Air enters a hot-air furnace at 7°C and leaves at 77°C. If the pressure does not change, each entering cubic meter of air expands to [tex]1.9 m^{3}[/tex]. The correct option tot his question is C.
According to Charles' Law, the volume of a gas is directly proportional to its temperature, provided that the pressure remains constant. Therefore, we can use the following formula to calculate the volume of air that enters the furnace:
[tex]\frac{V1}{T1}=\frac{V2}{T2}[/tex]
Where V1 is the initial volume of air, T1 is the initial temperature (in Kelvin), V2 is the final volume of air, and T2 is the final temperature (in Kelvin).
Converting the temperatures to Kelvin, we get:
T1 = 7 + 273 = 280 K
T2 = 77 + 273 = 350 K
Substituting the values in the formula, we get:
[tex]\frac{V1}{280} =\frac{V2}{350}[/tex]
Solving for V2, we get:
[tex]V2 = \frac{V1}{280} *350[/tex]
We know that each cubic meter of air enters the furnace, so [tex]V1 = 1 m^{3}[/tex]. Substituting this value, we get:
[tex]V2 = \frac{1}{280} *350 =1.25 m^{3}[/tex]
However, the question asks for the volume that each entering cubic meter of air expands to. Therefore, the answer is:
[tex]V2 - V1 = 1.25 - 1 = 0.25 m^{3}[/tex]
Therefore, the correct option is C,[tex]1.9 m^{3}[/tex].
Each entering cubic meter of air expands to[tex]1.9 m^{3}[/tex]when it enters the hot-air furnace.
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A man pushes a box across a floor. as he increases the force he applies horizontally to the box
a) the kinetic friction decreases
b) the kinetic friction may increase or decrease depending on the velocity of the box
c) the kinetic friction remains the same
d) the kinetic friction increases
When a man pushes a box across a floor, as he increases the force he applies horizontally to the box, then the kinetic friction remains the same.
To find the answer, we need to know about friction.
What is friction?Whenever a body moves, over the surface of another body, a force comes into play which acts parallel to the surface of contact and opposes the relative motion. This opposing force is called friction.There are two frictions acting on a surface.Static friction: It come into play between two bodies before when it starts moving. Self-adjusting force and the max value of it is called limiting static friction.Kinetic friction: It come into play between two bodies when it starts moving. It is not a self-adjusting force.As we increase applied force, kinetic friction will remain same.Thus, we can conclude that, kinetic friction remains the same when we increase the applied force.
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As a guy pushes a box across a floor, the kinetic friction stays constant no matter how much force is applied on the box horizontally.
We must understand friction if we are to find the solution.
Describe friction?A force that works parallel to the surface of contact and opposes the relative motion is always present whenever a body moves over the surface of another body. Friction is the name for this opposing force.On a surface, there are two frictions operating.Static friction: It occurs between two bodies before motion is initiated. Limiting static friction is the term used to describe the maximum amount of self-adjusting force.As soon as two bodies begin to move, kinetic friction is triggered. It is not a force that adjusts itself.The amount of kinetic friction will not change when we apply more force.We can therefore draw the conclusion that kinetic friction does not change as the applied force is increased.
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An 80-N crate is pushed at constant speed for a distance of 5.0 m upward along a smooth inclined plane that makes an angle of 30o with the horizontal. If the force on the crate is parallel to the slope, what is the work done by the pushing force? Group of answer choices 260 J 200 J 61 J 140 J -200 J
The work done by the pushing force is 200 J; option B.
What is work done in an inclined plane?The work done in an inclined plane is given by the formula below:
Work done = Force * distanceForce, F = mgsinθ + ma
where a = 0
Work done = 80 * 5 * sin 30°
Work done = 200 J
In conclusion, work done is the product of force and distance.
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A student is given a box containing ten similar plastic drinking straws, a 30 cm ruler and two set-squares. (a) Explain how the student determines an average value for the external diameter of the straws using this apparatus. Draw a diagram to illustrate your answer.
The way to perform the experiment is illustrated below.
How to perform the experiment?Place each straw tightly without deforming the roundness of the straw into the corner of the set square.
Measure the distance from the corner of the set square to where the straw touches the set square using the 30 cm ruler. This will be the radius of each straw.
Multiply this radius by 2 in order to obtain the diameter of each straw.
Sum the diameter of each of the 10 straws.
Divide this sum by 10 to obtain the average value for the diameter of a straw.
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As the volume of a chamber decreases, the pressure inside the chamber ____________ . as the volume increases, the pressure ____________ .
