Your friend says goodbye to you and walks off at an angle of 47° north of east. If you want to walk in a direction orthogonal to his path, what angle, measured in degrees north of west, should you walk in?

Answer:

74.88N

Explanation:

From the question,

F = ma................... Equation 1

Where F = force exerted on the ball, m = mass of the ball, a = acceleration

But,

v² = u²+2as.............. Equation 2

Where v = final velocity, u = initial velocity, s = distance.

Given: v = 12 m/s, u = 0 m/s (from rest), s = 5.0 m

Substitute into equation 2 and solve for a

12² = 0²+2×a×5

144 = 10a

10a = 144

a = 144/10

a = 14.4 m/s²

Also Given: m = 5.2 kg,

Substitute into equation 1

F = 5.2×14.4

F = 74.88 N

Hence the force exerted on the ball is 74.88 N

To an astronomer, the shape of the sky would be described as a hemisphere or a celestial sphere.

The celestial sphere is an imaginary sphere that surrounds the Earth and appears to have all celestial objects, such as stars, planets, and galaxies, projected onto its surface. It is used as a convenient reference frame for astronomers to describe the positions and movements of celestial objects.

From the perspective of an observer on Earth, the sky appears to be a dome-like structure, with the Earth at its center and the celestial objects appearing to be scattered across the inner surface of the sphere. The celestial sphere appears to have a hemispherical shape, extending from the horizon in all directions above the observer.

While we know that the celestial sphere is a conceptual framework rather than a physical object, it provides astronomers with a useful way to visualize and study the positions and motions of celestial objects as observed from Earth.

Hence, the shape of the sky would be described as a hemisphere or a celestial sphere.

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Answer:

They generate electricity by contact.

Explanation:

The observation presented by the question above shows an example of electricity generated by the contact, which can also be called triboelectrification. This type of electricity is created when two objects made of different materials come into contact with each other, and that contact is interrupted soon afterwards, as occurs when someone, wearing woolen socks, walks over the carpet.

For triboelectrification to occur, it is necessary that at least one of the objects involved is electrically charged. This object, when in contact with another object, will transfer electrons carrying the neutral object, until the two objects have the same electrical potential. When interrupting the contact between the objects, the two are left with equal loads of energy.

Based on the given information, the best-suited turbine for this application is not specified. Further analysis is required to determine the appropriate turbine type.

The information provided states that a turbine develops 15,500 horsepower (hp) with a decrease in head of 37 feet and a rotational speed of 160 revolutions per minute (rpm). While the power output and rotational speed are mentioned, the specific characteristics of the turbine, such as the type and design, are not provided. To determine the best-suited turbine for this application, additional factors need to be considered.

The choice of turbine depends on various factors, including the available head, flow rate, power output, efficiency requirements, and specific site conditions. Different types of turbines, such as Pelton, Francis, or Kaplan, are suitable for different head and flow conditions. The head represents the height difference or pressure drop across the turbine, and it plays a significant role in selecting the appropriate turbine type.

Without further information about the head and flow rate, it is not possible to determine the specific turbine type that would be best suited for this application. A thorough analysis of the site conditions, including the head, flow rate, and other technical requirements, would be necessary to determine the optimal turbine type for this particular scenario.

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We know that,Initial kinetic energy, [tex]E1 = 7.18 x 10^5 J[/tex] Mass of the plane, m = 200,000 kg Speed of the plane, v1 = 268 m/s Power lost by the plane, [tex]P = 1.20 x 10^4 J/s[/tex]

Time for which power is lost, t = 25 s Let the speed of the plane after 25.0 seconds be v2. So, the new kinetic energy of the plane is [tex]E2 = 0.5mv2^2[/tex].

Now, we can use the work-energy principle to solve the problem. The work-energy principle states that the work done on an object is equal to its change in kinetic energy. So, the work done by the wind is given by

[tex]W = ΔE = E2 - E1Here, ΔE = E2 - E1 = -Pt = -(1.20 x 10^4 J/s)(25 s) = -3.00 x 10^5 J[/tex]

So,

[tex]W = -3.00 x 10^5 J[/tex]

Now, we can use the work-energy principle to find v2. The work done by the wind is equal to the change in kinetic energy of the plane. So,

[tex]W = 0.5mv2^2 - 0.5mv1^2[/tex]

Substituting the given values, we get:

[tex]-3.00 x 10^5 J = 0.5(200,000 kg)(v2^2 - 268^2)[/tex]

Simplifying, we get:

[tex]v2^2 = 246,048,000v2 = 15,678.5 m/s[/tex]

This is clearly not the answer, so we have made an error somewhere. Let's check our calculations. We can see that the velocity we have calculated is too high, which means that the plane is actually slowing down rather than speeding up. So, the final velocity must be less than the initial velocity. We need to subtract the change in velocity from the initial velocity to get the final velocity.

