X Prob set #3 CMP1 [Due: May 25, 2022 (Wed)] 1. Consider electrons under a weak periodic potential in a one-dimension with the lattice constant a. (a) Calculate the average velocity of the electron wi

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Answer 1

Consider electrons under a weak periodic potential in a one-dimension with the lattice constant "a." Given that the electrons are under a weak periodic potential in one dimension, we have a potential that is periodic of the form: V(x + na) = V(x), where "n" is any integer.

We know that the wave function of an electron satisfies the Schrödinger equation, i.e.,(1) (h²/2m) * d²Ψ(x)/dx² + V(x)Ψ(x) = EΨ(x)Taking the partial derivative of Ψ(x) with respect to "x,"

we get: (2) dΨ(x)/dx = (∂Ψ(x)/∂k) * (dk/dx)

where k = 2πn/L, where L is the length of the box, and "n" is any integer.

We can rewrite the expression as:(3) dΨ(x)/dx = (ik)Ψ(x)This is the momentum operator p in wave function notation. The operator p is defined as follows:(4) p = -ih * (d/dx)The average velocity of the electron can be written as the expectation value of the momentum operator:(5)

= (h/2π) * ∫Ψ*(x) * (-ih * dΨ(x)/dx) dxwhere Ψ*(x) is the complex conjugate of Ψ(x).(6)

= (h/2π) * ∫Ψ*(x) * kΨ(x) dxUsing the identity |Ψ(x)|²dx = 1, we can write Ψ*(x)Ψ(x)dx as 1. The integral can be written as:(7)

= (h/2π) * (i/h) * (e^(ikx) * e^(-ikx)) = k/2π = (2π/L) / 2π= 1/2L Therefore, the average velocity of the electron is given by the equation:

= 1/2L.

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Related Questions

Which term is the rate at which work is done?
a. energy
b. power
c. joules
d. force

Answers

The rate at which work is completed is indicated by the power word, hence option b is correct. Power, which can be defined as the amount of work done W.

Is the time rate at which the job is completed or energy is given. Energy transferred, expressed as W/t or energy transferred against the time interval t. Work (or energy) per unit time, foot-pounds per minute, joules per second (or watts), and ergs per second are all ways to express power. Work is defined as involving both force applied to the body and displacement of the body. Consider a block that is resting on a horizontal, frictionless floor. A consistent force is acting on this block.

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Answer:  B.) power

Explanation: Get dem hearts up:)

Which component of health-related fitness is developed by performing a wall sit?
A, Body composition
B, Muscular endurance
C, Reaction time
D, Coordination ​

Answers

Answer:

The answer is Muscular endurance

Explanation:

It is this because your seeing how long your muscles can with stand. I answered by guessing lol.

Suppose that the sound level of a conversation is initially at an angry 71 dB and then drops to a soothing 54 dB. Assuming that the frequency of the sound is 504 Hz, determine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wave amplitudes. Assume the speed of sound is 346 m/s and the air density is 1.21 kg/m3.

Answers

Answer:

Explanation:

In the decibel scale , intensity of sound changes logarithmically as follows

\(10log\frac{I}{I_0} =\) Value in decibel scale , the value of I₀ = 10⁻¹² W /m².

Putting the values

\(10log\frac{I}{10^{-12}} = 71\)

\(log\frac{I}{10^{-12}} = 7.1\)

\(\frac{I}{10^{-12}} = 10^{7.1}\)

\(I= 10^{-4.9}\) W/m²

Similarly for 54 dB sound intensity can be given as follows

I = 10⁻¹² x \(10^{5.4}\)

\(I= 10^{-6.6 }\) W / m²

For intensity of sound the relation is as follows

I = 2π²υ²A²ρc where υ is frequency , A is amplitude , ρ is density of air and c is velocity of sound .

Putting the given values for 71 dB

\(I= 10^{-4.9}\)  = 2π² x 504²xA²x 1.21 x  346

A² = 60.03 x 10⁻¹⁶

A = 7.74 x 10⁻⁸ m

For 54 dB sound

\(10^{-6.6}\) = 2π² x 504²xA²x 1.21 x  346

A² = 1.1978 x 10⁻¹⁶

A = 1.1 x 10⁻⁸ m

explain the advantage of accuracy​

Answers

Answer:

Accuracy reduces on the rates of errors

Explanation:

\(.\)

An air-filled cavity for producing electromagnetic standing waves has two parallel, highly conducting walls separated by a distance L. One standing-wave pattern in the cavity produces nodal planes of the electric field with a spacing of 1.50 cm. The next-higher-frequency standing wave in the cavity produces nodal planes with a spacing of 1.25 cm. What is the distance L between the walls of the cavity?

