you apply 2 volts to a piezoelectric material and measure a displacement of 0.5 nm. what is the approximate piezoelectric coefficient d33 for this piezoelectric? you apply 2 volts to a piezoelectric material and measure a displacement of 0.5 nm. what is the approximate piezoelectric coefficient d33 for this piezoelectric? 250 pm/v 250 nm/v 500 nm/v 500 pm/v 1 nm/v

Answers

Answer 1

The piezoelectric coefficient, measured in volt meters per Newton, connects the stress placed on a crystal to the resulting electric field.

The definition of a piezoelectric device

The ability of piezoelectric devices to transform mechanical energy into electrical energy and through inverse piezoelectric effect makes them useful as actuators in a range of applications. The following benefits apply to actuators made of piezoelectric components. quick reaction. movement with grace.

What type of substance is piezoelectric?

When mechanical stress is applied to certain materials, it can result in the production of piezoelectric materials, or piezoelectrics. Quartz is a frequently used piezoelectric substance. When stress is applied, the electron moves, which results in the creation of an electric charge.

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Related Questions

A lunar lander is descending toward the moon's surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t)=b−ct+dt2, where b = 710 m is the initial height of the lander above the surface, c = 64.0 m/s , and d = 1.01 m/s2What is the initial velocity of the lander, at t = 0 and just before it reaches the lunar surface?

Answers

The initial velocity of the lander, at t = 0 and just before it reaches the lunar surface, is 64 m/s. This is because the velocity of the lander is given by c = 64 m/s.

What is velocity?

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It is the magnitude of an object's displacement per unit of time, expressed as a speed in a specific direction.

Velocity is calculated by dividing the change in position (displacement) by the time interval in which the displacement occurs. It has units of distance per time (e.g. meters per second). The direction of velocity is the same as the direction of displacement, and its magnitude represents the speed of an object's motion.

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consider an electromagnetic wave traveling in the positive z-direction. the x-component of the electric field in the wave, ex(z,t), is given by: ex(z,t)

Answers

Yes, that's correct! The span of a set of vectors is the set of all linear combinations of those vectors. You've found two elements of R4 that belong to the span of X1 and X2, and you've also found an element of R4 that does not belong to their span.

Although not all electromagnetic waves (EM) are sinusoidal plane waves, all EM waves can be thought of as a linear superposition of sinusoidal plane waves moving in any direction. The form of a plane EM wave moving in the x-direction is

B(x,t) is equal to Bmaxcos(kx - t + k), and E(x,t) is equal to Emaxcos(kx - t + k).

The EM wave's magnetic field vector is B, and its electric field vector is E. E and B are always perpendicular to one another and to the direction of propagation for electromagnetic waves. The direction of E x B is the direction of propagation.

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match the subatomic particles to the statements that describe them. some answer choices may be used more than once, and some descriptions require multiple answers.

Answers

There are protons, neutrons, and electrons, three types of subatomic particles. Protons have both a positive charge and a negative charge, making them two of the neutrinos with electrical charges.

What three kinds of subatomic particles are there?

These particles are frequently referred to as elementary particles since they are the building blocks of atoms. There are protons, neutrons, and electrons, three types of subatomic particles. Protons and electrons, two of something like the subatomic particles, each have  electrical charge of one or the other.

How would you explain the interactions between the subatomic particles?

Particles smaller than an atom are referred to as subatomic particles. The three primary subatomic particles present in an atom are protons, neutrons, and electrons. The charge of protons is positive (+). An easy method.

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. show answer no attempt 50% part (a) during this period, what is the dragster's acceleration expressed as a multiple of the acceleration due to gravity, g?

Answers

Acceleration may now be increased without running the risk of dominating the track because the dragster has grown in speed and the large rear wing's downforce is now pressing the car down onto the track surface.

What exactly does speed mean?

the definition of speed. a direction or speed at which an object's location changes. The distance traveled relative to the time it took to travel that distance is how fast something is moving. Due to its lack of magnitude and merely having a direction, speed is indeed a scalar number.

Which of these is the first speed rule?

Newton's first law states that a body will continue to move until it is acted on by an external power if it is at rest or moving in a specific direction at a fairly constant pace.