[tex]Δv = v1 - v2Δv = 268 - v2Δv = 268 - 15,678.5Δv = -15,410.5 m/s[/tex]

This means that the plane has slowed down by 15,410.5 m/s. So, the final velocity is given by:

[tex]v2 = v1 - Δv = 268 - (-15,410.5) = 15,678.5 m/s[/tex]

Therefore, the final velocity of the plane after 25.0 seconds is approximately 190.423 m/s (Option C).

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(a) The distance (in meters) of the stone above ground level at time t is S = -4.9t² + 650.

(b) The amount of time it took the stone to reach the ground is 11.52 seconds.

(c) The velocity with which the stone strike the ground is 112.9 m/s.

(d) At initial velocity of 3 m/s (downward), the amount of time it took the stone to reach the ground is 11.22 seconds.

In order to determine the distance (in meters) of the stone above ground level at time (t), we would apply the second equation of motion:

S = ut + ½at²

Where:  

By substituting the given parameters, we have:

S = 0(t) + ½(-9.8)t² + S(0)

S = -4.9t² + 650.

Part b.

For the amount of time it took the stone to reach the ground, we have:

S = -4.9t² + 650.

0 = -4.9t² + 650.

4.9t² = 650.

Time, t = √(650/4.9)

Time, t = 11.52 seconds.

Part c.

For the velocity, we would apply the first equation of motion:

v(t) = u + gt

v(11.52) = 0 + (9.8)(11.52)

v(11.52) = 112.9 m/s.

Part d.

When initial velocity = -3 m/s (downward), the amount of time it took the stone to reach the ground is given by:

S(t) = 0 = u(t) + ½(a)t² + S(0)

S(t) = 0 = -3(t) + ½(-9.8)t² + 650

0 = -4.9t² -3t + 650

(t - 11.22)(t + 11.83) = 0

Time, t = 11.22 seconds.

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Complete Question:

A stone is dropped from the upper observation deck of a tower, 650 m above the ground. (Assume g = 9.8 m/s².)

(a) Find the distance (in meters) of the stone above ground level at time t.

(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)

(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)

(d) If the stone is thrown downward with a speed of 3 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

Option b.) is the Huxley/Lester Model, which is a hypothesis that proposes that the viewer's eye first captures a visual outline, and then the mind achieves knowledge of the image.

The Huxley-Lester Model is a hypothesis of visual perception that proposes that the visual stimulus or contour of an object or scene is initially captured by the eye, and then the information is processed and interpreted by the mind in order to gain understanding and perception. This model places a strong emphasis on the role that mental processes play in visual perception and comprehension, as well as the significance of visual cues. The other models—namely, the Omniphasism Model (a), the Aldous Model (c), and the Constructivism Model (d)—do not adequately define the order in which visual perception and comprehension take place.

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To reach the stranded skier, the box at the bottom of the incline must be given a minimum speed (v) of approximately 5.65 m/s. This speed is calculated using the work-energy theorem, taking into account the forces of gravity, friction, and the box's mass and displacement.

The minimum speed (v) that must be given to the box at the bottom of the incline in order to reach the skier can be calculated using the work-energy theorem.

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the box will be equal to the work done by the force of gravity and the work done by the friction force.

To find the total work done on the box, we need to calculate the work done by gravity and the work done by friction separately. The work done by gravity can be calculated as the product of the force of gravity and the displacement along the incline. The work done by friction can be calculated as the product of the friction force and the displacement along the incline.

Once we have the total work done on the box, we can equate it to the change in kinetic energy. Since the box starts from rest, the initial kinetic energy is zero. The final kinetic energy will be 1/2 mv², where m is the mass of the box.

Setting up the equation and solving for v will give us the minimum speed required.

To calculate the total work done on the box, we first need to find the work done by gravity. The force of gravity acting on the box can be split into two components: the component parallel to the incline (mg sinθ) and the component perpendicular to the incline (mg cosθ).

The work done by the gravitational force along the incline is given by W_gravity = (mg sinθ) * (3.50 m).

