Show that the Gaussian wave is a solution to the one-dimensional wave equation. (Hint: Calculate the second partial derivatives and plug them into the wave equation. This will give you an expression of v as a function of a, b, and c.) If a = 5.00, b = 10.00, c = 100 (with a(bx-ct)2 unitless), determine the wave speed. In what direction is the wave moving?

Answers

Answer 1

The wave speed is c = sqrt(1/b) = sqrt(0.1) = 0.3162 and  the argument of the exponential function is negative, the wave is moving in the positive x direction.

The one-dimensional wave equation is given by:

∂²v/∂t² = c²∂²v/∂x²

where v is the wave function, t is time, x is position, and c is the wave speed.

Let's consider the Gaussian wave function:

v(x, t) = a * exp(-b(x - ct)²)

where a, b, and c are constants.

Taking the first partial derivative of v with respect to t:

∂v/∂t = -2abc(x - ct) * exp(-b(x - ct)²)

Taking the second partial derivative of v with respect to t:

∂²v/∂t² = 2ab(c(x - ct)² - 1) * exp(-b(x - ct)²)

Taking the first partial derivative of v with respect to x:

∂v/∂x = -2ab(x - ct) * exp(-b(x - ct)²)

Taking the second partial derivative of v with respect to x:

∂²v/∂x² = 2ab(1 - 2b(x - ct)²) * exp(-b(x - ct)²)

Now, plugging these partial derivatives into the wave equation:

∂²v/∂t² = c²∂²v/∂x²

2ab(c(x - ct)² - 1) * exp(-b(x - ct)²) = c² * 2ab(1 - 2b(x - ct)²) * exp(-b(x - ct)²)

Simplifying the equation:

c² = 1 / b

So the wave speed is c = sqrt(1/b) = sqrt(0.1) = 0.3162.

To determine the direction of the wave, we can look at the argument of the exponential function in the wave equation, which is:

-b(x - ct)²

If x > ct, then the argument is negative, meaning the wave is moving in the positive x direction. If x < ct, then the argument is positive, meaning the wave is moving in the negative x direction.

In our case, a = 5.00, b = 10.00, and c = 100, so the wave function is:

v(x, t) = 5.00 * exp(-10.00(x - 100t)²)

Since the argument of the exponential function is negative, the wave is moving in the positive x direction.

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Related Questions

What additional kind of energy makes Cv larger for a diatomic gas than for a monatomic one?
O Charismatic energy
O Translational energy
O Heat energy
O Rotational energy
O Solar energy

Answers

Answer:

translational energy

Explanation:

because is diatomic

what is the specific heat of an unknown substance if a 2.50 g sample releases 12 calories as its specific heat capacity is 0.96 J/gC. What is the temperature change?

Answers

Answer:

1) The specific heat is the heat required to be added to a unit mass of the substance to cause a unit rise in its temperature

2) The temperature change is 20.92°C

Explanation:

The given parameters are;

The mass of the substance, m = 2.50 g

The heat released by the sample, ΔQ = 12 calories = 50.208 J

The specific heat capacity of the substance, c = 0.96 J/(g·°C)

Therefore, we have;

Heat released, ΔQ = Mass, m × Specific heat capacity, c × Temperature change, ΔT

Substituting in the known values gives

50.208 J = 2.50 g × 0.96 J/(g·°C) × ΔT

ΔT = 50.208 J/(2.5 g× 0.96 J/(g·°C)) = 20.92°C

The temperature change = 20.92°C

Sharon pours salt into a glass of water. The salt dissolves. The substance in the glass is a_________
study island

Answers

Answer:

Issa Mixture.

A salt is a compound. ... Na exists in sodium compounds and Cl as Cl2 or chlorinated compounds. A common example would be table salt where both exist( Sodium Chloride). Sodium Chloride solution consisting of NaCl and water is a mixture. An example would be sea water which consists of several salts. Ur welcome.

Explanation: and

The salt is the solute; water is the solvent. Mixed together they become a solution.

If Justin races his Chevy S-10 down highway 37 north for 2,560 meters in 60 seconds, what is
his velocity? a. Draw Justin's trip. What are his distance and displacement? b. The Chevy S-10
started rounding at 10 meters per hour. What is the acceleration at 30 seconds on the
highway? c. The S-10 has a force of 30 N. What is the mass of the car?