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which of the following is an example of a nonrival resource? responses national park camping sites that can be reserved by anyone national park camping sites that can be reserved by anyone farmland that can be used to grow corn or soybeans farmland that can be used to grow corn or soybeans solar energy solar energy fish in the ocean fish in the ocean timber in a forest

Answers

Radio and the internet are two instances of nonrival resource. They can be accessed by many individuals simultaneously without compromising their quality or increasing the chance that the supply would run out.

What is a nonrival resource example?

Radio stations and the internet are two instances of nonrival goods. They are available to many individuals at once, and they can been consumed repeatedly without lowering their quality or increasing the chance that the energy will run out.

Which of the below economic models allocates resources and distributes goods primarily based on prices?

In a market economy, market forces govern the resources that are distributed and the costs of goods and services. mainly demand and supply. Since there is little government interference in market economies, all management choices are made by private ownership.

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the electric force on a charged particle in an electric field is f. what will be the force if the particles charge is tripled and the electric field strength is halved

Answers

The electric force will be 1.5f if the particles charge is tripled and the electric field strength is halved.

Given the electric force on a charged particle = f

Let the electric field strength = E

Let the charge on the particle = q

The electric force acting on the particle = f = qE

Here, the particles charge is tripled = q2 = 3q

The electric field strength is halved = E2 = E/2

Let the changed electric force = F2

We know that F = qE such that:

F2 = q2E2 = 3q x E/2 = 3/2(qE) = 1.5(f)

Hence the electric force  if the particles charge is tripled and the electric field strength is halved is 1.5 times the initial electric force is 1.5f

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For the same situation as in Part A, on which of the following quantities does the electric field at the electron's position depend?
a. the distance between the positive charge and the electron
b. the charge on the electron
c. the mass of the electron
d. the charge of the positive charge
e. the mass of the positive charge
f. the radius of the positive charge
g. the radius of the electron

Answers

The distance between the electron and the positive charge affects the electric field there.

What variables determine the electric field at the electron's location?

Only the charge that creates the electric field and its distance from it affect the electric field's value: the distance between the positive charge and the electron, as well as the positive charge itself.

What function does the electron perform within the electric field?

The force on a positive charge would be pointed in the direction of the electric field. Because of its negative charge, an electron will move against the electric field. It will therefore migrate to the left.

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When striking, the pike, a predatory fish, can accelerate from rest to a speed of 3.9m/s in 0.12s .
a) What is the acceleration of the pike during this strike?
Express your answer using two significant figures.
b) How far does the pike move during this strike?
Express your answer using two significant figures.

Answers

[tex]32.5m/s^{2}[/tex] is the acceleration of the pike during this strike. [tex]0.026 m[/tex] the pike move during this strike

How far did the pike move during this strike?

The distance travelled by the pike during this strike can be calculated using the equation for displacement:

The pike moves 0.03 m during this strike.

What is the difference between distance and displacement?

Distance refers to the total length travelled by an object, regardless of direction. It is a scalar quantity, meaning it has only magnitude and no direction. Displacement, on the other hand, is the change in the position of an object relative to its starting point.

[tex]a= (V_f - v_i) / t= (3.9 m/s - 0 m/s) / 0.12 s = 32.5 m/s^{2}[/tex]

[tex]d= v_i *t+(1/2) * a*t^{2}[/tex]

[tex]d=(1/2)*a*t^{2}=(1/2)*32.5m/s^{2}*0.12s^{2}=0.026m[/tex]

The acceleration of the pike during this strike is [tex]32m/s^{2}[/tex]

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1. earth is located at one blankof the moon's orbit.target 1 of 6 2. according to kepler's second law, jupiter will be traveling most slowly around the sun when at blank.target 2 of 6 3. earth orbits in the shape of a/an blankaround the sun.target 3 of 6 4. the mathematical form of keple

Answers

1. Earth is positioned at one focus of the Moon's orbit.

2. according to kepler's second regulation, jupiter may be journeying most slowly around the sun's aphelion

3. Earth orbits inside the form of a/an ellipse across the solar.

4. The mathematical shape of Kepler's 1/3 regulation measures the duration in years and the semimajor axis in astronomical gadgets (AU).