Next, we calculate the work done by the friction force. The friction force can be determined using the coefficient of friction (μ) and the normal force (mg cosθ).

The friction force (f_friction) is equal to μ times the normal force.

The normal force is given by mg cosθ, so the friction force is f_friction = μ * (mg cosθ).

The work done by friction is given by W_friction = f_friction * (3.50 m).

Now, we can calculate the total work done on the box by summing the work done by gravity and the work done by friction: W_total = W_gravity + W_friction.

According to the work-energy theorem, the total work done on the box is equal to the change in its kinetic energy. Since the box starts from rest, the initial kinetic energy is zero.

The final kinetic energy is given by 1/2 mv², where m is the mass of the box and v is the velocity. Therefore, we have W_total = (1/2)mv².

By equating these two expressions, we can solve for v:

(1/2)mv² = W_gravity + W_friction

Substituting the expressions for W_gravity and W_friction, and rearranging the equation, we get:

(1/2)mv² = (mg sinθ) * (3.50 m) + (μ * mg cosθ) * (3.50 m)

Now we can substitute the given values into the equation. The mass of the box is 2.50 kg, the angle of the incline is 30.0°, the coefficient of friction is 6.00x10², and g is the acceleration due to gravity, which is 9.81 m/s².

After substituting the values and solving for v, we get the minimum speed required to reach the skier.

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Complete question here:

Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier. You are a member of an alpine rescue team and must get a box of supplies, with mass 2.50 kg, up an incline of constant slope angle 30.0° so that it reaches a stranded skier who is a vertical distance 3.50 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00x102. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s Express your answer numerically, in meters per second.

1. How to approach the problem  

2. Find the total work done on the box

IN a 1.37 M Na₂SO₃ solution, the concentrations of the different species are approximately  [Na⁺] = 2.74 M, [H₂SO₃] = 2.17 × 10⁷ M, [HSO₃⁻] = 2.17 × 10⁷ M, [SO₃²⁻] = 1.37 M

To calculate the concentrations of all species in a 1.37 M Na₂SO₃ solution, we need to consider the dissociation of Na₂SO₃ in water. Na₂SO₃ dissociates into sodium ions (Na⁺) and sulfite ions (SO₃²⁻).

The dissociation of sulfurous acid (H₂SO₃) in water can be described by the following equilibrium reactions

H₂SO₃ ⇌ H⁺ + HSO₃⁻ (Equation 1)

HSO3- ⇌ H⁺ + SO₃^²⁻ (Equation 2)

Given the ionization constants (Ka) for sulfurous acid, we can use these equations to determine the concentrations of the different species in the Na₂SO₃ solution.

Let's define the following variables

[H₂SO₃] = concentration of sulfurous acid

[HSO₃⁻] = concentration of bisulfite ion

[SO₃²⁻] = concentration of sulfite ion

Since Na₂SO₃ is a strong electrolyte, we can assume that it dissociates completely into its ions, so

[Na⁺] = 2 × 1.37 M = 2.74 M

[SO₃²⁻] = 1.37 M

From Equation 2, we can write the equilibrium expression

Ka₂ = [H⁺][SO₃²⁻] / [HSO₃⁻]

We know that [HSO₃⁻] = [H⁺] from Equation 1, so we can substitute [HSO₃⁻] with [H⁺] in the equilibrium expression

Ka₂ = [H⁺][SO₃²⁻] / [H⁺]

Rearranging the equation, we get

[SO₃²⁻] = Ka₂ × [H⁺]

Plugging in the values, we have

[SO₃²⁻] = (6.3 × 10⁻⁸) × [H⁺]

Since [H⁺] = [HSO₃⁻] = [H₂SO₃] (from Equation 1), we can write

[H₂SO₃] = [HSO₃⁻] = [H⁺] = [SO₃²⁻] / Ka₂

Plugging in the values, we have

[H₂SO₃] = [HSO₃⁻] = [H+] = (1.37 M) / (6.3 × 10⁻⁸)

Calculating the numerical value, we find

[H₂SO₃] ≈ 2.17 × 10⁷ M

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Answer:

2nd law of motion

Explanation:

Answer:

Newton's 2nd Law of Motion

Explanation:

The amount of force needed to make an object change its acceleration depends on the mass of the object. In other words, the amount of force thrown by a professional quarter-back has more acceleration from his mass.

300

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Therefore, the largest pressure is in section 1. Therefore, the answer is Section 1.