Answers

Answer:

A.) 42.7 m/s

B.) 0.33 m/s^2

C.) 90 kg

Explanation:

A.) If Justin races his Chevy S-10 down highway 37 north for 2,560 meters in 60 seconds, what is his velocity? 

Velocity = displacement/time

Velocity = 2560/60

Velocity = 42.67 m/s

B.) The Chevy S-10 started rounding at 10 meters per hour. What is the acceleration at 30 seconds on the highway?

Acceleration = velocity/time

Acceleration = 10/30

Acceleration = 0.33 m/s^2

C.) The S-10 has a force of 30 N. What is the mass of the car?

Force = mass × acceleration

30 = mass × 0.33

Mass = 30/ 0.33

Mass = 90 kg

Help with physics please! Offering a bunch of points!

Help with physics please! Offering a bunch of points!

Answers

3.0m because the graph starts going at a constant pace of 1m per second

Determine whether the forces are balanced or unbalanced for the free-
body diagram below. *

Determine whether the forces are balanced or unbalanced for the free-body diagram below. *

Answers

Answer:

the answer for your question is that they are unbalanced

why no one is helping me!!!
please help me quickly will mean alotttt!!
THE VOLTAGE ACROSS THE GROUPING U=12 VOLTE
TAKE R1=39
AND R2=68
The question is
CALCULATE i1 and i2​

why no one is helping me!!!please help me quickly will mean alotttt!!THE VOLTAGE ACROSS THE GROUPING

Answers

Answer:

Hi

Explanation:

OK so

I2 = U/R2

or

I2 = 12 : 68

I1 = U /R1

I1= 12 : 39

Answer:

Relax 5-Min guide

Explanation:

How much work does the electric field do in moving a -7.7 hC charge from the ground to a point whose potential is +55 V higher?

Answers

I really don’t know I just need some points to help me though this test I’m very sorry

Which of the following has the longest wave length and the lowest frequency

A.infrared waves

B.radio waves

C.x-ray waves

D.microwaves

Answers

Answer:

B. radio waves

Explanation:

Trust me It's correct

what is velocity ratio ?​

Answers

Answer:

the ratio of a distance through which any part of a machine moves to that which the driving part moves during the same time.pls pls mark me branilest

ppositely
Which best describes the result of moving the charge to
the point marked X?
OIts electric potential energy increases because it has
the same electric field.
OIts electric potential energy increases because the
electric field increases.
Its electric potential energy stays the same because
the electric field increases.
OIts electric potential energy stays the same because
it has the same electric potential.

ppositelyWhich best describes the result of moving the charge tothe point marked X?OIts electric potential

Answers

The statement that  best describes the result of moving the charge to  the point marked X is: B. Its electric potential energy increases because the electric field increases.

Which best describes the result of moving the charge to the point marked X?

Moving the charge to the point marked X will change its electric potential energy because the electric field at that point is different from the electric field at its initial position.

At the initial position of the charge, the electric potential energy is determined by the electric potential at that point and the charge of the object. When the charge is moved to point X, the electric potential at that point changes, which means that the electric potential energy of the charge also changes. This is because the electric potential at a point is directly proportional to the electric field at that point.

Therefore, since the electric field is different at point X than at the initial position, the electric potential energy of the charge increases as it moves to point X.

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The world’s fastest elevator is in Taipei, Taiwan. It can lift passengers 1,010 m in 39 s. What is the speed of this elevator?

Answers

Answer: 25.90 m/sec

Explanation:

Speed = Distance / Time

Speed = 1010 / 39

Speed = 25.90 m/s

an electron has a total energy of 5.8×105ev . what is its speed?

Answers

The speed of the electron is approximately 2.235 × 10⁸ m/s.

How to calculate the speed of an electron from its total energy?