An ellipse is a type of conic section, a curve that results from the intersection of a cone and a plane. It is defined as a set of points such that the sum of the distances from two fixed points (called foci) to any point on the curve is constant. An ellipse has two axes: the major axis, which is the longest and the minor axis, which is the shortest. The foci lie on the major axis and the length of the major axis is twice the distance between the foci.

The shape of the ellipse is determined by the ratio of the lengths of the two axes, called the eccentricity. When the two axes are equal, the ellipse is a circle. Ellipses appear in many natural and man-made objects, including planetary orbits and the shapes of car headlights, bottle bottoms and egg yolks. They are also used in engineering and science to model real-world phenomena, such as the distribution of charges in a capacitor and the deformation of a metal rod under tension.

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Complete Question: -

earth is located at one of the moon's orbit.target 1 of 6 2. according to kepler's second law, jupiter will be traveling most slowly around the sun when at .target 2 of 6 3. earth orbits in the shape of a/an blankaround the sun.target 3 of 6 4. the mathematical form of kepler's third law measures the period in years and the blankin astronomical units (au).target 4 of 6 5. according to kepler's second law, pluto will be traveling fastest around the sun when at blank.target 5 of 6 6. the extent to which mars' orbit differs from a perfect circle is called its

an electron beam after being accelerated from rest through a potential difference of 5kv in vacum is allowed to imping normally on a fixed surface. if the incident current is 50 mew a determine the force exerted on the surface assuming that it bring the electron to rest .take mass of electron is 9.1*10^-

Answers

The force exerted on the surface assuming that it bring the electron to rest  is -6.1 * 10^-16 N

How to calculate?

The force exerted on the surface can be determined using the equation below:

Force = (incident current) * (change in kinetic energy) / (change in time)

The change in kinetic energy of each electron can be calculated as:

ΔKE = (1/2) * (mass of electron) * (final velocity^2 - initial velocity^2)

Since the electrons come to rest, the final velocity is 0. Hence the initial velocity can be calculated using the equation:

initial velocity = (2 * potential difference) / mass of electron

Therefore we calculate ΔKE and then find the force:

mass of electron = 9.1 * 10^-31 kg

potential difference = 5 kV = 5 * 10^3 V

time = 5 s

incident current = 50 * 10^-6 A

initial velocity = (2 * potential difference) / mass of electron = (2 * 5 * 10^3) / (9.1 * 10^-31) = 1.1 * 10^8 m/s

ΔKE = (1/2) * (mass of electron) * (0^2 - (1.1 * 10^8)^2) = -6.1 * 10^-19 J

Force = (incident current) * (ΔKE) / (time) = (50 * 10^-6) * (-6.1 * 10^-19) / (5) = -6.1 * 10^-16 N

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fill in the blank. an artist paints a scene with a large mountain, which lacks detail and is out of focus, and a tree, which is sharply defined and bright green. the viewer might assume that the mountain is___than the tree. group of answer choices

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An artist paints a scene with a large mountain, which lacks detail and is out of focus, and a tree, which is sharply defined and bright green. The viewer might assume that the mountain is further away than the tree. This condition is about Implied Depth.

What is Implied Depth?

Implied depth is building an illusion in works of art. The methods: value, space, and perspective are used by artists to provide the impression of three-dimensional depth in two-dimensional works of art.

Value: the lightness or darkness of an area

The painting used value to draw the object, especially the tree, which is painted bright green.

Space is the distance between identifiable points.

The painting used space to draw the objects. The mountain is large, but it lacks detail; it is assumed that the mountain is very big but still far away from the closer object (the tree), which is painted with sharp detail.

Atmospheric perspective: distant objects lack contrast; closer objects have more detail, sharpness, and focus.

The painting used atmospheric perspective. The distant object is the mountain, which is out of focus and lacks of detail. Meanwhile, the tree is the closer object, which is sharply defined.

So, it is obvious that the viewer might assume that the mountain is further away than the tree.

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An unknown gas has a volume of 110 mL and has a density of 15.24 g/ml. What is the mass of this unknown gas?

Answers

First the ideal gas law will be used to solve for the moles of unknown gas (n).

What is the mass of this unknown gas?