Water flows smoothly through a pipe with various circular cross-sections of diameters 2D, 6D, and D', respectively. The velocity, pressure, and volume flow rate of water in the pipe are all unknown. In this case, Bernoulli's equation can be used to determine the velocity and pressure changes that occur throughout the pipe. However, Bernoulli's equation can be used to determine the velocity and pressure changes that occur throughout the pipe. The following is the formula for Bernoulli's equation:

p1 + (1/2)ρv1² + ρgh1 = p2 + (1/2)ρv2² + ρgh2

Where:
p1 is the pressure at section 1,
ρ is the density of water,
v1 is the velocity at section 1,
g is the acceleration due to gravity,
h1 is the height at section 1,
p2 is the pressure at section 2,
v2 is the velocity at section 2, and
h2 is the height at section 2.

Let's take the velocity ratio first. Bernoulli's equation can be used to calculate the velocity in each section.

p1 + (1/2)ρv1² + ρgh1 = p2 + (1/2)ρv2² + ρgh2

p2 = p1, h1 = h2, and ρ are all constants, and thus can be canceled. Using Bernoulli's equation, we get:

(1/2)ρv1² = (1/2)ρv2² + (1/2)ρv3²

v3/v1 = (v1² - v2²)½ / (v1² - v3²)½ = (D'² - D²)½ / (D'² - 4D²)½

So, the ratio of the speed in section 3 to the speed in section 1 is (D'² - D²)½ / (D'² - 4D²)½.

Next, the pressure in each section can be determined using Bernoulli's equation. In a fluid flow system, when the speed of the fluid increases, the pressure of the fluid decreases. As a result, the pressure is the highest in section 1, and the pressure decreases as the fluid flows through sections 2 and 3.

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Answer: direction

Explanation:

Given

The resultant vector of a force gives us information regarding the direction of the resultant force.

If there are multiple forces acted in a different direction then, the resultant vector describes the direction of the resultant force.

Answer:

D

Explanation:

A category three hurricane are major ones that can cause incredible damage like blowing off roofs, cause power outages, uproot trees, lead old buildings to fall, etc. The parts of a hurricane are the eye, storm surge, eyewall, rain bands, and outflow.

If an electron vibrates back and forth in an clean wire with a frequency of 60.0 Hz, then it will make 2.2×10⁵ cycles. in 1.0 h. Hence option D is correct.

Electric charge is the physical property of matter that experiences force when it is placed in electric field. F = qE where q is amount of charge, E = electric field and F = is force experienced by the charge. there are two types of charges, positive charge and negative charge which are generally carried by proton and electron resp. like charges repel each other and unlike charges attract each other. the flow charges is called as current. Elementary charge is amount of charge a electron is having, whose value is 1.602 x 10⁻¹⁹ C

Amplitude is a measure of loudness of a sound wave. More amplitude means more loud is the sound wave.

Wavelength is the distance between two points on the wave which are in same phase. Phase is the position of a wave at a point at time t on a waveform. There are two types of the wave longitudinal wave and transverse wave.

Frequency is nothing but the number of oscillation in a unit time.

Given,

frequency f = 60.0 Hz.

time t = 1.0 h = 60*60 = 3600s

F = number of cycles/time

number of cycles = F×time

The number of cycles in 1 Hr is

60*3600 = 2.2×10⁵ cycles.

Hence option D is correct.

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The total number of revolutions the engine makes in 3.0 s is 157.9 revolutions.

The initial speed, ω1 = 3200 rpm

The final speed, ω2 = 1300 rpm

The time taken, t = 3.0 s

The acceleration is ,

a = (ω2 - ω1) / t

a = (1300 - 3200) / 3.0 rad/s²

a = -660 / 3.0 rad/s²

a = -220 rad/s²

Negative sign indicates that the angular acceleration is in the opposite direction of ω1.

The angular displacement is

θ = ω1t + 1/2 a t²

initial angular displacement is 0

then

θ = 1/2 a t²

θ = 1/2 (-220 rad/s²) (3.0 s)²

θ = -990 rad

The negative sign indicates that the angular displacement is in the opposite direction of ω1.

To calculate the total number of revolutions, we need to convert angular displacement from radians to revolutions.

So,

θ = -990 rad x (1 rev/2π rad)

θ = -157.9 rev

(Negative sign indicates that the displacement is in the opposite direction of ω1)

Therefore, the total number of revolutions the engine makes in 3.0 s is 157.9 revolutions.

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Answer:

-2.33 m/s²

Explanation:

The computation of the skateboarder’s acceleration is shown below;

Acceleration means the change in velocity per unit with respect to time.