Answer: Increases, decreases
Explanation:
As the volume of a chamber decreases the pressure inside the chamber increases. As the volume increases the pressure decreases
If themass is 50kg, what weight of water is to be displaced to float on water? why
Answer:if youre looking for the weight of the thermas in genral it should be 500n
Explanation:using the formula w=mg
w=500x10
giving us 500 newtons which is the weight.
A Carnot engine operates between a hot reservoir at 320 degrees Kelvin and a cold reservoir at 260 degrees Kelvin. If it absorbs 500 Joules of heat at the hot reservoir, how much work does it deliver
The work done delivered by the Carnot engine is 93.75 J.
What is Carnot Engine?Leonard Carnot proposed the Carnot engine, a hypothetical thermodynamic cycle. It calculates the highest feasible efficiency that a heat engine can have when converting heat into work and when operating between two reservoirs.Any system working between [tex]T_1[/tex] (hot reservoir) and [tex]T_2[/tex] (cold reservoir) will never have better efficiency than the Carnot engine running between the identical reservoirs.Additionally, the efficiency of this form of engine is only reliant on the temperature of the hot and cold reservoirs and is independent of the composition of the working substance.Solution:
[tex]T_c = 260 K\\ T_h = 320K\\ Q_h = 500J[/tex]
As we know that Carnot engine is ideal, the efficiency depends only on the temperature of the reservoirs(in kelvin scale):
[tex]n = 1 - \frac{T_c}{T_h} \\n = 1 - \frac{260}{320}[/tex]
[tex]n = 1- 0.8125\\n = 0.1875[/tex]
Also, we know that the work done is equal to product of efficiency and heat at hot reservoir:
[tex]W = n\times Q_h\\W = 0.1875 \times 500\\W = 93.75 J[/tex]
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Location C is 0.02 m from a small sphere which has a charge of 3 nanocoulombs uniformly distributed on its surface. Location D is 0.06 m from the sphere. What is the change in potential along a path from C to D?
sorry for the late reply back I have been working on this project for a year now so it will not care if we can get the best of him and also has a full one of the most common misconceptions is that Africa is one large country and its followers are known as Sikhs and is the last survivor from the whole family and the fearful of all that is a metaphor of joy organised by the way I have
The change in potential along a path from C to D due to a small charged sphere is 900 V.
Given:
Charge, Q = 3 nC = 3 × 10⁻⁹ C
Distance between the sphere and point C, r₁ = 0.02 m
Distance between the sphere and point D, r₂ = 0.06 m
Calculation:
We know that the electric potential is given as:
V = k Q/r - (1)
where, V is the electric potential
k is Coulomb's force constant
Qis the charge on the sphere
r is the separation distance
The electric potential at point C due to charged sphere can be given as:
V₁ = k Q/r₁
= (9×10⁹ Nm²/C²) [(3 × 10⁻⁹ C)/(0.02 m)]
= 1350 V
The electric potential at point D due to charged sphere can be given as:
V₂ = k Q/r₂
= (9×10⁹ Nm²/C²) [(3 × 10⁻⁹ C)/(0.06 m)]
= 450 V
Now, the change in potential along the path from C to D can be calculated as:
ΔV = V₂ - V₁
= 450 V - 1350 V
= -900 V
The negative sign indicates that the work is done against the electric field in moving the charge from C to D.
Therefore, the change in potential along a path from C to D is 900 V against the direction of the electric field.
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Several short trips taken from a cold start can use ....... as much fuel as a longer multi-purpose trip covering the same distance when the engine is warm.
Several short trips taken from a cold start can use ...twice... as much fuel as a longer multi-purpose trip covering the same distance when the engine is warm.
In cold weather, properly designed gasoline aids in engine starting, while in hot weather, it helps prevent vapor lock. In order to meet the requirements of a modern engine, the fuel must have the volatility for which the engine's fuel system was built and an antiknock quality strong enough to prevent knock during routine operation.
During the intake phase, the air and fuel are combined before being introduced into the cylinder. The spark ignites the fuel-air mixture after the piston compresses it, resulting in combustion. During the power stroke, the piston is propelled by the expansion of the combustion gases.
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How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?.
The thicker wire has one-fourth the resistance of the thinner wire.
What are resistance and resistivity?The characteristic of a substance that prevents the flow of current is known as resistance. The free electrons begin to move in a specific direction when a voltage is applied across the conductor. These electrons collide with atoms or molecules as they move, creating heat in the process. These atoms or molecules prevent free electrons from moving through a substance. Resistance is represented by the symbol R.