The unit that is used to measure the molar mass is grams per moles (g/mol). The mass of gas in a one-mole sample is equal to the molar mass of gas. If the molar mass of gas X was 40 g/mol, this means that the weight of gas X in a one-mole sample is equal to 40 grams.

An ideal gas is considered to be a "point mass". A point mass is a particle so small, its mass is very nearly zero. This means an ideal gas particle has virtually no volume.

Matter is anything that occupies space and has mass. Gas is one of the states of matter, hence, gases also have mass.According to Boyle's law, for a fixed mass of gas, at the constant temperature, the volume is inversely proportional to its pressure. According to Avogadro's law, the volume of a gas is directly proportional to the number of molecules at constant temperature and pressure.

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What would the power (Watts) be for a speaker if it draws 3.0 Amps of current when connected to a 12.0 Volt source?

Answers

The power needed for a speaker is 36.0 Watts.

Power is the amount of energy needed to run an electronic device every second. The equation to calculate power

P = V × IP = W ÷ tP = I² × RP = V² ÷ R

where

V = electrical voltage = 12.0 VoltI = electrical current = 3.0 AR = the resistor (Ω)W = work done (J)t = time (s)P = power (Watts)The unit Watts equals
1 Watts = 1 VA
1 Watts = 1 J/s
1 Watts = A²/Ω
1 Watts = V²/Ω

P = V × I

P = 12.0 × 3.0

P = 36.0 Watts

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Two equal masses are floating in space. The distance between their centers is X. How would the gravitational force between them change if the mass of one of the objects was cut in half?

Group of answer choices

The force would be one-half as much.

The force would be one-fourth as much.

The force would be twice as much.

The force would be the same.

Answers

The force would be one-fourth as much.

What is force?

Force is a push upon an object resulting from its interaction with another object. It is a vector quantity that is described by both magnitude and direction. Forces cause an object to accelerate.

Therefore, The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. So if one of the objects has its mass halved, the gravitational force between them will decrease by a factor of (1/2)^2 = 1/4.

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of the following units of distance measurement, the one that is most convenient in describing distances in the solar system is the

Answers

When discussing distances inside the solar system, the astronomical unit (au) that represents the typical distance between the Earth and the Sun is a useful unit of measurement.

How can we calculate the separation between planets?

Radar has been used to measure extraterrestrial distances since 1961. To do this, we send a radar signal to another planet (or moon, asteroid, etc.), time the time it takes is for radar echo to return, and record the result. Astronomers would just have to rely on those other (more direct) geometric techniques prior to radar.

What measurement system should I use to determine the distance?

Length is measured in distance. For instance, the length of a road equals its distance. The most popular units of measurement for distance in the measurement measurements are millimeters.ω = √k/M. According to the rule that was cited, the effect of spring energy was to change M in the formula for to M + m/3.

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in his speech about inc., tom wanted to show the relatively flat hierarchy in the company's chain of command so he used a___as a presentational aid.

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Tom utilized an organizational chart as a presentational tool in his speech about Inc. to highlight the company's chain of command's relatively flat hierarchy.

Visual presentation aids, such as images, diagrams, charts, graphs, maps, and the like, are the most common form used by speakers. Sound effects, audio voice snippets, and musical excerpts are all examples of audible aids. Presentation tools can serve a range of purposes, including enhancing audience comprehension of the information you are presenting, audience memory and retention of the message, adding diversity and interest to your speech, and enhancing your reputation as a speaker. Presentation tools make a speaker's message easier for the audience to understand.

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A car comes to a complete stop from an initial speed of 55 mi/hr in a distance of 120 ft.a) Calculate the constant acceleration in ft/sec? b) With the same constant acceleration, what would be the stopping distance (s), (in ft) from an initial speed of 70 mi/hr?

Answers

The car that comes to a complete stop has:

a) A constant acceleration in ft/sec of: -27.06 ft/sec²

b) A stopping distance, (in ft) from an initial speed of 70 mi/hr of: 194.50 ft

What is acceleration?

It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2

The formulas for uniformly varied rectilinear motion (UVRM) and procedures we will use to solve this exercise are:

a = ((vf²- vi²) /2* xx = (vf²-vi²)/ (2a)

Where:

x = distancevf = final velocityvi = initial velocitya = acceleration

Information about the problem:

vi1= 55 mi/hrvf= 0 ft/secx1= 120 fta1 = ?vi2= 70 mi/hx2=?