Answers

If higher-frequency standing wave in the cavity produces nodal planes with a spacing of 1.25 cm, the distance L between the walls of the cavity is 7.5cm.

The general formula for both ends closed is (n+1) λ/2

Let's say for n, \(\frac{\pi }{2} n = 1.5 = \pi = 3cm\)

for (n+1), λ(n+1)/2 = 1.25 = λ(n+1) = 2.5cm

∴ (n+1) (1.5) = (n+2)(1.25) = n = 4

∴  L = (4+1)(3/2) = L = 7.5cm.  

Electromagnetic waves, or EM waves, are waves produced by oscillations between electric and magnetic fields. In other words, EM waves consist of oscillating magnetic and electric fields. Gamma rays have the highest frequencies in the electromagnetic spectrum.

Most sunrise alarm clocks are yellow to simulate the brightness of the sun. This energizing color is the color your body naturally associates with the morning. Colors like purple and red are often used for simulating the sunset and may be more conducive to falling asleep.

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How far was the beam of constructive interference deflected in the diagram below? (Assume the original beam of constructive interference was at 90° on the protractor.)

A. 15°
B. 35°
C. 55°
D. 75°

Answers

Answer is C

But yaaaaaaaa

Roxy weighs 120 lbs and dead lifts 150 lbs. What is her absolute strength?

Answers

Answer:

Absolute strength = 1.25

Explanation:

Given:

Body weight of body = 120 lbs

Body weight of thing = 150 lbs

Find:

Absolute strength

Computation:

Absolute strength = Body weight of thing / Body weight of body

Absolute strength = 150 / 120

Absolute strength = 1.25

A shopper in a supermarket pushes a loaded 31 kg cart with a horizontal force of 15 N. What is the distance moved the cart in the following cases: a) Disregarding friction how far will the cart move in 4.3 s, starting from rest? b) How far will the cart move in the 4.3 s if the shopper places a(n) 88 N child in the cart before pushing it?

Answers

The  cart will move 32.9 meters in 4.3 seconds, starting from rest, if the shopper places an 88 N child in the cart.

a) Disregarding friction, we can use the equation:

distance = (1/2) * acceleration * time^2

where acceleration is the net force divided by the mass of the cart:

acceleration = force_net / mass

In this case, the net force is the horizontal force applied by the shopper:

force_net = 15 N

And the mass of the cart is given as 31 kg. Therefore:

acceleration = 15 N / 31 kg = 0.48 m/s^2

Plugging this into the distance equation, we get:

distance = (1/2) * 0.48 m/s^2 * (4.3 s)^2 = 4.6 meters

Therefore, the cart will move 4.6 meters in 4.3 seconds, starting from rest, if we disregard friction.

b) If the shopper places an 88 N child in the cart, the net force applied by the shopper will be:

force_net = 15 N + 88 N = 103 N

Using the same equation as before, the acceleration of the cart is:

acceleration = 103 N / 31 kg = 3.32 m/s^2

Plugging this into the distance equation, we get:

distance = (1/2) * 3.32 m/s^2 * (4.3 s)^2 = 32.9 meters

Therefore, the cart will move 32.9 meters in 4.3 seconds, starting from rest, if the shopper places an 88 N child in the cart.


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what is the definition of energy in scientific terms?responses a force used on an object a force used on an object a change in temperature a change in temperature the motion of an object the motion of an object the ability to do work

Answers

Answer: The ability to do work.

Explanation: Scientists define energy as the ability to do work. There is potential energy (where an object at rest has the capacity to have motion) and kinetic energy (where an object is in motion).

Light wave A has a greater frequency than light wave B. Which has a greater wavelength?
A) Wave A
B) Wave B
C) They're equal
D) Not enough info

Answers

Wave B has a greater wavelength. Option B is correct.

The frequency and wavelength of a wave are inversely proportional to each other. Mathematically, the relationship between the two is given by the equation:

c = λf

where c is the speed of light, λ is the wavelength, and f is the frequency of the wave.

Since light wave A has a greater frequency than light wave B, we can conclude that light wave B has a greater wavelength than light wave A. This is because as the frequency increases, the wavelength decreases, and as the frequency decreases, the wavelength increases. Therefore, if two waves have different frequencies, the one with the lower frequency will have a greater wavelength. Hence Option B is correct.