Specific resistance is another name for resistivity. A substance with certain dimensions, such as one meter in length and a cross-sectional area of one square meter, has a resistance that is represented by its resistivity. Resistivity or specific resistance is represented by ρ.
The relation between resistance R and resistivity ρ is given as:
R = ρL/A
where,
R = resistance of the conductor
ρ = resistivity of the material
L = length of the conductor
A = cross-sectional area of the conductor
Calculation:Given,
r₁ = 2r₂
L₁ = L₂
where
r₁ = radius of the first conductor
r₂ = radius of the second conductor
L₁ = length of the first conductor
L₂ = length of the second conductor
To find
R₁/R₂ =? (the ratio of R₁ and R₂)
If the radius is twice the other then the area will become,
A₁ = π r₁²
A₂ = π r₂²
A₁ = π (2r₂)²
= 4π r₂²
Therefore,
A₁ = 4 A₂
Now put the values in the formula,
R = ρL/A
R₁/R₂ = ρ L₁ A₂/ ρ L₂ A₁
R₁/R₂ = L A₂/ L (4A₂)
R₁/R₂ = 1/4
R₁ = R₂/4
Hence, the thicker wire with twice the radius of the thin wire has one-fourth the resistance of the thinner wire.
I understand the question you are looking for is this:
How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?
(a) The thicker wire has half the resistance of the thinner wire
(b) The resistance is the same in both wires
(c) The thicker wire has one-fourth the resistance of the thinner wire
(d) The thicker wire has twice the resistance of the thinner wire.
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What tidal volume typically maintains normal oxygenation and elimination of carbon dioxide acls?
The tidal volume which typically maintains normal oxygenation and elimination of carbon dioxide is 8 to 10 ml/kg of body mass.
What is tidal volume?Tidal volume refers the amount of air that moves in and out of the lungs in one respiratory cycle.
During a respiratory cycle, oxygen moves into the lungs and the tissues during inhalation, while carbon dioxide moves out of the lungs during exhalation.
The continuous outward movement of carbon dioxide and inward movement of oxygen ensures that the body maintains homeostasis and internal or tissue respiration continues.
The normal tidal volume is about 500 ml per inspiration or 7 ml/kg of body mass.
However, for normal oxygenation and elimination of carbon dioxide, a tidal volume of about 8 to 10 ml/kg of body mass is required.
In conclusion, the tidal volume is a measure of the amount of air flow in the lungs for each respiratory cycle.
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If a star appears to move relative to other stars over a one-year period, this motion is due to the star's: Doppler shift. radial motion. parallax shift. transverse motion. true space motion.
If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.
What is the proper motion of stars?
Proper motion is the angular change in position of a star across our line of sight, measured in arc seconds per year, and symbolized with the letter μ.
Proper motion is generally measured by measuring the movement of the image of a star with respect to more distant background stars over that time period.
Here we are told that star appears to move relative to other stars over 1 year period.
So we know that,
True space motion is the annual apparent motion of a star across the sky.
True Space Motion is Combination of radial velocity, proper motion, and distance.
Hence,
If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.
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A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:
The rate of change of the current in the larger inductor is 0.3mA/s.
To find the answer, we need to know about the relation between the emf and inductance.
What's the mathematical expression to find the emf in term of inductance?Mathematically, emf induced across an inductor= L× (dI/dt)L= inductance and dI/dt = rate of change of currentWhat is the rate of change of current in 4.5 mH when when the total emf of the combination is 16 V?As both the inductors are connected in parallel, so emf of the combination remains same across each inductor.Emf induced in 4.5mH = 16 V dI/dt = 4.5mH / 16 = 0.3 mA/sThus, we can conclude that the rate of change of the current in the larger inductor is 0.3mA/s.
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Why is the molten metallic outer core and the magnetic field important to life on earth?.
Earth's magnetic field and molten metallic outer core creates barrier to stop Sun's radiation to strip away our atmosphere.
As we know that inside the earth there are several layers of the earth. The outer one is the Earth's crust which is all the ground we have , then we have the mantle that consist upper and lower crust. And then after we have outer and inner crust.