By Converting the velocities from (mi/hr) to (ft/sec) we have:

vi1= 55 mi/hr /* 5280 ft/ 1 mi * 1 hr/3600 sec

vi1= 80.6 ft/sec

vi2= 70 mi/hr /* 5280 ft/ 1 mi * 1 hr/3600 sec

vi1= 102.6 ft/sec

Applying the acceleration formula we get:

a = ((vf²- vi²) /2* x

a = [(0 ft/sec) ²- (80.6 ft/sec )² /2* 120 ft

a = [0 ft²/sec²- 6496.36 ft²/sec² /240 ft

a = -27.06 ft/sec²

Acceleration is negative because the car is decelerating

Applying the distance formula, we get:

x = (vf²-vi²)/ (2a)

x2 = [(0 ft/sec)²- (102.6 ft/sec)²]/ (2 * -27.06 ft/sec²)

x = (0 ft²/sec²- 10526.76 ft²/sec²)/ -54.12 ft/sec²

x = 194.50 ft

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A hand pushes a book against a wall. Both the book and the hand are at rest. Select two forces in this situation which are a third-law pair.
1. the normal force of the book on your hand
2. the normal force of the wall on the book
3. the normal force of the book on the wall
4. the weight of the book
5. the force of friction on the book

Answers

Option 2 is correct, The force with which the person is pushing is F. The equal but opposite force is exerted by the wall on the book, which is -F.

The weight of the book "Mg" is acting downwards, and as the book did not move the equal and opposite amount of frictional force is acting upwards F(f).Any action that tends to sustain, change, or distort a body's motion is said to be using force. The three laws of motion outlined in Isaac Newton's Principial Mathematical are frequently used to illustrate the idea of force. Newton's first law states that until a force is applied to a body, it will remain in either its resting or uniformly moving state in a straight path. According to the second law, when an external force acts on a body, the body accelerates in the force's direction.

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which of the following conditions are required for electricity to flow through a simple circuit? (choose all that apply)

Answers

Correct options are Option A and D, In series connections, the flow of electrons follow the same path as the current remains constant in all the elements of the circuits. And the total resistance of the circuit increases as more resistors are added to the circuit in serial manner.

There are both active and passive components in a circuit. The flow of current and potential drop across the passive devices will also be determined based on the connections between them.

Similar to how the voltage drop will remain the same even if the passive devices are connected in parallel, the current flow through each device will vary. Similar to this, if the passive devices are wired in series, the potential drop will change but the current flow will remain constant.

Due to the constant current flowing through all of the circuit's components in series connections, electrons follow the same route. And as more resistors are added to the circuit, its overall resistance rises.

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Complete question -

Which of the following statements accurately describes a series circuit? Select all that apply.

The flow of electrons follow the same path.

The flow of electrons split and follow different paths.

Different amounts of charge will be dropped across each resistor in the circuit.

The total resistance of the circuit increases as more resistors are added to the circuit.

The total resistance of the circuit decreases as more resistors are added to the circuit.

two small metaphlic spheres each with a mass of 0.20 g pendulums equilibrium 30.0 cm what is the mangnitude of the charge on each sphere

Answers

The magnitude of the charge on each sphere is 7.22nC when two small metallic spheres each with a mass of 0.20 g pendulums equilibrium 30.0 cm.

Given the mass of each metallic sphere (m) = 0.20g = 20 x 10^-3kg

The length of the spring is (L) = 30cm = 30 x 10^-2m

The charge on two spheres is same = q

The angle of equilibrium = 5°

A force acting in the same direction as the string is called tension.

Let's denote the horizontal component as = Fx and

the vertical component as = Fy then the magnitude of tension is:

T = √Fx^2 + Fy^2

We can observe that the weight of gravity is the only other vertical force acting on mass. W = ma where a is acceleration due to gravity= -9.8m/s^2 Fy and W are equal because we are in equilibrium (mass is fixed and does not change position) (equal magnitude, opposite directions).