To calculate the speed of an electron given its total energy, we can use the relativistic energy-momentum equation:

E² = (mc²)² + (pc)²

Where:

E is the total energy of the electron

m is the rest mass of the electron

c is the speed of light

p is the momentum of the electron

v is the speed of the electron

Since we are given the total energy, we can rearrange the equation to solve for the speed (v):

v = c × √(1 - (m₀c² / E)²)

Where:

m₀ is the rest mass of the electron

c is the speed of light

E is the total energy of the electron

First, let's convert the energy from electron volts (eV) to joules (J):

1 eV = 1.6022 × 10⁻¹⁹ J

Given:

Total energy (E) = 5.8 × 10⁵ eV = 5.8 × 10⁵ × 1.6022 × 10⁻¹⁹ J

Next, we need to know the rest mass of an electron (m₀):

Rest mass of electron (m₀) = 9.10938356 × 10⁻³¹ kg

Now we can calculate the speed (v):

v = c × √(1 - (m₀c² / E)²)

v = c × √(1 - (9.10938356 × 10⁻³¹ kg × (3 × 10⁸ m/s)² / (5.8 × 10⁵ × 1.6022 × 10⁻¹⁹ J))²)

The speed of light, c, is approximately 3 × 10⁸ m/s.

Calculating the expression above will give us the speed of the electron.

To calculate the speed (v) of the electron, let's substitute the values into the equation:

v = c × √(1 - (9.10938356 × 10⁻³¹ kg × (3 × 10⁸ m/s)² / (5.8 × 10⁵ × 1.6022 × 10⁻¹⁹ J))²)

Substituting the given values:

v = (3 × 10⁸ m/s) × √(1 - ((9.10938356 × 10⁻³¹ kg) × (3 × 10⁸ m/s)²) / ((5.8 × 10⁵ × 1.6022 × 10⁻¹⁹ J))²)

Calculating the expression:

v ≈ 2.235 × 10⁸ m/s

Therefore, the speed of the electron is approximately 2.235 × 10⁸ m/s.

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The cleavage properties of mica result from the -
Choose matching term
hardness
weak bonds between flat layers.
A graduated cylinder and a balance
color of the powdered form of the mineral

Answers

The cleavage properties of mica result from the weak bonds between flat layers. Mica is a mineral that belongs to the silicate group and is characterized by its excellent cleavage in one direction, resulting in thin, flat sheets.

This cleavage is due to the weak chemical bonds between the mineral's layers, which allows the layers to easily slide past each other along a plane of weakness.

The strength of the cleavage and the thin, flat nature of the resulting sheets make mica a useful material in a variety of applications, including electronics, insulation, and cosmetics. Hardness, a graduated cylinder and a balance, and the color of the powdered form of the mineral are not directly related to mica's cleavage properties.

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Answer the following.
Copyright © 2018 Georgia Public Broadcasting. All rights reserved. Use or distribution by an unintended recipient is
prohibited. Unit 50 Series Circuits STUDENT
5. For the following series circuit, at each black dot along the circuit write how much
voltage remains. Assume that 1) the resistors are all the same, and 2) the wires do not use
up any voltage.
V
6.
+
As the number of resistors in a series circuit increases, the overall resistance
Decreases. Remains the same. The current in the circuit
Ieroncos

Answer the following.Copyright 2018 Georgia Public Broadcasting. All rights reserved. Use or distribution

Answers

As the number of resistors in a series circuit increases, the overall resistance increases.

What is a series circuit?

A series circuit is a current pathway that lets electrons flow to one or more resistors.

In series circuit, the current flowing in each circuit component is the same, while the voltage across the circuit components are differnt.

The equivalent resistance of a series curict is obtained by adding all the inididual resistance of the circuit.

Re = R1 + R2 + R3

where;

R1, R2, R3 are the individual resistance of the circuit.

So in a series circuit, as the number of resistance increases, the overall resistance or equivalent resistance increases.

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10000 dyne into Newton.​

Answers

Divide the value by 100000 because;1 Newton = 100000 Dyne

\( \sf\therefore \: 10000 \: dyne = \frac{10000}{100000} = 0.1 \: newton\)

What is the period if a wave with a wavelength of 4.25 cm travels at 5.46 cm/s? Answer to the hundredths place or two decimal places.

Answers

We can calculate the period by taking the reciprocal of the frequency: T = 1/f = 1/1.283 Hz = 0.78 s (rounded to two decimal places). Therefore, the period of the wave is 0.78 s.

The period of a wave is the time it takes for one complete cycle or wavelength to pass a given point. It is represented by the symbol T and is measured in seconds (s). The formula for calculating the period of a wave is T = 1/f, where f represents the frequency of the wave.

The speed of a wave is given by the equation: speed = wavelength * frequency. Rearranging this equation, we have: frequency = speed / wavelength.