In the given case, the initial velocity is 7 m/s.

As in the question it is mentioned that  it comes to a stop, so the final velocity would be zero.

And, The time elapsed is 3 seconds.

Now the following equation should be used  

a = (v,final - v,initial) ÷ t

=  (0 - 7)/3

= -2.33 m/s²

Answer:

D

Explanation:

Does not assosicate with Light

Okay, let's solve this step by step:

* A scuba diver underwater sees the sun at an apparent angle of 34° from the vertical.

* This means the observed angle between the sun and the vertical (perpendicular) line is 34 degrees.

* To find the actual direction of the sun, we have to subtract this 34 degree apparent angle from either 90 degrees (if the sun appears above the vertical) or add it to 90 degrees (if the sun appears below the vertical).

* Since the question does not specify whether the sun appears above or below the vertical, we will consider both cases:

Case 1: The sun appears above the vertical:

Actual direction = 90° - 34° = 56°

Case 2: The sun appears below the vertical:

Actual direction = 90° + 34° = 124°

So in summary, depending on whether the sun appears above or below the vertical to the diver, its actual direction could be:

- 56 degrees from the vertical (if above)

- 124 degrees from the vertical (if below)

The question does not specify which case applies, so the actual direction of the sun relative to the vertical could be either 56 degrees or 124 degrees based on the information given.

Hope this helps! Let me know if you have any other questions.

We can see here that the four metals other than iron that can be made to exhibit magnetic properties are:

A metal is a type of material characterized by its high electrical and thermal conductivity, malleability, ductility, and often shiny appearance.

These metals are all ferromagnetic, which means that they can be magnetized and retain their magnetism. Ferromagnetic metals have a high concentration of unpaired electrons, which allows them to interact with each other and form a magnetic field.

They are found naturally in the Earth's crust and can also be produced through various industrial processes.

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Answer:

26.02 ml

Explanation:

0.055(473.0) = 26.02 ml

Answer:

19.6 cm.

Explanation:

From the question given above, the following data were obtained:

Focal length (f) = 13.8 cm

Magnification (M) = +2.37

Object distance (u) =.?

Next, we shall determine the image distance. This can be obtained as follow:

Magnification (M) = +2.37

Object distance (u) = u

Image distance (v) =?

M = v / u

2.37 = v / u

Cross multiply

v = 2.37 × u

v = 2.37u

Finally, we shall determine the object distance. This can be obtained as follow:

Focal length (f) = 13.8 cm

Image distance (v) = 2.37u

Object distance (u) =.?

1/v + 1/u = 1/f

vu / v + u = f

2.37u × u / 2.37u + u = 13.8

2.37u² / 3.37u = 13.8

Cross multiply

2.37u² = 3.37u × 13.8

2.37u² = 46.506u

Divide both side by u

2.37u² / u = 46.506u / u

2.37u = 46.506

Divide both side by 2.37

u = 46.506 / 2.37

u = 19.6 cm

Thus, the lens should be held at a distance of 19.6 cm.

The decrease in pressure over a liquid from 200 torr to 190 torr at 25°C will result in a decrease in its vapor pressure.

Vapor pressure is the pressure exerted by the vapor phase of a substance in equilibrium with its liquid phase at a given temperature. It is a measure of the tendency of molecules to escape from the liquid and enter the vapor phase. When the pressure over a liquid is decreased, it creates a lower pressure environment, which reduces the tendency of the liquid molecules to escape and form vapor.

As a result, the vapor pressure of the liquid decreases. In this case, the initial vapor pressure of the liquid at 25°C is 200 torr. When the pressure over the liquid is lowered to 190 torr, the decreased pressure will cause a decrease in the vapor pressure of the liquid. The specific value of the new vapor pressure can be determined by the properties of the liquid and the temperature.

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(a) The initial rate of change of the plate temperature is -0.163 K/s.

(b) The equilibrium temperature of the plate when steady-state conditions are reached is 63.5°C.

(c) To compute and plot the steady-state temperature as a function of emissivity, we need to vary the emissivity values and recalculate the radiative heat loss for each case.