The outer core is made of molten material that consist of mainly iron and other ferrous metals. The core is important for many reasons-
The inner core rotates counter to the outer core which in return creates powerful magnetic field. And this magnetic field creates barrier to stop Sun's radiation to strip away our atmosphere.The outer core is conveniently under the crust which is fragmented into tectonic plates. Because of this, the terrain changes and sometimes holes are formed in the crust allowing volcanoes to form. The volcanoes provide all sorts of natural gases which is essentials to life and also help in creating very fertile land in which animals can thrive.Learn more about earth's magnetic field here:
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A 55 kg track and field athlete has an average power output of 5.4 kW during the 200 meter dash. How quickly did she finish the race?
Group of answer choices
a. 20 s
b. 22 s
c. 23 s
d. 18 s
The time taken for the athlete to finish the race is 20 s (Option A)
What is power?Power is simply defined as the rate at which work is done. It can be expressed mathematically as
Power (P) = work (W) / time (t)
But
Work = weight × distance
Therefore,
Power = (weight × distance ) / time
How to determine the time Mass (m) = 55 KgAcceleration due to gravity (g) = 9.8 m/s²Weight = mg = 55 × 9.8 = 539 NPower (P) = 5.4 KW = 5.4 × 1000 = 5400 WDistance (d) = 200 mTime (t) =?Power = (weight × distance ) / time
5400 = (539 × 200) / t
5400 = 107800 / t
Cross multiply
5400 × t = 107800
Divide both side by 5400
t = 107800 / 5400
t = 20 s
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Which of the zodiac constellations will be highest at midnight?
Answer:
Virgo will be the highest zodiac constellations at night.
Why do we tallk about radio waves as a group and not the frequeny of radio waves
Technical skills: knowledge base of sport rearrange our coaching skills from best (at the top) to worst (at the bottom) by dragging each skill to where you think it belongs. this should help you identify your current strengths and limitations as a teacher/coach. after organizing each group of skills, describe steps you think you can take to enhance your strengths and being to address your limitations as a coach.
The steps which enhance strengths and address limitations as a coach include:
Identifying weakness.Setting goals.Consistency.Who is a Coach?This is referred to a professional who gives special training about a particular subject or topic.
It is best to identify weakness and work towards improvement through determination and consistency.
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A stone is thrown horizontally from the top of a tower at the same instant a ball is droppedvertically. Which object is traveling faster when it hits the level ground below?
The ball is travelling faster when the two objects hits the level ground below.
Time of motion of the objectsThe time of motion of the objects depends on height and initial velocity of projection of the objects.
The stone has no initial vertical velocity while the ball has initial vertical velocity.
Thus, the ball is travelling faster when the two objects hits the level ground below.
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question down below need rply fast
The resultant magnitude and direction of the vectors are as follows:
A. A = 6.6; θ = 30.8° from the x-axisB. B = 10.4; θ = 196.7° from the x-axisC. C = 23.3; θ = 300° from the x-axisD. D = 40.4; θ = 138° from the x-axisE. E = 49.5; θ = 346° from the x-axisWhat is the resultant magnitude and direction of the given vectors?The resultant magnitude and direction of the vectors are as follows:
A. A = √(5.7² + 3.4²)
A = 6.6
θ = tan⁻¹(3.4/5.7)
θ = 30.8° from the x-axis
B. B = √{(-10)² + (-3²)}
B 10.4
θ = tan⁻¹(3/10) + 180
θ = 16.7° + 180°
θ = 196.7° from the x-axis
C. C = √{(12)² + (-20²)}
C = 23.3
θ = 360° - tan⁻¹(20/12)
θ = 300° from the x-axis
D. D = √{(-30)² + (27²)}
D = 40.4
θ = 180 - tan⁻¹(27/30)
θ = 138° from the x-axis
E. E = √{(48)² + (12²)}
E = 49.5
θ = 360° - tan⁻¹(12/48)
θ = 346° from the x-axis
In conclusion, the resultant of the vectors and direction are obtained using the resultant vector formula.
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A thin stream of water bends toward a negatively charged rod. When a positively charged rod is placed near the stream, it will bend in the same direction, not the opposite direction. Why
Water bends in the same direction irrespective of the charge of the rod placed near it is because water is dipole- that hydrogen is positively charged and oxygen is negatively charged and thus either of the particle is attracted by the charged rod.
The reason behind it:
As a neutral substance, water has an equal number of positive and negative charges. The negatively charged electrons migrate away from the negatively charged rod and the positively charged protons move toward the rod when the negatively charged rod is placed closer to the water. Water then adheres to the rod. Protons migrate away from the positively charged rod, just as they do when it is moved closer to the water, while electrons flow in its direction. As a result, the water and rod form a relationship.
The partial +ve charge on H is drawn to the -ve charged rod when it is installed, which causes the water stream to bend in the direction of the charged rod.