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why is it impossible for an induction motor to operate at synchronous speed

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An induction motor cannot operate at synchronous speed because the relative motion between the stator magnetic field and the rotor conductors is necessary for the induction of current in the rotor.

In an induction motor, the stator creates a rotating magnetic field that interacts with the rotor conductors, inducing current in them. This induced current in the rotor creates a magnetic field that opposes the stator's magnetic field, resulting in rotor motion.

The speed at which the rotor rotates is slightly less than the synchronous speed, which is the speed of the rotating magnetic field.

If an induction motor were to operate at synchronous speed, the relative motion between the stator magnetic field and the rotor conductors would be zero.

This would eliminate the change in magnetic flux linking the rotor conductors, and as a result, no current would be induced in the rotor. Without the induced current, there would be no opposing magnetic field in the rotor, and therefore no torque generated to sustain rotation. Thus, an induction motor cannot operate at synchronous speed.

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vector g is 40.3m long in a -35 direction. vector h is 63.3 m long in a 270 direction. find the direction of their vector sum

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The direction of their vector sum is 92.51.

How do you determine the vector addition's direction?

Finding the angle that the resultant creates with either the north-south or the east-west vector will reveal the direction of the resultant. The resultant makes an angle with west at a value of theta.

Thus, the length of the first vector G in a -35 degree direction is 40.3 m.

Let's locate the elements of G.

\(G_{x}\) = 40.3 cos (-35) = 33.018

\(G_{y}\) = 40.3 sin(-35) = -23.1151

The length of the second vector, H, is 63.3 m in the direction of 270.

\(H_{x}\) = 63.3 cos(270) = 0

\(H_{y}\) = 63.3 sin(270) = -63.3

The corresponding components can be combined to find the resultant vector:

\(R_{x} = G_{x}+H_{x}\) = 33.018+0 = 33.018

\(R_{y} = G_{y} +H_{y}\) = -23.1151+(- 63.3) = -86.4151.

To find the magnitude of (\(R_{x}, R_{y}\))  which is given by the formula \(\sqrt{R^{2} _{x} +R^{2} _{y} }\)

\(\sqrt{33.018+ (-86.4151)}\) = \(\sqrt{8557.34844}\) = 92.51.

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If two excess electrons are placed on a long straight copper wire, where are they most likely to be found?

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i don’t know i need points im sorry !!

ANSWER ALL QUESTIONS IN DETAIL AND WILL MARK BRAINLIEST IF ANSWERED CORRECTLY AND WELL. 20 POINTSSSSS

ANSWER ALL QUESTIONS IN DETAIL AND WILL MARK BRAINLIEST IF ANSWERED CORRECTLY AND WELL. 20 POINTSSSSS

Answers

Answer:

(a) - \(R_{eq.}=8 \ \Omega\)

(b) - \(I_1=3 \ A, \ I_2= 1.8 \ A, \ I_3=1.2 \ A\)

(c) - \(\Delta V_1=6 \ V, \ \Delta V_2= 18\ V, \ \Delta V_3= 18 \ V\)

Conceptual:

Things to know about parallel/series resistors:

\(\boxed{\left\begin{array}{ccc}\text{\underline{Resistors in Series:}}\\\\R_s=R_1+R_2+R_3+\dots +R_n\\\\I_1=I_2=I_3= \dots = I_n\\\\\Delta V_1+\Delta V_2+\Delta V_3+ \dots +\Delta V_n=\Delta V\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Resistors in Parallel:}}\\\\\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+ \dots + \frac{1}{R_n} \\\\\Delta V_1=\Delta V_2=\Delta V_3= \dots =\Delta V_n\\\\I_1+I_2+I_3+ \dots + I_n=I\end{array}\right}\)

What is a resistor?

A resistor takes electrical energy and converts it to some other form of energy, such as heat. In doing so this can alter a circuit's current and divide voltages.

What is current?

Electrical current is the flow of charged particles.

What is voltage?

To put it simply, voltage is what "pushes" current through a circuit.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Ohm's Law:}}\\\\\Delta V=IR\end{array}\right}\)

How you should tackle these types of problems:

I recommend combining resistors until you have one resistor. This one resistor is what your total resistance is, which I call the equivalent resistor. Then work backwards from the equivalent resistor to find any information you need, utilizing Ohm's law and properties of parallel/series resistors.

Step-by-step:

Refer to the attached image(s).

