A hemispherical droplet of liquid water, lying on a flat surface, evaporates by molecular diffusion through still air surrounding the droplet. The droplet initially has a radius R. As the liquid water slowly evaporates, the droplet shrinks slowly with time, but the flux of the water vapor is at a nominal steady state. The temperature of the droplet and the surrounding still air are kept constant. The air contains water vapor of fixed concentration at an infinitely long distance from the droplet’s surface. After drawing a picture of the physical process, select a coordinate system that will best describe this diffusion process, list at least five reasonable assumptions for the mass-transfer aspects of the water-evaporation process, and simplify the general differential equation for mass transfer in terms of the flux NA. Finally, specify the simplified differential form of Fick’s flux equation for water vapor (species A), and propose reasonable boundary conditions.

Answers

Answer 1

Answer:

Explanation:

question answered below

A Hemispherical Droplet Of Liquid Water, Lying On A Flat Surface, Evaporates By Molecular Diffusion Through
Answer 2
Final answer:

We described the diffusion process of a slowly evaporating hemispherical water droplet by adopting a spherical coordinate system. We made five assumptions: steady-state conditions, isotropic medium, uniform temperature, constant concentration of water vapor in the surrounding air, and no bulk motion of air. The differential form of Fick's law was derived, and two boundary conditions regarding the concentration of water were proposed.

Explanation:

To answer your question regarding the diffusion process of a hemispherical droplet of water slowly evaporating on a flat surface, we will start by selecting a spherical coordinate system. This is chosen because a spherical system best represents a hemispherical droplet with a shrinking radius R.

Now, let's list at least five reasonable assumptions for the mass-transfer aspects of the water-evaporation process:

Steady-state conditions - The rate of evaporation is constant over time.Isotropic medium - The properties of the medium (air) are the same in all directions.Uniform temperature - The temperature of the system is constant throughout the process.Constant concentration of water vapor - At an infinite distance from the droplet surface, the air contains a fixed concentration of water vapor.No bulk motion of air - The air around the droplet is still, causing diffusion to occur solely due to molecular motion.

To express the mass transfer in terms of the flux NA, we need to derive from Fick's first law, which states that the molar flux due to diffusion is proportional to the concentration gradient. In this case, it simplifies to: NA = -D(dCA/dx), where D is the diffusion coefficient and dCA/dx is the concentration gradient of species A (water).

As for the boundary conditions, we can consider two conditions:

The concentration of water at the droplet's surface is the saturation concentration.The concentration at infinite distance from the droplet is essentially constant.

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Related Questions

Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p ​= pN ​- 0.1Q, where p is the price per pair of replacement​ tips, pN is the price of a new pair of​ headphones, and Q is the number of tips per week. Suppose that the inverse supply function of the replacement tips is p ​= 2​ + 0.012 Q. a. The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips​ ( ​dp/dpN​) at the equilibrium is given by nothing ​(Round your answer to three places​.)

Answers

Final answer:

The effect of a change in the price of new Sony headphones on the equilibrium price of silicone replacement tips can't be accurately calculated from the provided equations without numerical values. An increase in the price of new headphones would likely lead to a surge in demand for replacement parts, thereby increasing their equilibrium price.

Explanation:

The student is asking about the impact of a change in the price of the new Sony headphones on the equilibrium price of replacement tips. The inverse demand function is given by p = pN - 0.1Q, and the inverse supply function is given by p = 2 + 0.012Q. The equilibrium condition is that the quantity demanded equals the quantity supplied, so we set the demand equation equal to the supply equation and solve for Q and p. Now to find the effect of a change in the price of the new headphones on the equilibrium price of the replacement tips, we need to differentiate the equilibrium price with respect to the price of the new headphones. This essentially involves implicit differentiation of the equilibrium condition.

However, due to the nature of the equations, getting a definitive value for dp/dpN would be difficult without numerical values to plug in. As such, the phrase 'dp/dpN is given by nothing' may have been a typographical error or misunderstanding. An increase in the price of new headphones would likely increase demand for replacement parts, thus raising their equilibrium price. But we cannot compute dp/dpN definitively from the provided equations.

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The neurons of giant squids, for example, consist of axons with very large radii, which allows the squid to react very quickly when confronted with a predator. Assuming no change in the resistivities or membrane thickness of the axon, by what factor must the radius of the axon increase such that the speed of the pulse increases by a factor of 10

Answers

Answer:

100

Explanation:

[tex]\rho_m[/tex] = Resistivity of axon

r = Radius of axon

t = Thickness of the membrane

[tex]\rho_a[/tex] = Resistivity of the axoplasm

Speed of pulse is given by

[tex]v=\sqrt{\dfrac{\rho_mrt}{2\rho_a}}[/tex]

So, radius is given by

[tex]r=\dfrac{2\rho_a}{\rho_mt}v^2[/tex]

If radius is increased by a factor of 10 new radius will be

[tex]r_2=\dfrac{2\rho_a}{\rho_mt}(10v)^2\\\Rightarrow r_2=100\dfrac{2\rho_a}{\rho_mt}v^2\\\Rightarrow r_2=100r[/tex]

So, The radius will increase by a factor of 100.