The frequency of a wave represents the number of cycles per unit time. In this case, we want to find the period, which is the reciprocal of the frequency. So, the period is given by: period = 1 / frequency.

To find the frequency, we divide the speed (5.46 cm/s) by the wavelength (4.25 cm): frequency = 5.46 cm/s / 4.25 cm.

Now, we can calculate the period by taking the reciprocal of the frequency: period = 1 / (5.46 cm/s / 4.25 cm).

Evaluating this expression, we find the period of the wave to be approximately 0.778 seconds, rounded to the hundredths place or two decimal places.

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For a group class project, students are building model roller coasters. Each roller coaster needs to begin at the top of the first hill, where a horizontal spring that is initially compressed 0.25 m will push a small car forward.

A hill with a compressed spring at the top. There is a car sitting against the compressed spring. The portion of the hill is vertically colored orange, the middle section is vertically colored yellow and the last section colored green.
Each group of students will choose a car and a spring to push the car and then build a track. The assignment is to make the car go 5.0 m/s when it reaches the bottom of the first hill. Four groups of students choose springs and build tracks as described in the table.

A 4 column table with 4 rows. The first column is labeled group with entries A, B, C, D. The second column is labeled car mass in kilograms with entries .75, .60, .55, .84. The third is labeled spring constant in newtons per meter with entries 65, 35, 40, 32. The last column is labeled hill height in meters with entries 1.2, .90, 1.1 , .95.
Which group’s roller coaster will most likely make the car travel closest to 5.0 m/s when it is at the bottom of the first hill?

A
B
C
D

Answers

The group that will make the car travel closest to 5 m/s when it is at the bottom of the first will is of:

Group C.

How to obtain the velocity for each car?

The velocity that each car will assume at the bottom of the hill is given by the equation presented as follows:

v = square root (2gh + kx²/m).

The parameters are given as follows:

g = 9.8 m/s is the acceleration relative to the gravity.h is the height of the hill.k is the spring constant.x = 0.25 represents the initial compression of the spring.m is the mass of the car.

The parameters are given by the table in this problem, hence the velocities of each car are given as follows:

Group A: v = square root(2 x 9.8 x 1.2 + (65 x 0.25²)/0.75) = 5.38 m/s.Group B: v = square root(2 x 9.8 x 0.9 + (35 x 0.25²)/0.6) = 4.61 m/s.Group C: v = square root(2 x 9.8 x 1.1 + (40 x 0.25²)/0.55) = 5.05 m/s. -> closest to 5 m/s.Group D: v = square root(2 x 9.8 x 0.95 + (32x 0.25²)/0.84) = 4.58 m/s.

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Answer: group C

Explanation:

PLEASE HELP WILL MARK BRAINLIEST IF YOU EXPLAIN HOW YOU GOT THE ANSWER!!!

The answer for the questions are
a. 57N
b. 0 m/s^2
I just need to know how to solve it

PLEASE HELP WILL MARK BRAINLIEST IF YOU EXPLAIN HOW YOU GOT THE ANSWER!!!The answer for the questions

Answers

Answer:

Explanation:

To determine the magnitude of the normal force on the crate, you can use the equations of motion and Newton's laws of motion.The equation for the normal force is:

F = W - f

where W is the weight of the object (in this case, the crate) and f is the force of friction.Substituting in the values for the weight and the force of friction, you get:

F = (196 N) - (80 N)

which simplifies to:

F = 116 NThus, the magnitude of the normal force on the crate is 116 N. This answer assumes that the weight and the force of friction are both acting at an angle of 60° relative to the horizontal. If the angle is different, the calculations will be slightly different.


To determine the acceleration of the crate, you can use the equations of motion and Newton's laws of motion.The equation for the net force (F) acting on an object is:

F = ma

where m is the mass of the object and a is its acceleration.In order to solve for the acceleration, you will need to know the mass of the crate and the net force acting on it. Assuming the crate has a mass of m, the equation for the net force becomes:

F = ma = (m)(a)You can then use the equation for the net force to solve for the acceleration. For example, if the mass of the crate is 50 kg and the net force acting on it is 276 N, the equation becomes:

(276 N) = (50 kg)(a)Dividing both sides by the mass of the crate, you get:

a = 5.52 m/s^2This is the acceleration of the crate. Note that this answer assumes that the net force is acting at an angle of 60° relative to the horizontal. If the angle is different, the calculations will be slightly different.