Fy = 20 x 10^-3 x 9.8 = 196 x 10^-3N

We can write utilizing the angle of the string as:

Fy = Tcos(5°)

Fx = Tsin(5°)

We know that electric force (Fe) = kq1q2/r^2 = 0.00197 * sin5

196 x 10^-3 * sin5 = 9 * 10^9 * q^2 / (0.3*(sin5)*2)^2)

q = 7.22nC

Hence, the charge on metallic sphere is 7.22nC

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complete question: Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in Figure. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 5.0° with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere?

A diver bounces straight up from a diving board, avoiding the diving board on the way down, and falls feet first into a pool. She starts with a velocity of 4.00 m/s and her takeoff point is 1.80 m above the pool. (a) What is her highest point above the board? (b) How long a time are her feet in the air? (c) What is her velocity when her feet hit the water?

Answers

So the diver's velocity when her feet strike the water is 1.37 m/s.

What is velocity?

Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s).

Here,

(a) To find the diver's highest point above the board, we can use the conservation of energy principle. The initial potential energy of the diver at the takeoff point is given by

PEi = mgh

where m is the mass of the diver, g is the acceleration due to gravity (9.8 m/s² ), and h is the height of the takeoff point (1.80 m). The final potential energy of the diver at the highest point is zero, since she is at her maximum height and has no potential energy. The initial kinetic energy of the diver at the takeoff point is given by

KEi = 0.5 * m * v²

where v is the initial velocity of the diver (4.00 m/s). The final kinetic energy of the diver at the highest point is also zero, since she has no velocity at that point.

The total mechanical energy of the system (the diver) is conserved, so the initial potential and kinetic energies are equal to the final potential and kinetic energies:

PEi + KEi = PEf + KEf

Substituting the expressions for the initial and final potential and kinetic energies, we have

mgh + 0.5 * m * v²  = 0

Solving for h, the height of the highest point above the board, we have

h = v²  / (2g) + h

h = 4.00²  / (2 * 9.8) + 1.80 = 2.63 m

So the diver's highest point above the board is 2.63 m.

(b) To find the time that the diver's feet are in the air, we can use the kinematic equation for vertical motion with constant acceleration:

y = y0 + v0 * t + 0.5 * a * t²

where y0 is the initial height of the diver's feet (1.80 m), v0 is the initial upward velocity of the diver (4.00 m/s), a is the acceleration due to gravity (9.8 m/s² ), and t is the time in the air.

We can find the final height of the diver's feet when they hit the water by setting y = 0 and solving for t:

0 = 1.80 + 4.00 * t - 4.9 * t²

t = √(4 * 1.80 / 4.9) = 0.81 s

So the time that the diver's feet are in the air is 0.81 s.

(c) To find the velocity of the diver when her feet hit the water, we can use the kinematic equation for vertical motion with constant acceleration:

v = v0 + a * t

where v0 is the initial upward velocity of the diver (4.00 m/s), a is the acceleration due to gravity (9.8 m/s² ), and t is the time in the air (0.81 s).

v = 4.00 - 9.8 * 0.81 = 1.37 m/s

So the velocity of the diver when her feet hit the water is 1.37 m/s.

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A set S◆ of vertices in a graph is independent if no two vertices of S◆ are ?

Answers

An Independent Set S of graph G = (V, E) is a set of vertices such that no two vertices in S are adjacent to each other. It consists of non-adjacent vertices.

What is a Vertice?

A vertex is a location in geometry where two or more curves, lines, or edges converge.

As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

Hence, in order to find when a set of vertices in a graph is independent, this means that no two vertices in S are adjacent to each other. It consists of non-adjacent vertices.

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let $a$ and $b$ be distinct complex numbers on the unit circle. find the maximum possible value of $\left|\dfrac{a-b}{1-\overline{a}b}\right|$.

Answers

The maximum possible value of [tex]$\left|\dfrac{a-b}{1-\overline{a}b}\right|$[/tex] is 2.

The maximum possible value of [tex]$\left|\dfrac{a-b}{1-\overline{a}b}\right|$[/tex] is 2.

To see why, consider two complex numbers a and b on the unit circle with a [tex]\neq[/tex] b.