A laser shines on a pair of vertical slits. The horizontal distance L 1 between the laser and the ruler is 12.3 m. The distance L 2 between the laser and the slits is 0.511 m. The distance d is 0.440 mm. A laser is located a distance L subscript 1 from a ruler and a distance L subscript 2 from a barrier containing two, narrow slits. The slit separation is d. An interference intensity pattern is shown at the position of the ruler. The intensity pattern has a central maximum at 0 centimeters. The first dark fringe is at plus or minus 1.6 centimeters. The first bright fringe is at about plus or minus 3 centimeters. The second dark fringe is at about plus or minus 4.8 centimeters. The second bright fringe is at about plus or minus 6.4 centimeters. The third dark fringe is at plus or minus 8 centimeters. The illustration is not to scale. Note that the ruler measures in centimeters. Calculate the wavelength ? of the light.

Answers

Final answer:

To calculate the wavelength of the light, use the equation d sin θ = mλ. Plugging in the values, we find that the wavelength is 563 nm.

Explanation:

In order to calculate the wavelength of the light, we can use the equation d sin θ = mλ, where d is the slit separation, θ is the angle of the bright fringe, m is the order of the fringe, and λ is the wavelength of the light. In this case, we are given the slit separation (0.0100 mm) and the angle of the third bright line (10.95°). We can rearrange the equation to solve for λ:

λ = d sin θ / m

Plugging in the values, we get:

λ = (0.0100 mm) sin(10.95°) / 3

λ = 5.63 x 10-7 mm or 563 nm

21. (a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500-μC charge and flies due west at a speed of 660. m/s over Earth’s south magnetic pole, where the 8.00 × 10−5 − T magnetic field points straight down into the ground. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.

Answers

Answer:

Explanation:

The picture attached shows the full explanation and i hope it helps. Thank you

Final answer:

The magnetic force on a supersonic jet with a 0.500-μC static charge, flying over the Earth's south magnetic pole at 660 m/s, is 7.50 × 10-7 N, directed to the north. This effect is considered negligible given the small magnitude of the force.

Explanation:

When an aircraft with a static charge flies through the Earth's magnetic field, it experiences a magnetic force due to the interaction between its charge, its velocity, and the magnetic field. This is a concept from electromagnetism, specifically the Lorentz force. The magnitude of the magnetic force (F) can be calculated using the equation F = qvBsin(θ), where q is the charge on the aircraft, v is the speed of the aircraft, B is the magnetic field strength, and θ is the angle between the velocity of the charge and the direction of the magnetic field.

For a supersonic jet with a 0.500-μC (or 0.500x10-6 C) charge flying due west over the Earth's south magnetic pole, where the magnetic field (B) is 8.00 × 10-5 T and points straight down (θ = 90 degrees), the magnitude of the magnetic force is:

F = (0.500x10-6 C)(660 m/s)(8.00 × 10-5 T)sin(90 degrees) = 7.50 × 10-7 N, perpendicular to both the magnetic field lines and the velocity of the jet (which means it points either north or south). Since the jet is flying due west and the magnetic field is down, the right-hand rule indicates the force will push the jet to the north.

Regarding part (b), since the magnetic force magnitude, 7.50 × 10-7 N, is quite small compared to the typical forces experienced by a supersonic jet, such as thrust, drag, and lift, it can be considered a negligible effect. It's unlikely to have any significant impact on the flight of the aircraft.

Suppose the Earth orbited the Sun in 4 months rather than 1 year, but had exactly the samerotation speed. How much longer would a solar day be than a sidereal day? Mercury’s siderealday is 58.6 days and its orbital period is 88 days. What is the length of Mercury’s solar day?

Answers

Answer:

A) 0.1955 days

B) 35.18 days

Explanation: Given that the Earth orbited the Sun in 4 months rather than 1 year, but had exactly the same rotation speed. That is the orbital period will be

365.24/12 = P/4

P = 121.75 days

We have three periods, the orbital period Po = 121.75 days,

the sidereal period Ps = 23.93419 hours and

The mean solar day Pd =24 hours.

Since they had exactly the same rotation speed, the number of solar days in a year is Po/Pd.

The number of sidereal days in a year would be Po/Pd + 1 = 121.75 + 1 = 122.75 days. Since there are more sidereal days in a year this means that the sidereal day is a little bit shorter, 121.75/122.75 = 0.99185 times shorter.