The partial -ve charge on O is drawn to the +ve rod when it is installed, causing the water stream to bend in the direction of the rod.
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Energy in should always be equal to energy out. select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer.
a. true
b. false
Energy in should always be equal to energy out. This is a False statement.
- Energy In: Energy put into the body in form of calories from food like fats, carbohydrates and proteins.
- Energy Out: Energy burn for basic functions of the body like beating of the heart during physical movements.
When we consume more energy but does not consume it upto its potential, the body keeps storing the excess amount of energy as body fat. Maintaining a balance between Energy In and Energy Out is important to live a healthy lifestyle since the disbalance creates problems to the body.
It is easier to accurately measure change in energy than to measure the amount of energy present.
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2. A ball is tossed straight upwards with a velocity of 60m/s. Using an estimate of gravity of -10m/s², about how many seconds would it take to reach the peak (top of the flight). A.) 10 seconds B.) 3 seconds C.) 6 seconds D.) 12 seconds
Answer: A
Explanation:
Answer the following regarding Momentum Change and Force:
A) A top-class tennis player can serve the ball, of mass 57 g, at an initial horizontal speed of 50 m/s. The ball remains in contact with the racket for 0.05 s. Calculate the average force exerted on the ball during the serve.
B) A motor car of mass 3000 kg moving with 72 km h-1 made to reduce its speed to 18 km h^-1, in 40 s, by applying brakes. Find the resistive force.
A. The average force exerted on the ball during the serve is 57 N
B. The resistive force, given the data is -1125 N
A. How to determine the average forceMass (m) = 57 g = 57 / 1000 = 0.057 KgInitial velocity (u) = 50 m/sTime (t) = 0.05 sAcceleration (a) = u / t = 50 / 0.05 = 1000 m/s²Force (F) = ?F = ma
F = 0.057 × 1000
F = 57 N
B. How to determine the resistive forceMass (m) = 3000 KgInitial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/sFinal velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/sTime (t) = 40 sForce (F) = ?F = m(v – u) / t
F = 3000(5 – 20) / 40
F = -1125 N
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What type of energy drives plate motion?
a) external
b) internal
c) gravitational
d) radiative
b) internal energy drives plate motion
Lithospheric plates are part of a planetary scale thermal convection system. The energy source for plate tectonics is Earth’s internal heat while the forces moving the plates are the “ridge push” and “slab pull” gravity forces.
A tectonic plate (also called lithospheric plate) is a massive, irregularly shaped slab of solid rock, generally composed of both continental and oceanic lithosphere.
The motion of tectonic plates is driven by convection in the mantle. Convection: The process of heat transfer from one part of a fluid to another part by the actual movement of the particles of the fluid is called convection. Liquid and gases are heated by the process of convection.
In simple terms, convection is the idea that dense, cold things sink, and buoyant, warm things rise. In the earth the cold sinking things are slabs (subducting plates) and the warm things are plumes, or just rising material from deeper in the mantle.
hence , correct option is b) internal
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You are raising up a big bucket of water from a 22.5 m deep well. The combined mass of the water and the bucket is 11.3 kg. The bucket is attached to a heavy duty steel chain. The mass of the chain is 17.9 kg. How much work do you perform during the lifting process? Tries 0/12 If it takes 1.75 minutes for you to raise the bucket of water out of the well, then what was your average power?
The amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.
Given:
Depth of the well, h = 22.5m
Mass of heavy-duty steel chain, M = 17.9 kg
The combined mass of the water and bucket, m = 11.3 kg
time taken to raise the bucket out of the water, T = 1.75 min = 105 s
Calculation:
Consider that the center of mass of the steel chain is at the midpoint of the depth of the well.
Now, the work done during the lifting process can be calculated as:
W.D = (Work done in lifting bucket filled with water) + (work done to lift
the steel chain)
W.D = mgh + Mg (h/2) -( 1 )
where g is the acceleration due to gravity
Applying values in the above equation we get:
W.D = mgh + Mg (h/2)
= (11.3 kg)(9.8 m/s²)(22.5 m) + (17.9 kg)(9.8 m/s²)(22.5 m / 2)
= 2491.65 + 1973.475
= 4465.125 J
We know that the average power is given as:
P_avg = W.D / T - ( 2 )
where W.D is the work done during the lifting process
T is the time taken to raise the bucket out of the well
Applying values in the above equation, we get:
P_avg = W.D / T
= (4465.125 J)/(105 s)
= 42.525 W
Therefore, the amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.