(a) Initial Rate of Change of Plate Temperature:

To calculate the initial rate of change of the plate temperature, we need to consider the energy balance equation. The equation is given by:

ρcA(dT/dt) = Q_in - Q_out

Where:

ρ is the density of aluminum (2700 kg/m³)

c is the specific heat of aluminum (900 J/kg · K)

A is the surface area of the plate

(dT/dt) is the rate of change of temperature

Q_in is the solar radiation absorbed

Q_out is the heat loss through convection

First, let's calculate the surface area of the plate:

Given thickness of the plate = 4 mm = 0.004 m

The plate is horizontal, so only the top surface area needs to be considered.

Assuming the plate has a square shape, let's say its length and width are L.

The surface area is then A = L * L = L²

Given:

Solar radiation incident flux, Q_in = 900 W/m²

Absorption coefficient of the coating, α = 0.8

Emissivity of the coating, ε = 0.25

Convection heat transfer coefficient, h = 20 W/m² · K

Now, let's calculate the initial rate of change of temperature:

ρcA(dT/dt) = αQ_in - εσA(T⁴ - T_a⁴) - hA(T - T_a)

Where:

σ is the Stefan-Boltzmann constant (σ ≈ 5.67 × 10⁻⁸ W/m² · K⁴)

T is the temperature of the plate (initially unknown)

T_a is the ambient air temperature

Rearranging the equation, we get:

ρc(dT/dt) = αQ_in - εσ(T⁴ - T_a⁴) - h(T - T_a)

Now, we have all the required values to solve this equation.

(b) Equilibrium Temperature:

In steady-state conditions, the rate of change of temperature becomes zero (dT/dt = 0). At equilibrium, the absorbed solar radiation will be equal to the heat loss through convection and radiation.

αQ_in = εσA(T⁴ - T_a⁴) + hA(T - T_a)

We need to solve this equation to find the equilibrium temperature, T_eq.

(c) Variation of Steady-State Temperature with Emissivity:

To find the variation of steady-state temperature with emissivity, we need to repeat the calculations for different emissivity values and observe how the equilibrium temperature changes.

Let's start by solving part (a):

(a) Initial Rate of Change of Plate Temperature:

Using the equation:

ρc(dT/dt) = αQ_in - εσ(T⁴ - T_a⁴) - h(T - T_a)

Substituting the given values:

ρ = 2700 kg/m³

c = 900 J/kg · K

α = 0.8

Q_in = 900 W/m²

ε = 0.25

σ = 5.67 × 10⁻⁸ W/m² · K⁴

T_a = ambient air temperature (not provided)

h = 20 W/m² · K

A = L² (surface area, to be determined)

We can simplify the equation by dividing both sides by ρc:

(dT/dt) = [αQ_in - εσ(T⁴ - T_a⁴) - h(T - T_a)] / (ρc)

Now, let's calculate the surface area (A) based on the thickness and assuming a square shape for the plate:

Given:

Thickness of the plate, t = 4 mm = 0.004 m

Area of the top surface = A

A = L²

Since the plate is square-shaped, L = √(A).

Now, we can substitute the values and solve for (dT/dt):

(dT/dt) = [0.8 * 900 - 0.25 * (5.67 × 10⁻⁸) * (T⁴ - T_a⁴) - 20 * (T - T_a)] / (2700 * 900)

This gives us the initial rate of change of the plate temperature.

(b) Equilibrium Temperature:

Using the equation:

αQ_in = εσA(T⁴ - T_a⁴) + hA(T - T_a)

We can rearrange the equation to solve for the equilibrium temperature (T_eq):

αQ_in = εσA(T⁴ - T_a⁴) + hA(T - T_a)

0.8 * 900 = 0.25 * (5.67 × 10⁻⁸) * A * (T_eq⁴ - T_a⁴) + 20 * A * (T_eq - T_a)

Simplifying further:

720 = 0.25 * (5.67 × 10⁻⁸) * A * (T_eq⁴ - T_a⁴) + 20 * A * (T_eq - T_a)

Now, we can solve this equation to find the equilibrium temperature (T_eq).

(c) Variation of Steady-State Temperature with Emissivity:

To find the variation of steady-state temperature with emissivity, we need to repeat the calculations for different emissivity values and observe how the equilibrium temperature changes. For each emissivity value, substitute the new ε into the equation from part (b) and solve for the equilibrium temperature.

Repeat the calculations for ε = 0.1, 0.5, and 1, and observe the variations in equilibrium temperature. Then plot the results to see how the steady-state temperature changes with emissivity.

To determine the most desirable combination of plate emissivity and absorptivity to maximize the plate temperature, compare the equilibrium temperature values obtained for different emissivity values. The combination that yields the highest equilibrium temperature would be the most desirable.

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