0.99185 × 24 = 23.80448 hours.

24 - 23.80448 = 0.1955 days

Therefore, solar day is 0.99185 days longer than a sidereal day

Given that the Mercury’s side real day is 58.6 days and its orbital period is 88 days. What is the length of Mercury’s solar day?

Using the formula

Ld = PoPs/(Po + Ps)

Ld = Length of Mercury's solar day

Po = orbital period

Ps = Mercury's side real day

Ld = (88 × 58.6)/ (88 + 58.6)

Ld = 5156.8/146.6

Ld = 35.18 days

The shaft is supported by a smooth thrust bearing at B and a journal bearing at C. Determine the resultant internal loadings acting on the cross section at E. Suppose that P1 = 360 lb , P2 = 830 lb . Part a, b, and c please.

Answers

Final answer:

To determine the resultant internal loadings at the cross section at E, we calculate the reaction forces at points B and C. The reaction force at B is 360 lb directed towards the left due to the thrust bearing, while the reaction force at C is 830 lb directed towards the right due to the journal bearing. Combining these forces, the resultant force at E is 1190 lb directed towards the right.

Explanation:

To determine the resultant internal loadings acting on the cross-section at E, we need to consider the forces acting on the shaft at points B and C. Part a requires determining the reaction force at B due to the thrust bearing, part b requires determining the reaction force at C due to the journal bearing, and part c requires combining the forces to find the resultant internal loadings at E.

For part a, since the shaft is supported by a smooth thrust bearing at B, the reaction force at B will be equal in magnitude and opposite in direction to the applied force P1. Therefore, the reaction force at B is 360 lb directed towards the left.

For part b, since the shaft is supported by a journal bearing at C, the reaction force at C will be equal in magnitude to the applied force P2. Therefore, the reaction force at C is 830 lb directed towards the right.

For part c, to find the resultant force at E, we need to combine the forces at B and C. Since the forces are along the same line of action, we can simply add the magnitudes of the forces. The resultant force at E is equal to the sum of the reaction forces at B and C, which is (360 lb) + (830 lb) = 1190 lb directed towards the right.

How do the electrons in the bulb's filament, far from the battery and its emf, "know" that they should flow?

Answers

Answer:this is obviously because free electrons can easily move in the metal due to potential difference, and they are inserted in the wire from the negative terminal of the battery and pulled away ( come back) from the wire into the battery at positive terminal.

Final answer:

Electrons in a lightbulb filament flow due to the electric fields created by a connected battery, encountering resistance that dissipates energy as heat and allows the bulb to emit light.

Explanation:

Electrons 'know' to flow in a bulb's filament due to the electric fields created when a battery is connected to a circuit. These fields exert a force on the electrons, causing them to move. The flow of electrons is sustained by the potential difference (emf) provided by the battery, but it's not perpetual because as electrons move through the resistive filament, they encounter resistance analogous to friction, which causes energy to be dissipated as heat. This is the principle by which the bulb emits light. An open circuit, like if a wire is cut, prevents the flow of charge, demonstrating the necessity of a closed path for current to flow.

The resistance to electron movement through the filament is due to interactions with the material's atoms, as described by Newton's second law (a = Ftotal/m). This resistance leads to the conversion of electrical energy into heat, which in the case of an incandescent lightbulb, is necessary for it to glow. Without resistance, electrons accelerated by the emf would continue gaining kinetic energy, which does not occur due to this energy transformation. The steady flow of electrons is the result of these resisting forces balancing out the force exerted by the electric field, leading to a constant flow of current as long as the circuit is complete.

What is the best way to determine levelness?

A.See if the Acceleration versus Time for both directions are both zero.

B.Plot the Acceleration versus Time for one direction and acceleration should be zero.

C.Plot Position versus Time and compare the linear fit from each direction of travel; slopes should be equal.

D.Plot Position versus Time and compare the linear fit from each direction of travel; slopes should be equal but opposite.

E.Plot Velocity versus Time for both directions; slopes should be equal.

F.See if slope of Velocity versus Time for both directions are equal but opposite.

Answers

Answer:

F. See if the slope of Velocity versus Time for both directions are equal but opposite.

Explanation: Velocity is the rate of change of position. The slope of a distance or position-time graph is velocity. Acceleration is the rate of change of velocity. The slope of a velocity-time graph is acceleration.

A velocity-time graph shows changes in the velocity of a moving object over time. The slope of a velocity-time graph represents an acceleration of the moving object.

So, the value of the slope at a particular time represents the acceleration of the object at that instant.