ANSWER ALL QUESTIONS IN DETAIL AND WILL MARK BRAINLIEST IF ANSWERED CORRECTLY AND WELL. 20 POINTSSSSS
ANSWER ALL QUESTIONS IN DETAIL AND WILL MARK BRAINLIEST IF ANSWERED CORRECTLY AND WELL. 20 POINTSSSSS
ANSWER ALL QUESTIONS IN DETAIL AND WILL MARK BRAINLIEST IF ANSWERED CORRECTLY AND WELL. 20 POINTSSSSS

Camden constructs a model of a double convex lens using two clear plastic circles that are round on one side and flat on the other. He attaches the circles at the edges. How does his model look?

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Using two circular, flat, clear plastic circles that he attaches at the edges, Camden creates a model of a double convex lens that appears thicker in the center and thinner at the edges.

What do you call a double convex lens?

Bi-convex (Double-convex) lenses focus parallel light rays to a single point similarly to plano-convex lenses because they have the same radius of curvature on both sides of the lens. As a general rule, bi-convex lenses work best with conjugate ratios between 5:1 and 1:5.

By twice refractively (bending) the light rays from a distant object, a double convex lens, also known as a converging lens, concentrates the diverging, or blurred, light rays.

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why do we use a circuit breaker ?

Answers

Answer:to protect an electrical circuit from damage caused by excess current from an overload or short circuit.

Explanation:

the free-fall acceleration on mars is 3.7 m/s2. (a) what length of pendulum has a period of 1.8 s on earth?

Answers

The free-fall acceleration on mars is 3.7 m/s2. length of pendulum has a period of 1.8 s on earth is L= 53.98cm.

What is the equation used to determine acceleration?

According to the equation a = v/t, acceleration (a) is the product of the change in velocity (v) and the change in time (t). In terms of meters per second squared (m/s2), this enables you to calculate how quickly velocity varies.  

How can acceleration be calculated without utilizing the equations of motion?

Calculate the result by subtracting the initial velocity from the final velocity and dividing it by the time interval. Your average acceleration throughout that period is the result.

given:-

pendulum has a period of T= 1.8 s on earth

T = 2π√(L/g)

T^2=4π^2(l/g)

l=  T^2*g/4π^2

l= 2.4^2*9.8/4*π^2

l= .53m= 53.98cm

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a fairly common chronic inflammatory disease of the alimentary canal involving all layers of the bowel, which causes chronic diarrhea, is

Answers

Inflammatory Bowel Disease (IBD) is a prevalent chronic inflammatory condition affecting the entire gastrointestinal tract, leading to persistent diarrhea.

Inflammatory Bowel Disease (IBD) encompasses two main conditions: Crohn's disease and ulcerative colitis. Both of these diseases cause inflammation and damage to the digestive tract, resulting in chronic diarrhea. Crohn's disease can affect any part of the gastrointestinal tract, from the mouth to the anus, while ulcerative colitis specifically affects the colon and rectum.

The inflammation in IBD occurs due to an abnormal immune response, where the body's immune system mistakenly attacks the healthy cells in the digestive tract. The exact cause of IBD is not yet fully understood, but it is believed to involve a combination of genetic, environmental, and immunological factors.

Chronic diarrhea is a prominent symptom of IBD, along with abdominal pain, cramping, fatigue, weight loss, and rectal bleeding. The disease often follows a relapsing and remitting course, with periods of active inflammation (flare-ups) alternating with periods of reduced or no symptoms (remission).

The diagnosis of IBD involves a thorough evaluation of symptoms, medical history, physical examination, and various diagnostic tests such as blood tests, endoscopy, colonoscopy, and imaging studies. Treatment for IBD aims to reduce inflammation, control symptoms, and prevent complications.

It usually involves a combination of medications, such as anti-inflammatory drugs, immunosuppressants, and biological therapies. In severe cases, surgery may be necessary to remove the affected portion of the bowel.

In conclusion, Inflammatory Bowel Disease (IBD) is a chronic inflammatory condition affecting the entire gastrointestinal tract, characterized by chronic diarrhea. It encompasses Crohn's disease and ulcerative colitis, which involve inflammation in different parts of the digestive tract. The underlying cause of IBD is complex and multifactorial.

Chronic diarrhea is a significant symptom, along with other gastrointestinal manifestations. Diagnosis involves a comprehensive assessment, and treatment focuses on reducing inflammation and managing symptoms through medication and, in some cases, surgery.