What country landed the first spacecraft on the moon?

Answers

The United States of America was the first country to land a spacecraft on the moon.

The historical event occurred on July 20, 1969, when the Apollo 11 mission successfully placed the lunar module, "Eagle," on the moon's surface. Astronauts Neil Armstrong and Edwin "Buzz" Aldrin became the first human beings to walk on the moon, while Michael Collins orbited above in the command module. This achievement marked a major milestone in space exploration and demonstrated American technological superiority during the Cold War.

This mission marked the first successful soft landing on the moon and was a major milestone in space exploration. The Luna 9 spacecraft was the first of many lunar landers and rovers sent to the moon, laying the foundation for more ambitious lunar missions such as the Apollo 11 mission in 1969, which was the first mission to put humans on the moon.

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Alfred fell effort fell in love with Dianna while talking to her at the party Africa shirt that there should be a natural logical explanation for his attraction to her Alfred weighs 87 kg and the other weighs 60 kg what is the force of attraction between if they are sitting 0.5 meters apart

Answers

Answer:

\(1.4*10^-7N\)

Explanation:

Step one:

given data

mass m1= 87 kg

mass m2=60kg

sitting distance r= 0.5m

The gravitational constant G= 6.67*10^-11Nm^2/kg^2

Required

The Force of attraction between the two bodies

Step two:

Applying the formula for the force of attraction by gravity on two  bodies

\(F=\frac{Gm1m2}{r^2}\)

substituting our data we have

\(F=\frac{6.67*10^-^1^1 *87*60}{0.5^2}\\\\F=\frac{3.48174*10^-^7}{0.25^2}\\\\F=1.4*10^{-7}N\)

a halo around the sun or moon indicates that this cloud type is present is called

Answers

A halo around the sun or moon is often an indication that cirrostratus clouds are present.

Cirrostratus clouds are high-level clouds that form above 20,000 feet (6,000 meters). They are composed of ice crystals and have a thin, often transparent appearance. When these clouds are present, they can create a halo effect around the sun or moon.

The halo is formed when light from the sun or moon is refracted, or bent, as it passes through the ice crystals in the cirrostratus clouds. This refraction causes the light to spread out and create a ring or halo-like appearance around the sun or moon.

The presence of a halo is often an indication of thin, high-level cloud cover, typically preceding an approaching warm front or an area of moisture. It can also be a sign of changing weather conditions.

It is worth noting that halos can also be formed by other cloud types, such as altostratus or thin, wispy cirrus clouds, depending on the specific atmospheric conditions.

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what did johannes rydberg and walter ritz discover about atomic spectra?

Answers

Johannes Rydberg and Walter Ritz discovered the Rydberg-Ritz combination principle, a mathematical relationship in atomic spectra.

Johannes Rydberg and Walter Ritz discovered the mathematical relationship between the wavelengths of spectral lines in atomic spectra, known as the Rydberg-Ritz combination principle.

This principle states that the difference between the reciprocals of two wavelengths corresponds to an integer ratio of two characteristic numbers, revealing a pattern in the spectral lines.

By applying this principle, they were able to develop a formula that accurately predicted the wavelengths of spectral lines emitted by various elements, leading to a better understanding of atomic structure and the development of spectroscopy as a powerful tool in physics and chemistry.

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if an object with a velocity of 50m/s has the same momentum as that of a 10 kg Mass moving with a velocity of 20 m/s the mass of the object is​

Answers

Answer:

4 kg

Explanation:

momentum = mass x velocity

10 x 20 = 200

200 / 50 = 4

An electric geyser consumes 2.2 units of electrical energy per hour of its use. It is designed to work on the mains voltage of220V
.
a) What is the ‘power-rating’ of this device?

Answers

The power-rating of the electric geyser can be calculated using the formula: Power = Energy/time. Here, the device consumes 2.2 units of electrical energy per hour. 1 unit of electrical energy is equal to 1 kilowatt-hour (kWh).

So, the power-rating of the electric geyser is:
Power = 2.2 kWh/hour
We know that voltage (V) is related to power (P) and current (I) by the formula: P = VI. Here, the device is designed to work on the mains voltage of 220V. So, we can rearrange the formula to find the current (I) flowing through the device:
I = P/V
I = (2.2 kWh/hour) / (220V)
I = 0.01 kA or 10A
So, the power-rating of the electric geyser is 2.2 kW and the current flowing through it is 10A.