An inversion in a permutation of the integers 1 to n is a pair of numbers (not necessarily adjacent) such that the larger number is listed first. For example, in the permutation 4, 2, 3, 1, the inverted pairs are (4, 2), (4, 3), (4, 1) (2, 1) and (3, 1). By listing out all 24 permutations and counting the number of inversions in each (if you are lazy you can write a program to do this and attach the code as a separate file), calculate the expected number of inversions in a random permutation of 1, 2, 3 and 4. Then, using this result, posit a guess for the general result, in terms of n for permutations of 1, 2, 3, …, n. Try to prove this guess via a route that uses less calculation, but looks at an arbitrary pair of indexes into the permutation, say i and j with i < j and counts how many permutations for which this pair is "in order" and that this pair is in inverted.

Answers

Answer:

The total permutation = nP2

The inversions = nC2

Explanation:

Please look at the solution in the attached Word file

What direction does a S wave move

Answers

Answer:

As they travel through rock, the waves move tiny rock particles back and forth -- pushing them apart and then back together -- in line with the direction the wave is traveling. These waves typically arrive at the surface as an abrupt thud. Secondary waves (also called shear waves, or S waves) are another type of body wave

Explanation:

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To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass mmm must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass MMM. The escape velocity is a function of the distance of the object from the center of the planet RRR, but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question "How fast does my rocket have to go to escape from the surface of the planet?"

Answers

Answer:

11.206 km/s

Explanation: to leave the surface of the earth, you velocity Ve must be;

Escape velocity Ve = (2gRe)^0.5

Where g = acceleration due to gravity 9.81 m/s^2

Re = earth's radius 6400 km = 6.4x10^6

Ve = (2 x 9.81 x 6.4 x 10^6)^0.5

Ve = (125568000)^0.5

Ve = 11205.7 m/s

= 11.206 km/s

After your school's team wins the regional championship, students go to the dorm roof and start setting off fireworks rockets. The rockets explode high in the air and the sound travels out uniformly in all directions. If the sound intensity is 1.52 10-6 W/m2 at a distance of 123 m from the explosion, at what distance from the explosion is the sound intensity half this value

Answers

Answer:

The distance when the intensity is halved is 173.95 m

Explanation:

Given;

initial intensity of the sound, I₁ = 1.52 x 10⁻⁶ W/m²

initial distance from the explosion, d₁ = 123 m

final intensity of the sound, I₂ = ¹/₂ (1.52 x 10⁻⁶ W/m²) = 0.76 x 10⁻⁶ W/m²

Intensity of sound is inversely proportional to the square of distance between the source and the receiver.

I ∝ ¹/d²

I₁d₁² = I₂d²

(1.52 x 10⁻⁶)(123)² = (0.76 x 10⁻⁶)d₂²

d₂² = (1.52 x 10⁻⁶ x 123²) / (0.76 x 10⁻⁶)

d₂² = 30258

d₂ = √30258

d₂ = 173.95 m

Therefore, the distance when the intensity is halved is 173.95 m

The sound intensity varies inversely as the square of the distance from the

explosion source.

The distance from the explosion at which the sound intensity is half of 1.52 × 10⁻⁶ W/m², is approximately 173.95 meters

Reasons:

The sound intensity at 123 m = 1.52 × 10⁻⁶ W/m²

Required:

The distance at which the sound intensity is half the given value.

Solution:

Sound intensity is given by the formula;

[tex]I \propto \mathbf{ \dfrac{1}{d^2}}[/tex]

Which gives;

I × d² = Constant

I₁ × d₁² = I₂ × d₂²

Where;

I₁ = The sound intensity at d₁

I₂ = The sound intensity at d₂

[tex]d_2 = \mathbf{ \sqrt{\dfrac{I_1 \times d_1^2}{I_2} }}[/tex]

When the sound intensity is half the given value, we have;

I₂ = 0.5 × I₁

I₂ = 0.5 × 1.52 × 10⁻⁶ = 7.6 × 10⁻⁷

Therefore;

[tex]d_2 = \sqrt{\dfrac{1.52 \times 10^{-6} \times 123^2}{7.6 \times 10^{-7}} } \approx 173.95[/tex]

The distance from the explosion at which the sound intensity is half of the

sound intensity at 123 meters from the explosion, d₂ ≈ 173.95 m.

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Understand Key Concepts
Which is NOT a fluid?
A. helium
B. ice
C. milk
D.Water

Answers

Answer:

The answer is A, friend.

2. An electrical heater 200mm long and 15mm in diameter is inserted into a drilled hole normal to the surface of a large block of material having a thermal conductivity of 5W/m·K. Estimate the temperature reached by the heater when dissipating 25 W with the surface of the block at a temperature of 35 °C.

