΔV = π(0.019 m)^2(25.0 m) = 0.0227 m^3

Therefore, the work done by the compressor is:

/W = PΔV = (4.13 x 10^5 Pa)(0.0227 m^3) =

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The correct option is (c) 11709J. The work done by the compressor on the refrigerant is given by: W = PΔV; where P is the constant pressure of 4.13 x 10^5 Pa, and ΔV is the refrigerant's volume change.

We can use the formula for the volume of a cylinder to find the initial and final volumes: V1 = πr^2h1 = π(0.019 m)^2(0 m) = 0 m^3; V2 = πr^2h2 = π(0.019 m)^2(25.0 m) = 0.0225 m^3. Where h1 is the initial height (which we take to be 0 m), and h2 is the final height (which is given as 25.0 m). Therefore, the change in volume is: ΔV = V2 - V1 = 0.0225 m^3. Substituting the values into the formula for work, we get: W = (4.13 x 10^5 Pa)(0.0225 m^3) = 9292.5 J

This is the amount of work done on the refrigerant by the compressor during each cycle. Since the change in internal energy is 0 J, the work must be equal to the heat removed from within the refrigerator. Therefore, the answer is: c.) 11,709 J; which is obtained by multiplying the work per cycle by the number of cycles, assuming that the same amount of heat is removed in each cycle.

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so ummmm what about ?

because I cant see any actual question?

Answer:

Distance travel s = 296.8 m

Explanation:

Given:

Initial velocity u = 6.5 m/s

Constant acceleration a = 2.1 m/s²

Time T = 14 s

Find:

Distance travel s

Computation:

s = ut + (1/2)at²

s = (6.5)(14) + (1/2)(2.1)(14)²

s = 91 + 205.8

Distance travel s = 296.8 m

Answer:

A.protons and neutrons in the nucleus.

The true azimuth of the AB alignment is 91º 52' (east of north), the magnetic azimuth is 100º 22' (east of north), and the grid azimuth is 108º 52' (east of north).

To find the true azimuth, magnetic azimuth, and grid azimuth of the AB alignment, we need to consider the magnetic declination. The magnetic declination indicates the angle between true north and magnetic north at a specific location. In this case, the magnetic declination is 8º 30' E, which means that the magnetic north is 8º 30' east of the true north.

To calculate the true azimuth, we subtract the magnetic declination from the grid azimuth. The grid azimuth is given as 100º 22', so subtracting the magnetic declination of 8º 30' E gives us a true azimuth of 91º 52' (east of north).

The magnetic azimuth remains the same as the grid azimuth, which is 100º 22' (east of north).

The grid azimuth is calculated by adding the magnetic declination to the true azimuth. Since the magnetic declination is east, we add it to the true azimuth. Adding 8º 30' E to the true azimuth of 91º 52' gives us a grid azimuth of 108º 52' (east of north).

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Answer:

Explanation:

as soon as you are offered one  :P

Answer:

In the surface of the moon, gravitational acceleration is 1.63 m/s*2.

Explanation:

An object of mass M will accelerate gravitationally at a distance R if it is at the following distance:

g = G*M/R^2

Where the gravitational constant is G.

G = 6.67*10^(-11) m^3/(kg*s^2)

At the surface of a moon, the distance between its surface and its center will be equal to its radius, since a moon's mass is concentrated at its center, thus:

R = 1740 km

It's important to remember that we need meters in order to work:

1 km = 1000 m

so:

1740 km = (1740)*1000 m = 1740000 m

R =  1740000 m

Basically, the mass consists of:

M = 7.4x10^22 kg

Incorporating all that into the gravitational acceleration equation, we get:

g = (6.67*10^(-11) m^3 / (kg*s^2))*(7.4x10^22 kg) / ( 1740000 m)^2

g = 1.63 m / s^2

In the surface of the moon, gravitational acceleration is 1.63 m / s*2.

Answer:

thanks for the points

Explanation:

The interaction energy for two point charges, q₁ and q₂, a distance 'a' apart is q₁q₂/4πε₀a.

In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being evaluated. The interaction energy generally depends on the relative position of the objects.

For example q₁q₂/4πε₀Δr is the electrostatic interaction energy between two objects with charges q₁ and q₂.

\(W_{tot}\) = ε₀/2(∫E²dτ)

= ε₀/2{(∫E₁ + E₂)²dτ}

= ε₀/2(∫E₁² + E₂² + 2E₁E₂)dτ

= W₁ + W₂ + ε₀(∫E₁ × E₂)²dτ

E₁ = 1/4πε₀(q₁/r²)r

E₂ = 1/4πε₀(q₂/ᴫ²)ᴫ

\(W_{i}\) = ε₀q₁q₂/(4πε₀)²[∫{(1/r²ᴫ²)cosβr²sinθdrdθdφ}]

Where (from the figure)

ᴫ = √(r² + a² - 2ra cosθ), cosβ = (r - a cosθ)/ᴫ

Therefore

\(W_{i}\)  = {q₁q₂/(4π)²ε₀} 2π∫{(r - acosθ)/ᴫ³} sinθ drdθ

First do the r integral first, changing variables to ᴫ:

2ᴫdᴫ = (2r - 2a cosθ)

⇒(r - a cosθ)dr = ᴫdᴫ

As r : 0→∞, ᴫ : a→∞, so

\(W_{i}\) = {q₁q₂/8πε₀a} \(\int\limits^\pi _0\)(∫limit 0 to ∞ 1/ᴫ² dᴫ) sinθ dθ

The ᴫ integral is 1/a, so

\(W_{i}\) = {q₁q₂/8πε₀a} \(\int\limits^\pi _0\) sinθ dθ

\(W_{i}\) = q₁q₂/4πε₀a

This is the exact interaction energy of two-point charges.

To know more about electrostatic, here

https://brainly.com/question/14889552

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Neon gas does not absorb orange and red wavelengths because its electronic energy levels do not match the energy of photons corresponding to those wavelengths.

Neon atoms have specific energy levels for their electrons, and these energy levels are quantized. When a neon atom is excited, for example, by an electric discharge, electrons within the atom can jump to higher energy levels.

As these excited electrons return to their original energy states, they release energy in the form of light. This light emission corresponds to specific energy differences between the excited and ground states, resulting in the characteristic orange and red wavelengths associated with neon.

However, when it comes to absorption, neon's energy levels do not align with the orange and red wavelengths. Therefore, neon atoms do not readily absorb photons at those wavelengths. Instead, they tend to emit light in those specific wavelengths when returning from excited states to lower energy states.

In summary, the electronic energy levels of neon atoms do not correspond to the energy of orange and red photons, which is why neon gas does not absorb those wavelengths. Instead, it emits light in the orange and red range when excited electrons transition to lower energy states.

Learn more about wavelength here; brainly.com/question/10750459

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Answer:

Explanation:

If a ship sets out to sail to a point 154 km due north and an unexpected storm blows the ship to a point 72 km due east of its starting point, then the ships distance from the original destination can be gotten by finding the displacement of the ship and this can be gotten by using pythagoras theorem.

Let D be the unknown displacement

According to the theorem;

D² = 154² + 72²

D² = 23716 + 5184

D² = 28900

D = √28900

D = 170km

This means that the ship must now sail a distance of 170km for it to reach its original destination.