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A new CFD method for determination of translational added mass coefficients of an underwater vehicle
A new CFD method for determination of translational is RANS simulations
What is CFD?Using numerical analysis and data structures, the field of computational fluid dynamics (CFD) studies and resolves issues involving fluid flows. The computations necessary to model the fluid's free-stream flow and its interactions with surfaces constrained by boundary conditions (both liquids and gases) are done on computers. Better answers can be found using high-speed supercomputers, which are frequently needed to address the most challenging issues.
Five prominent CFD methods -
Finite Difference Method (FDM)Finite Volume Method (FVM)Finite Element Method (FEM)Lattice Boltzmann Method (LBM)Smoothed Particle Hydrodynamics (SPH)to learn more about Fluid dynamics go to - https://brainly.com/question/5144636
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Which of the following, if eliminated, would completely prevent the greenhouse effect from occurring on earth?
Group of answer choices
a. Atmosphere
b. Acid rain
c. Fossil fuels
d. Clouds
The substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels (option C).
What is greenhouse effect?Greenhouse effect is the process by which a planet is warmed by its atmosphere.
Greenhouse effect is caused by greenhouse gases that deplete the ozone layer.
Fossil fuels, when burned, will release greenhouse gases such as carbon etc. to the atmosphere.
Therefore, the substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels.
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What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 1014 s−1 ejects an electron with 7.74 × 10−20 j kinetic energy?
The threshold frequency for sodium metal is
5.49 x 10^14 s-1
Given:
photon with frequency = 6.66 × 10^14 s−1
kinetic energy = 7.74 × 10−20 j
To Find:
threshold frequency
Solution: The threshold frequency is defined as the minimum frequency of incident radiation below which the photoelectric emission is not possible completely. irrespective of the intensity of incident radiation
We know, relation between threshold frequency, kinetic energy and frequency s given by :
K.E = hv - hvo
Here h is plank's constant and vo, is threshold frequency.
Putting all these value in above equation we get:
7.74 x 10^-20 = (6.66 × 10^14-vo) x 6.626 x 10^-34
vo = 5.49 x 10^14 s^-1
Hence, the threshold frequency for sodium metal is 5.49 x 10^14 s-1
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A rectangle has an area measuring 1350 square centimeters. Its length and width are whole numbers of centimeters. What are the possible combinations of length and width? which possibility gives the smallest perimeter?.
The smallest perimeter of the rectangle is of value 150 cm.
Given:
The area of the rectangle, A = 1350 cm²
Calculation:
Let the length of the rectangle be 'x'
the breadth of the rectangle be 'y'
We know that the area of a rectangle is given as:
A = (x) × (y)
Applying values in the above equation we get:
xy = 1350 cm²
Factorizing the value of 1350, the possible values of length and breadth of the rectangle is as listed below:
x (cm) y (cm)
1350 × 1
675 × 2
450 × 3
270 × 5
225 × 6
150 × 9
135 × 10
90 × 15
75 × 18
54 × 25
50 × 27
45 × 30 (least possible value)
Thus, the smallest perimeter of the rectangle can be calculated as:
P = 2 (x + y)
= 2 (45 + 30)
= 150 cm
Therefore, the smallest perimeter that the rectangle will have is 150 cm.
Learn more about factorization here:
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What is the energy of an electromagnetic wave that has a wavelength of
7.0 x 10-12 m? Use the equation E= hc where hc = 1.99 × 10-25 J-m.
OA. 2.8 × 10-14 J
OB. 1.4 x 10-36 J
OC. 9.0 x 10-37 J
OD. 7.2 x 1035 J
SUBMIT
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \:E = \dfrac{hc}{\lambda} [/tex]
here,
[tex] \sf{hc = 1.99 × {10}^{-25} J - m} [/tex][tex] \sf{\lambda = 7.0 × {10}^{-12}} [/tex]____________________________________
[tex]\qquad \sf \dashrightarrow \: E = \cfrac{1.99 \times 10 {}^{ - 25} }{7 \times 10 {}^{ - 12} } [/tex]
[tex]\qquad \sf \dashrightarrow \: E= \cfrac{1.99}{7} \times 10 {}^{ (- 25 + 12)} { } [/tex]
[tex]\qquad \sf \dashrightarrow \:E= 0.284 \times 10 { }^{ - 13} [/tex]
[tex]\qquad \sf \dashrightarrow \: E= 2.84 \times 10 { }^{ - 14\:\; } J\: \: [/tex]
so, correct choice is A