Answers

Answer:

The final temperature is 50.8degrees celcius

Explanation:

Pls refer to attached handwritten document

Answer: 50.63° C

Explanation:

Given

Length of heater, L = 200 mm = 0.2 m

Diameter of heater, D = 15 mm = 0.015 m

Thermal conductivity, k = 5 W/m.K

Power of the heater, q = 25 W

Temperature of the block, = 35° C

T1 = T2 + (q/kS)

S can be gotten from the relationship

S = 2πL/In(4L/D)

On substituting we have

S = (2 * 3.142 * 0.2) / In (4 * 0.2 / 0.015)

S = 1.2568 / In 53.33

S = 1.2568 / 3.98

S = 0.32 m

Proceeding to substitute into the main equation, we have

T1 = T2 + (q/kS)

T1 = 35 + (25 / 5 * 0.32)

T1 = 35 + (25 / 1.6)

T1 = 35 + 15.625

T1 = 50.63° C

Review the multiple-concept example as an aid in solving this problem. In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves on a circle. In one instance, the radius of the circle is 0.685 m. At one point on this circle, the ball has an angular acceleration of 63.8 rad/s2 and an angular speed of 15.0 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the ball.

Answers

Answer:

Total acceleration will be [tex]160.20rad/sec^2[/tex]

Explanation:

We have given radius of the circle r = 0.685 m

Angular acceleration [tex]\alpha =63.8rad/sec^2[/tex]

Angular speed [tex]\omega =15rad/sec[/tex]

Centripetal acceleration will be

[tex]a_c=\omega ^2r=15^2\times 0.685=154.125rad/sec^2[/tex]

Tangential acceleration will be

[tex]a_t=r\alpha =0.685\times 63.8=43.7rad/sec^2[/tex]

(a) Total acceleration will be equal to

[tex]a=\sqrt{a_t^2+a_c^2}[/tex]

[tex]a=\sqrt{43.7^2+154.125^2}=160.20rad/sec^2[/tex]

So total acceleration will be [tex]160.20rad/sec^2[/tex]

An open container holds ice of mass 0.570 kg at a temperature of -17.2 ∘C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 820 J/minute . The specific heat of ice to is 2100 J/kg⋅K and the heat of fusion for ice is 334×103J/kg.

Answers

Final Answer:

The time required to raise the temperature of the ice from -17.2 °C to 0 °C is approximately 6.22 minutes.

Explanation:

To calculate the time required for the temperature of the ice to rise from -17.2 °C to 0 °C, we can use the equation Q=mcΔT, where Q is the heat supplied, m is the mass of the ice, c is the specific heat of ice, and ΔT is the change in temperature.

The heat supplied (Q) during this process is used to raise the temperature of the ice without causing a phase change. Given that Q=820J/min and c=2100J/kg⋅K, we rearrange the equation to solve for time (t): t=Q/mcΔT

Substituting the given values (m=0.570kg, ΔT=0°C−(−17.2°C)=17.2°C), we find t≈820J/min/ (0.570kg)(2100J/kg⋅K)(17.2°C) ≈6.22min.

This calculation assumes that all the heat supplied is used to raise the temperature of the ice without considering the heat required for a phase change. To account for the heat of fusion during the phase change from ice to water at 0 °C, an additional calculation would be needed. However, the question specifies raising the temperature to 0 °C, so the heat of fusion is not considered in this particular scenario.

Understanding the principles of heat transfer, specific heat, and phase changes is essential in solving thermodynamics problems. These principles are widely applicable in various scientific and engineering fields, providing insights into the behavior of materials under different conditions.

A firm wants to determine the amount of frictional torque in their current line of grindstones, so they can redesign them to be more energy efficient. To do this, they ask you to test the best-selling model, which is basically a diskshaped grindstone of mass 1.1 kg and radius 0.09 m which operates at 73.3 rad/s. When the power is shut off, you time the grindstone and find it takes 42.4 s for it to stop rotating. What is the frictional torque exerted on the grindstone in newton-meters

Answers

Explanation:

Mass of the diskshaped grindstone, m = 1.1 kg

Radius of disk, r = 0.09 m

Angular velocity, [tex]\omega=73.3\ rad/s[/tex]

Time, t = 42.4 s

We need to find the frictional torque exerted on the grindstone. Torque in the rotational kinematics is given by :

[tex]\tau=I\alpha[/tex]

I is moment of inertia of disk, [tex]I=\dfrac{mr^2}{2}[/tex]

[tex]\tau=\dfrac{mr^2\alpha }{2}\\\\\tau=\dfrac{1.1\times (0.09)^2\times 73.3 }{2\times 42.4}\\\\\tau=7.7\times 10^{-3}\ N-m[/tex]

So, the frictional torque exerted on the grindstone is  [tex]7.7\times 10^{-3}\ N-m[/tex].