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A cord of mass 0.65 kg is stretched between two supports 7.2 m apart. If the tension in the cord is 120 N, how long will it take a pulse to travel from one support to the other

Answers

It will take approximately 0.0054 seconds for the pulse to travel from one support to the other.

The time it takes for a pulse to travel from one support to the other in a stretched cord can be calculated using the wave speed formula. In this case, the wave speed is equal to the tension in the cord divided by the linear mass density of the cord. The linear mass density is equal to the mass of the cord divided by its length.

Given:
Mass of the cord (m): 0.65 kg
Distance between supports (L): 7.2 m
Tension in the cord (T): 120 N

First, we need to find the linear mass density (μ) of the cord:
μ = m/L
μ = 0.65 kg / 7.2 m
μ ≈ 0.0903 kg/m

Next, we can calculate the wave speed (v) of the pulse:
v = T/μ
v = 120 N / 0.0903 kg/m
v ≈ 1327.57 m/s

Finally, we can calculate the time (t) it takes for the pulse to travel from one support to the other:
t = L/v
t = 7.2 m / 1327.57 m/s
t ≈ 0.0054 s

In conclusion, it will take approximately 0.0054 seconds for the pulse to travel from one support to the other.

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What can we say when one force
is greater than another force?
A. There is no net force.
B. There is no change in motion.
C. There is a change in motion.
D. The forces are in equilibrium.

Answers

When one force is greater than another force, we can say that there is a change in motion. The correct answer is option C: "There is a change in motion."

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. When one force is greater than another force, the net force acting on the object is not zero. If the net force acting on an object is not zero, it will cause the object to accelerate in the direction of the larger force. This acceleration leads to a change in motion. The object may speed up, slow down, change direction, or a combination of these.

Option A, "There is no net force," is incorrect because if one force is greater than another, there is a net force acting on the object.

Option B, "There is no change in motion," is incorrect because, as explained above, a greater force leads to a change in motion.

Option D, "The forces are in equilibrium," is incorrect because if one force is greater than another, the forces are not balanced, and the object is not in equilibrium.

Therefore, the correct statement is that there is a change in motion when one force is greater than another force.

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what quantity of heat energy is needed to melt 120g of ice at -20°C to water at 30°c? (SHC of water = 4200J/kg/k, SHC for ice = 2100J/kg/K, Specific latent heat of fusion of ice = 3.36x10^5 J/kg)​

Answers

Answer:

59, 720 Joules

Explanation:

\(q = mc(t2 - t1) + m(lf) + mc(t2 - t1)\)

first term=ice to 0 degrees

second term=water to ice

third term-water to 30 degrees

\(q = 0.12 \times 2100 \times 20 + 0.12 \times 3.36 \times {10}^{5} + 0.12 \times 4200 \times 30\)

\(q = 59720 \: joules\)

To measure a population’s baseline genetic state, it must have _____________ to be in hardy-weinberg equilibrium

Answers

Answer:

b

Explanation:

b

13. An airplane travels at a constant speed of 800 kilometers per hour (km/h).
Approximately how long will it take the airplane to travel 200 kilometers?

Answers

Answer:

The time taken for the airplane to cover the distance is 15 minutes.

Explanation:

Given;

velocity of airplane, u = 800 km/h

distance traveled by the airplane, s = 200 km

The time of this motion is given by;

s = ut + ¹/₂at²

at constant velocity, acceleration, a = 0

s = ut

t = s / u

t = (200 km) / (800 km/h)

t = 0.25 hour = 15 mins

Therefore, the time taken for the airplane to cover the distance is 15 minutes.

The process of fusion that keeps our Sun shining begins with which building blocks?
A) two electrons
B) two deuterons
C) two protons
D) two Einsteinium nuclei
E) two neutrinos

Answers

The process of fusion that keeps our Sun shining begins with which building blocks is neutrons. The correct answer is C.

The process of fusion that powers the Sun, known as nuclear fusion, begins with two protons, which are the positively charged particles found in the nucleus of an atom.

During the fusion process in the Sun's core, two protons combine to form a deuteron, which is a nucleus of deuterium, an isotope of hydrogen. This deuteron then undergoes further fusion reactions to produce helium and release a tremendous amount of energy in the form of light and heat. This continuous fusion process is what keeps our Sun shining.

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in 10 seconds, a total of 5 waves crash onto the shore of a beach. The distance between each wave crest on the water is 8 meters.

Find the:


A. Wavelength:

B. Period:

C. Frequency

D. Wave speed

Answers

In ten seconds,a total of 5 waves crash onto the shore of the beach .