Then, we can write:

[tex]$$|a - b| = 2 \sin \left(\frac{1}{2} \angle (b - a)\right)$$[/tex] and [tex]$$|1 - \overline{a} b| = 2 \sin \left(\frac{1}{2} \angle (1 - \overline{a}b)\right)$$[/tex]

where angle (z) denotes the argument of the complex number z.

Since a and b are on the unit circle,

[tex]\left|\overline{a}\right| = \left|a\right| = 1$\\$\left|\overline{b}\right| = \left|b\right| = 1[/tex]

Hence, using above we can write it as:

[tex]$$\angle (1 - \overline{a}b)\\ = \angle (1 - b\overline{a}) \\= \angle (1) - \angle (b\overline{a}) \\= 0 - \angle (b) + \angle (a) \\= -\angle (b) + \angle (a)$$[/tex]

Thus,

[tex]$$2 \sin \left(\frac{1}{2} \angle (1 - \overline{a}b)\right) \\= 2 \sin \left(\frac{1}{2} (-\angle (b) + \ang\\le (a))\right) \\= 2 \sin \left(\frac{1}{2} (\angle (a) - \angle (b))\right)$$[/tex]

So from above,

we can write it as:

[tex]$$\left|\dfrac{a-b}{1-\overline{a}b}\right| = \frac{|a - b|}{|1 - \overline{a} b|} = \frac{2 \sin \left(\frac{1}{2} \angle (b - a)\right)}{2 \sin \left(\frac{1}{2} (\angle (a) - \angle (b))\right)}$$[/tex]

Since the sine function is always between -1 and 1,

So, we can again write it as:

[tex]$$\left|\dfrac{a-b}{1-\overline{a}b}\right| \leq \frac{1}{1} = 1$$[/tex]

However, we can see that this maximum value is achieved when a and b are diametrically opposed on the unit circle,

so

[tex]$$\left|\dfrac{a-b}{1-\overline{a}b}\right| = \frac{2}{2} = 2$$[/tex]

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which of the following are non-si units commonly used in chemical measurement? select all that apply. multiple select question. btu degree celsius atomic mass unit angstrom degree fahrenheit

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atomic mass unit, angstrom, degree Celsius are non-si units commonly used in chemical measurement.

The SI units have a worldwide acceptance and are the units from which other units are generated. A non-SI unit is one that is not standardized like a SI unit. Using a meter as an example, a millimeter is not a SI unit.

The term "non-SI units" shall be used to refer to any units that are employed in other systems of measurement but are not SI-compliant. Non-SI Units are rarely employed in science courses.

Worldwide, there is a lot of use of the International Standard of Units (SI) as a system of measuring. The number 10 serves as the foundation for this updated version of the metric system. Prefixes have been established as a specific unit.

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The Copernican system was no more accurate than the Ptolemaic system in predicting the positions of the planets because ___________just as in the Ptolemaic system.

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The Copernican system was no more accurate than the Ptolemaic system in predicting the positions of the planets because it still used epicycles, just as in the Ptolemaic system.

Copernican heliocentrism is referred as the astronomical model which was developed by Nicolaus Copernicus. It was published in 1543. This model positioned the Sun at the center of the Universe which is motionless, and with Earth and the other planets orbiting around it in circular paths, modified by epicycles, at uniform speeds.

In Ptolemaic system each planet revolves in uniform along a circular path (epicycle), the centre of which revolves around Earth along a larger circular path (deferent).

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can generate heavy surf h strongest winds near the surface [ choose ] weakens with height [ choose ] energy source is horizontal temperature differences [ choose ] cold-core low [ choose ] air in the center is rising

Answers

A hurricane is a warm-core tropical cyclone fueled by latent heat release from the condensation of moist air, while a mid-latitude cyclone is a cold-core low-pressure weather system caused by the convergence of warm and cold air masses leading to the ascent of air and precipitation.