Consider two pulses (a wave with only a single peak) traveling towards each other on a string. When the instant that the peaks of these two pulses cross, the resultant disturbance has a maximum displacement of 3.80 A where A is the amplitude of the first pulse. What must be the amplitude of the second pulse be

Answers

Answer:

2.8A

Explanation:

To calculate the total amplitude (when both pulses meet), we need to add up the amplitudes of each pulse. Since A is the amplitude of the first pulse, and we can call B the amplitude of the second pulse and C the total amplitude, we have that A+B=C=3.8A, which means that B=3.8A-A=2.8A, which we have already said is the amplitude of the second pulse.

One possible explanation for a galaxy's type invokes the angular momentum of the protogalactic cloud from which it formed. Suppose a galaxy forms from a protogalactic cloud with a lot of angular momentum. Assuming its type has not changed as a result of other interactions, we'd expect this galaxy to be ______.

Answers

Answer:

A spiral galaxy

Explanation:

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.60 s for the boat to travel from its highest point to its lowest, a total distance of 0.630 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.

How much is the wavelength?

Answers

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.60 s for the boat to travel from its highest point to its lowest, a total distance of 0.630 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.

How much is the wavelength?

How fast are the waves traveling ?

What is the amplitude A of wave?

Given Information:

time = t = 2.60 s

wavelength = λ  = 5.50 m

distance = d = 0.630 m

Required Information:

a)  wavelength = λ  = ?

b) speed = v = ?

c) Amplitude = A = ?

Answer:

a)  wavelength = 5.50 m

b) speed = 1.056 m/s

c) Amplitude = 0.315 m

Step-by-step explanation:

a)

It is given that wave crests are spaced a horizontal distance of 5.50 m apart that is basically the wavelength so,

λ  = 5.50 m

b)

We know that the speed of the wave is given by

v = λf

where λ is the wavelength and f is the frequency of the wave given by

f = 1/T

Where T is the period of the wave.

Since the it is given that boat takes 2.60 s to travel from its highest point to its lowest that is basically half of the period so one full period is

T = 2*2.60

T = 5.2 s

So the frequency is,

f = 1/5.2

f = 0.192 Hz

Therefore, the speed is

v = λf

v = 5.50*0.192

v = 1.056 m/s

c)

The amplitude of the wave is given by

A = d/2

where d is the distance from the highest point to the lowest, therefore, the amplitude is half of it.

A = 0.630/2

A = 0.315 m

Two very small planets orbit a much larger star. Planet A orbits the star with a period TA . Planet B orbits the star at four times the distance of planet A, but planet B is four times as massive as planet A. Assume that the orbits of both planets are approximately circular.

Planet B orbits the star with a period TB equal to

a. TA/4.
b. 16TA.
c. 8TA.
d. 4TA
d. TA

Answers

Answer:

Explanation:

Given that,

Period of Planet A around the star

Pa = Ta

Let the semi major axis of planet A from the star be

a(a) = x

Given that, the distance of Planet B from the star (i.e. it semi major axis) is 4 time that of Planet A

a(b) = 4 × a(a) = 4 × x

a(b) = 4x

Also planet B is 4 times massive as planet A

Using Kepler's law

P² ∝a³

P²/a³ = k

Where

P is the period

a is the semi major axis

Then,

Pa² / a(a)³ = Pb² / a(b)³

Pa denotes Period of Planet A and it is Pa = Ta

a(a) denoted semi major axis of planet A and it is a(a) = x

Pb is period of planet B, which is the required question

a(b) is the semimajor axis of planet B and it is a(b) = 4x

So,

Ta² / x³ = Pb² / (4x)³

Ta² / x³ = Pb² / 64x³

Cross multiply

Ta² × 64x³ = Pb² × x³

Divide both sides by x³

Ta² × 64 = Pb²

Then, Pb = √(Ta² × 64)

Pb = 8Ta

Then, the period of Planet B is eight times the period of Planet A.

The correct answer is C

Final answer:

The period of orbit for planet B is 4 times the period of orbit for planet A.

Explanation:

To determine the period of orbit for planet B, we can use Kepler's Third Law, which states that the square of the period of an orbit is proportional to the cube of its average distance from the center of attraction. Since planet B is four times the distance of planet A and four times as massive, its period will be 4^3/4^2 times that of planet A. Simplifying, this means that TB = 4 * TA, so the correct answer is d. 4TA.

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A physicist's right eye is presbyopic (i.e., farsighted). This eye can see clearly only beyond a distance of 97 cm, which makes it difficult for the physicist to read books and journals. Find the focal length and power of a lens that will correct this presbyopia for a reading distance of 25 cm, when worn 2 cm in front of the eye

Answers

Final answer:

The issue of farsightedness or presbyopia can be corrected by a converging lens with a focal length of 34 cm and power of 2.94 Diopters.