Summary: The power-rating of an electric geyser can be calculated using the formula: Power = Energy/time. The device consumes 2.2 units of electrical energy per hour and is designed to work on the mains voltage of 220V. The power-rating of the electric geyser is 2.2 kW and the current flowing through it is 10A.

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The twisting joint (type T) of an industrial robot has a range of 322° rotation. In order to study the mechanical errors in the joint and the input/output links, a statistical experiment was conducted by taking 10 samples, each one as follows: the joint was commanded to turn and stop at a certain addressable angle and the deviation (in degrees) from that specific angle was recorded. The results of taking 10 samples are presented in the table below: 0.176 0.04 -0.345 0.079 0.309 -0.004 -0.102 0.12 0.075 0.1 Supposing that the statistical distribution of the mechanical errors is normal, determine the number of storage bits required in the controller memory so that the accuracy of the joint is as close as possible to, but less than, its repeatability. Use six standard deviations as the measure of repeatability.

Answers

To determine the number of storage bits required in the controller memory for the twisting joint (type T) of the industrial robot, we need to calculate the repeatability, round the deviations to a reasonable precision, and then calculate the number of addressable positions based on the range of the joint and the chosen accuracy level.


First, let's calculate the repeatability of the joint. Given that the range of rotation is 322°, the repeatability can be calculated as 6 times the standard deviation. Since the standard deviation is a measure of how spread out the data is, multiplying it by 6 ensures that the accuracy of the joint is as close as possible to, but less than, its repeatability.
Next, let's analyze the given data. The 10 samples of deviations from the commanded angles are: 0.176, 0.04, -0.345, 0.079, 0.309, -0.004, -0.102, 0.12, 0.075, and 0.1.
To calculate the standard deviation of these deviations, we need to find the mean and then calculate the differences from the mean. Squaring these differences and taking the average will give us the variance, which we can then take the square root of to obtain the standard deviation.

After calculating the standard deviation, we multiply it by 6 to obtain the repeatability.
Now, to determine the number of storage bits required, we need to consider the accuracy of the joint. The accuracy depends on the precision required for representing the deviations. Assuming a reasonable level of precision, we can round the deviations to, for example, 3 decimal places.
Finally, the number of storage bits required in the controller memory can be calculated by multiplying the range of the joint (322°) by the accuracy (e.g., 0.001°, considering 3 decimal places). This will give us the number of addressable positions, which can be represented by the required number of storage bits.

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For the following six questions, match the descriptions to the below people (A-J)
A) Eratosthenes B) Aristarchus C) Isaac Newton D) Aristotle E) Ptolemy F) Galileo G) Hipparchus H) Kepler I) Nicolaus Copernicus J) Tycho Brahe
23. Discovered the phases of Venus using a telescope.
24. First to consider ellipses as orbits.
25. Foremost ancient Greek philosopher.
26. Ancient Greek who believed in a sun-centered universe.
27. First to measure the size of the Earth to good accuracy.
28. Developed the first predictive model of the solar system.

Answers

The correct match of the descriptions to the below people are 23 - F, 24 - H, 25 - D, 26 - I, 27 - A, 28 - B.

23 - F Galileo: Galileo Galilei is credited with discovering the phases of Venus using a telescope. Through his observations, he observed that Venus went through a series of phases similar to those of the Moon, which supported the heliocentric model of the solar system.

24 - H Kepler: Johannes Kepler was the first to consider ellipses as orbits. He formulated the laws of planetary motion, known as Kepler's laws, which stated that planets move in elliptical paths with the Sun at one of the foci. Kepler's work revolutionized our understanding of celestial mechanics.

25 - D Aristotle: Aristotle, the ancient Greek philosopher, is considered one of the foremost thinkers in history. While his contributions span various fields, including philosophy and natural sciences, his views on astronomy were geocentric. He believed that the Earth was the center of the universe and that celestial bodies moved in perfect circles around it.

26 - I Nicolaus Copernicus: Nicolaus Copernicus was an astronomer who proposed the heliocentric model of the solar system, in which the Sun, rather than the Earth, was at the center. Copernicus's revolutionary idea challenged the prevailing geocentric view and laid the foundation for modern astronomy.