The distance between each wave crest on the water is 8 meters.

Wave length is the length between two wave crests that is the distance between two wave crests.

We know distance between each wave crest is 8 meters

Total of 5 wave crests, the distance between first and second wave crest is 8 meters

the distance between second and third wave crest is 8 meters

So wave length = 8+8 = 16 meters

What is Wave length?Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire. In wireless systems, this length is usually specified in meters (m), centimeters (cm) or millimeters (mm). In the case of infrared (IR), visible light, ultraviolet (UV), and gamma radiation (γ), the wavelength is more often specified in nanometers (nm), which are units of 10-9 m, or angstroms (Å), which are units of 10-10 m.Wavelength is inversely related to frequency, which refers to the number of wave cycles per second. The higher the frequency of the signal, the shorter the wavelength.

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Please help me out on this physics subject

Please help me out on this physics subject

Answers

Liquid gasoline is moving through a hose as she fills the car. If the speed of the gasoline decreases, then the pressure within the gasoline will increase. Thus, the correct option is A.

What is Bernoulli's principle?

Bernoulli’s principle has been formulated by Daniel Bernoulli and this states that as the speed of a moving fluid increases such as liquid or gas, the pressure of the fluid within decreases. Although Bernoulli deduced this law, it was later derived by Leonhard Euler, he derived Bernoulli’s equation in its usual form in the year 1752.

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in the static pressure or a decrease in the potential energy of the fluid.

Therefore, the correct option is A.

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why is it necessary for cells to be so small​

Answers

Answer:

Cells are small because they need to keep a surface area to volume ratio that allows for adequate intake of nutrients while being able to excrete the cells waste.

Explanation:

That is why the cell needs to be small

A large truck is moving at 22.0 m/s. if its momentum is 125,000 kg • meters per second, what is the truck's mass? 176 kg 2750 kg 5680 kg 11,400 kg

Answers

The  mass of the large truck is determined as 5680 kg.

Mass of the truck

The mass of the truck is calculated as follows;

P = mv

where;

P is momentumm is massv is velocity

m = P/v

m = 125000/22

m = 5680 kg

Thus, the  mass of the large truck is determined as 5680 kg.

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Answer:

C. 5680

Explanation:

edg2023

9. An object moving at a constant velocity accelerates at a constant rate of 20 m/s for a distance of
100 m. At the end of the acceleration the object has a velocity of 80 m/s. What was its velocity
before accelerating?

9. An object moving at a constant velocity accelerates at a constant rate of 20 m/s for a distance of100

Answers

Answer:

I believe the answer is roughly 49m/s

Explanation:

List all given variables:

Accel=20m/s^2

Dist=100m

Final velocity=80m/s

Initial velocity=?

Using the equation i=sqrt(f^2-2a*d) where i =initial velocity, f=final velocity, a=acceleration, and d=distance, we can plug in the known values and solve for initial velocity

i=sqrt(80^2-2*20*100)

i=sqrt(6400-4000)

i=sqrt(2400)

i=48.99, rounded up to 49m/s as the initial velocity

This is my speculation about this answer would appreciate if anyone can confirm this.

In an experiment to determine the density of Paraffin by Hare's apparatus, the following results were obtained: 16 cm length of water column length of paraffin column 30cm Calculate the density of paraffin?

Answers

The density of Paraffin is 536.8 kg/m³. To calculate the density of Paraffin, we can use the formula: Density = Mass/Volume

However, we do not have the mass of Paraffin, so we need to use Hare's apparatus to determine it indirectly. We know that the pressure exerted by the water column is equal to the pressure exerted by the paraffin column, so we can use this information to find the density of paraffin.

The pressure exerted by the water column is given by:
Pressure = ρgh

where ρ is the density of water, g is the acceleration due to gravity and h is the height of the water column. In this case, ρ = 1000 kg/m³ and h = 16 cm.

So, the pressure exerted by the water column is:
Pressure = 1000 x 9.81 x 0.16 = 1569.6 Pa

Now, we can use the same equation to find the density of paraffin. The height of the paraffin column is 30 cm, so the pressure exerted by the paraffin column is:
Pressure = ρgh = Density x g x h

We can rearrange this equation to find the density of paraffin:
Density = Pressure / (g x h)

Plugging in the values, we get:
Density = 1569.6 / (9.81 x 0.3) = 536.8 kg/m³

Therefore, the density of Paraffin is 536.8 kg/m³.

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