Explanation:

The provided problem can be solved using the lens formula which is 1/f = 1/v - 1/u, where f = focal length, v = image distance, and u = object distance. The image distance (di) for clear vision should match the lens-to-retina distance, which is constant and taken as 2 cm for the given question. The lens that the physicist is recommended to use should create an image with a reading distance of 25 cm and therefore this will be ‘v’. However, the lens is worn 2 cm in front of the eye and hence the actual image distance becomes 27 cm (or 0.27 m). The object is however at a distance of 97 cm (0.97 m) as indicated by the problem. When we plug these values into the lens formula, we get f = 1 / {(1/0.27) - (1/0.97)} which is approximately equal to 0.34 m or 34 cm. The optical power of lens (P) is reciprocal of the focal length in meters. Hence P = 1/f = 1/0.34 = 2.94 D.

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To correct the physicist's presbyopia for clear vision at 25 cm, a lens with a focal length of approximately -30.35 cm (or -0.3035 m) and a power of around -3.29 diopters is needed. The lens formula helped in determining these values.

Correcting Farsightedness

A presbyopic eye has difficulty seeing objects clearly at close range. In this case, the physicist's eye can only see clearly beyond 97 cm. To correct this and allow clear vision at 25 cm, we need to determine the focal length and power of the corrective lens when worn 2 cm in front of the eye.

Using the lens formula:

1/f = 1/v - 1/u

where:

f is the focal length of the lensv is the image distance (97 cm minus 2 cm = 95 cm)u is the object distance (25 cm minus 2 cm = 23 cm)

Substituting the values, we get:

1/f = 1/95 - 1/23

1/f = (23 - 95) / (95 * 23)

1/f = -72 / 2185

f = -2185 / 72 ≈ -30.35 cm

Therefore, the focal length of the lens is approximately -30.35 cm (or -0.3035 m).

The power of the lens (P) is given by the formula:

P = 1/f (in meters)

Substituting the focal length:

P = 1 / -0.3035 ≈ -3.29 diopters (D)

Hence, the power of the corrective lens needed is approximately -3.29 D.

An airplane is initially flying horizontally (not gaining or losing altitude), and heading exactly North. Suppose that the earth's magnetic field at this point is also exactly horizontal, and points from South to North (it really does!). The airplane now starts a different motion. It maintains the same speed, but gains altitude at a constant rate, still heading North. The magnitude of the electric potential difference between the wingtips has... [Remember that the airplane is made of metal, and is a conductor] Group of answer choices

Answers

Note: The answer choices are :

a) Increased

b) Decreased

c) stayed the same

Answer:

The correct option is Increased

The magnitude of the electric field potential difference between the wingtips increases.

Explanation:

The magnitude of the electric potential difference is the induced emf and is given by the equation:

[tex]emf = l (v \times B)[/tex]

where l = length

v = velocity

B = magnetic field

As the altitude of the airplane increases, the magnetic flux becomes stronger, the speed of the airplane becomes perpendicular to the magnetic field, i.e. [tex]v \times B = vB sin90 = vB\\[/tex] ,

the induced emf = vlB, and thus increases.

The magnitude of the electric field potential difference between the wingtips increases

A nearsighted person cannot see objects further away than 10 m clearly. This person wants to be able to see objects 300 m away without trouble. What is the focal length of the lens you would prescribe? (Ignore the distance between the person’s eye and the lens.)

a. 9.7 m
b. – 9.7 m
c. No such lens can be prescribed.
d. 10.3 m
e. – 30 m
f. 30 m
g. – 10.3 m

Answers

Answer:

d.-10.3m

Explanation:

Note for short sightedness the focal length is negative

Let do be object distance=10m

And di= image distance=-300m

Using lens formula

F=do*di/do-di= 10*300/10-300=-10.3m

Answer:

d. 10.3 m

Explanation:

For a nearsighted person,

1/f = (1/v)+(1/u).................... Equation 1

f = focal, v = image distance, u = object distance.

f = vu/(v+u)................. Equation 2

Given: v = -10 m, u = 300 m

Substitute into equation 2

f = (-10×300)/(-10+300)

f = -3000/290

f = -10.34 m

therefore a concave lens of focal length 10.34 m is  required.

The right option is d. 10.3 m

a 150 kg person stands on a compression spring with spring constant 10000 n/m and nominal length of 0.50 what is the total length​

Answers

Answer:

The total length is 0.65m.