27 - A Eratosthenes: Eratosthenes was an ancient Greek mathematician and astronomer who made significant contributions to geography and astronomy. He is known for his accurate measurement of the Earth's circumference. By measuring the angle of the Sun's rays at two different locations, he estimated the Earth's circumference with remarkable accuracy.

28 - B Aristarchus: Aristarchus of Samos is credited with developing the first predictive model of the solar system. He proposed a heliocentric model centuries before Copernicus, suggesting that the Sun was at the center of the universe, with the Earth and other planets orbiting it. Aristarchus's model was a significant departure from the prevalent geocentric view of the time.

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a mass weighing 54 pounds stretches a spring 3.84 inches. determine the amplitude and period of motion if the mass is initially released from a point 8 inches above the equilibrium position with an upward velocity of 5 ft/s

Answers

The restoring force F of a spring is proportional to its displacement x from its equilibrium position. This law is called Hooke's law, and it can be written mathematically as follows:

F = − kx

where k is the spring constant

The period of motion can be determined by the following formula:

T=2π\(\sqrt{\frac{m}{k} }\)

where, m = the mask = spring constant

Let the amplitude of motion be A. The total energy of a mass attached to a spring is given by:

E=\(\frac{1}{2}\)k\(A^2\)

The maximum kinetic energy of the mass is given by

K = \(\frac{1}{2}\)m\(v^2\)

The maximum potential energy is given by

U = \(\frac{1}{2}\)k\((A + x_0)^2\)

where \(x_0\) is the displacement of the mass from the equilibrium position when it is released from a point 8 inches above the equilibrium position with an upward velocity of 5 ft/s. The maximum potential energy is equal to the maximum kinetic energy.

Equating the two, we have:

\(\frac{1}{2}\)m\(v^2\) = \(\frac{1}{2}\)k\((A + x_0)^2\) ⇒ A + \(x_0\) = \(\sqrt{\frac{mv^2}{k} }\)

Using this value of A + \(x_0\), we can determine the amplitude of motion as follows:

A = \(\sqrt{\frac{mv^2}{k} }\) − \(x_0\)

The mass in pounds can be converted to slugs as follows: \(m = \frac{54}{32.2} = 1.68\) slugs.

The displacement x of the spring from its equilibrium position can be determined as follows: \(x = \frac{3.84}{12} = 0.32\) ft.

The spring constant k can be determined using the formula:

\(k=\frac{k}{x}\)

where F is the force exerted on the spring when it is stretched by the mass.

The force F can be determined using the formula: F = m * g where g is the acceleration due to gravity.

Substituting the values, we get: F = 1.68 * 32.2 = 54.1 lbf

Substituting these values into the formula for k, we get \(k =\frac{54.1}{0.32} = 169.0\) lbf/ft.

The period of motion can be determined using the formula: T = 2π\(\sqrt{\frac{m}{k} }\).

Substituting the values, we get: T = 2π\(\sqrt \frac{1.68}{169.0}\) = 0.504 s.

Using the value of \(x_0\), we can determine the amplitude of motion as follows: A = \(\sqrt{\frac{mv^2}{k} }\)  − \(x_0\).

Substituting the values, we get: A = \(\sqrt{ \frac{1.68*\frac{25}{9} }{169.0}} - 0.67A\)= 0.062 ft or 0.74 .

When a mass is hung on a spring, it extends from its original length to a new length. This change in length is known as the displacement. The point where the mass hangs without moving up or down is known as the equilibrium position. The restoring force, which is proportional to the displacement from the equilibrium position, acts on the mass when it is displaced from its equilibrium position. This law is known as Hooke's law. The constant of proportionality is known as the spring constant. The period of motion of the mass attached to the spring can be determined using the formula T = 2π\(\sqrt{\frac{m}{k} }\), where m is the mass and k is the spring constant. The amplitude of motion is the maximum displacement of the mass from its equilibrium position.

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Suggest two ways in which the force in an electromagnet could be made quicker

Answers

By increasing the number of turns of wire in the coilAnswer:

Explanation:

HELP ASAP 10 points to whoever gets this right

HELP ASAP 10 points to whoever gets this right

Answers

Answer:

is it B to C?

I think thats it but I'm not 100 percent

Answer: i think its a

Explanation: sorry if its wrong

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