The following characteristics are applied to only a hurricane (H), to only a mid-latitude cyclone (MLC), or could apply to both a hurricane and a mid-latitude cyclone (BOTH), in the Northern Hemisphere:

Can generate heavy surf: HStrongest winds near the surface: Hweakens with height: BOTHenergy source is horizontal temperature differences: Hcold-core low: MLCair in the center is rising: MLC

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Your question seems to be missing, but I suppose the question was:

"For each of the following characteristics, choose whether it applies to only a hurricane (H), to only a mid-latitude cyclone (MLC), or could apply to both a hurricane and a mid-latitude cyclone (BOTH), in the Northern Hemisphere.

can generate heavy surf:

Strongest winds near the surface:

weakens with height:

energy source is horizontal temperature differences:

cold-core low:

air in the centre is rising:"

a mountain climber in the process of crossing between two cliffs by a rope, pauses to rest. she weighs 535 n. as the drawing shows

Answers

The tension in rope to the left and to the right of the mountain climber (she weighs 535 N):

To the left = 918.5 N

To the right = 845.3 N

The climber is not moving, hence there is no acceleration, and because the defined angles are not in the typical direction, sin rather than cos is actually required for the horizontal.

Fx = T right x - T left x = max = 0

T right x = T right sin (80.0⁰) = T left sin (65.0⁰) = T right left

T left = T right {sin (80.0⁰) / sin (65.0⁰)}

T right Y + T left Y = T right cos 80.0⁰ + T left cos 65.0⁰ = W

T right = 535 N / 0.6329

= 845.3 N

T left = (845.3) (sin 80.0⁰/sin 65.0⁰)

= 918.5 N

The question is incomplete, it should be:

A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 535 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber!

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(0)A square hole 8.0cm along each side is cut in a sheet of copper. (a) calculate the change in the area of this hole resulting when the temperature of the sheet is increased by 50.0K. (b) Does this change represents an increase or a decrease in the area enclosed by the hole?

Answers

(a) The coefficient of linear expansion for copper is about 0.000016 per Kelvin. This means that for every increase in temperature of 1 K, the length of a material will increase by 0.000016 times its original length. For an 8 cm square hole, the original area is 8 cm * 8 cm = 64 cm^2.

The change in the area of the hole will be 64.0512 cm^2 - 64 cm^2 = 0.0512 cm^2.

(b) The change in the area represents an increase in the area enclosed by the hole.

Temperature is a physical property of matter that measures the degree of hotness or coldness of an object or substance. It is expressed in units such as Celsius, Fahrenheit, or Kelvin. The temperature of an object or substance is related to the average kinetic energy of its molecules or atoms. The higher the temperature, the faster the molecules or atoms move, and the more energy they possess.

Temperature can be measured using various devices, such as thermometers, thermocouples, and infrared thermometers. It is also possible to determine the temperature of an object or substance indirectly, by measuring its heat capacity, specific heat, or thermal conductivity. Understanding the concept of temperature and its role in various processes is essential for many fields, including physics, biology, chemistry, engineering, and environmental science.

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a plane monochramtic light wave is incident on adouble lsit as isslutradein figuer 24.4 if the viewsin screen is moved away from the double slit g

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The space between the interference fringes on the screen grows when the viewing screen is pushed away from the double-slit. The edges become wider apart. This is due to the fact that the space between the fringes is proportional to the space between the screen and the slits.

What is monochromatic light?

Light with a single wavelength is referred to as monochromatic light. Such radiations are accessible in a wide range of wavelengths. The electromagnetic spectrum refers to the entire range of wavelengths. Monochromatic light is light with a single wavelength; for example, a sodium lamp is a source of monochromatic light. White light has a wavelength range of 400 nm to 700 nm and comprises a variety of colors. As a result, white light is polychromatic rather than monochromatic. Monochromatic light has a single wavelength or frequency. Because sunlight contains several frequencies or wavelengths of light, it is referred to as polychromatic light.

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Complete question:

A plane monochromatic light wave is incident on a double slit.

(i) As the viewing screen is moved away from the double slit, what happens to the separation between the interference fringes on the screen?

(ii) As the slit separation increases, what happens to the separation between the interference fringes on the screen?

At a track meet, a runner runs the 100-m dash in 8.2 s. What was the runner's average speed?

Answers

As the  runner runs the 100-m dash in 8.2 s, the average speed of the runner is 12.20 meter/second.

What is speed?

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar quantity.

The distance travelled by an object in a time interval is divided by the length of the interval to determine its average speed.

As the  runner runs the 100-m dash in 8.2 s, the average speed of the runner is = (100 ÷ 8.2) meter/second

= 12.20 meter/second.

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