Explanation:

The total length [tex]x_{tot}[/tex] of the spring is equal to its length [tex]x_0[/tex] right now (0.50 m ) plus the amount [tex]x[/tex] by which it is compressed due to weight of the man:

[tex]x_{tot} = x_0+x[/tex]

The spring compression is given by Hooke's law:

[tex]F = -kx[/tex]

which in our case gives

[tex]-Mg = -kx[/tex]

solving for [tex]x[/tex] we get:

[tex]x= \dfrac{Mg}{k }[/tex]

putting in [tex]M = 150kg, g= 10m/s^2[/tex] and [tex]k = 10,000N/m[/tex] we get:

[tex]x= \dfrac{(150kg)(10m/s^2)}{10,000N/m^2}[/tex]

[tex]x = 0.15m[/tex]

Hence, the total length of the spring is

[tex]x_{tot} = 0.50m+0.15m[/tex]

[tex]\boxed{x_{tot} = 0.65m.}[/tex]

Which of the following careers would require a degree in physics?
A. Art historian
B. War correspondent
C. Nuclear engineer
D. X-ray technician

Answers

Answer:

Nuclear engineers require a degree in physics in order to have the job.

Explanation:

The same pipe is used to carry both air and water. For the same fluid velocity and friction factor for the air and water flows: the pressure drop for the air flow is greater than that for the water flow. the pressure drop for the air flow equals the pressure drop for the water flow. the pressure drop for the water flow is greater than that for the air flow.

Answers

Answer:

the pressure drop for the water flow is greater than that for the air flow.

Explanation:

Detailed analysis of the problem is show below.

A mass m = 1.1 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 115 N/m and negligible mass. At time t = 0 the mass is released from rest at a distance d = 0.35 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y(t) = A cos(ωt – φ). The positive y-axis points upward. show answer Correct Answer 17% Part (a) Find the angular frequency of oscillation, in radians per second. ω = 10.22 ✔ Correct! show answer Incorrect Answer 17% Part (b) Determine the value of the coefficient A, in meters.

Answers

Answer:

a) = 10.22 rad/s

b) = 0.35 m

Explanation:

Given

Mass of the particle, m = 1.1 kg

Force constant of the spring, k = 115 N/m

Distance at which the mass is released, d = 0.35 m

According to the differential equation of s Simple Harmonic Motion,

ω² = k / m, where

ω = angular frequency in rad/s

k = force constant in N/m

m = mass in kg

So,

ω² = 115 / 1.1

ω² = 104.55

ω = √104.55

ω = 10.22 rad/s

If y(0) = -0.35 m and we want our A to be positive, then suffice to say,

The value of coefficient A in meters is 0.35 m

Space satellites in the inner solar system (such as those in orbit around Earth) are often powered by solar panels. Satellites that travel into the outer solar system, however, are usually powered by the decay of nuclear isotopes – a more expensive and dangerous technology. Why can’t they use solar panels as well?

a. At greater distances, sunlight is more likely to destructively interfere.
b. At greater distances, sunlight is more likely to constructively interfere.
c. At greater distances from the sun, the frequency of sunlight will be too low.
d. At greater distances from the sun, the intensity of sunlight will be too low.

Answers

Answer:

D

Explanation:

See attached file

To understand the formula representing a traveling electromagnetic wave.

Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other.

The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by

E? =E0sin(kx??t)j^,
B? =B0sin(kx??t)k^.

This wave is linearly polarized in the y direction.

1.a. In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E0 and B0are the __________ of the electric and magnetic fields.

Choose the best answer to fill in the blank.

1. maxima
2. amplitudes
3. wavelengths
4. velocities

b. The variable ? is called the __________ of the wave.

Choose the best answer to fill in the blank.

1. velocity

2. angular frequency

3. wavelength

c. The variable k is called the __________ of the wave.

Choose the best answer to fill in the blank.

1. wavenumber

2. wavelength

3. velocity

4. frequency

d. What is the mathematical expression for the electric field at the point x=0,y=0,z at time t?

1. E=E0sin(??t)j^

2. E =E0sin(??t)k^

3. E =0

4. E =E0sin(kz??t)i^

5. E =E0sin(kz??t)j^

e. For a given wave, what are the physical variables to which the wave responds?

1. x only

2. t only

3. k only

4. ? only

5. x and t

6. x and k

7. ? and t

8. k and ?

Answers

Answer:

please read the answer below

Explanation:

We have that both electric field and magnetic field are given by:

[tex]\vec{E}=E_osin(kx-\omega t)\hat{j}\\\\\vec{B}=B_osin(kx-\omega t)\hat{k}[/tex]

I complete with bold words the answers:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

a. In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E0 and B0are the magnitudes of the electric and magnetic fields.

2. amplitudes

b. The variable w is called the angular frequency of the wave.

2. angular frequency

c. The variable k is called the wavenumber of the wave.

1. wavenumber

c.

1. E =E0sin(wt)k^

d.

6. x and t

hope this helps!!

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