find the net force σf⃗ 3 acting on particle 3 due to the presence of the other two particles. report you answer as a magnitude σf3 and a direction θ measured from the positive x axis.

Answers

Answer 1

Therefore, the net force acting on particle 3 is 139.68 × 10—5 N, and the angle made it by with at the +x axis is 19.1°.

The charge of particle 1 is q1.

q1 = -6.6nC

The charge of particle 2 is q2.

q2 = -13.2 nC

Sides of the equilateral triangle = 3 cm = 3 × 10 —² m.

The force acting on particle 1 is,

\(F _{1} = \frac{kq_{1} q_{3}}{a ^{2} } \)

\( = \frac{9 \times 10 ^{9} \times 6.6 \times 10 ^{ - 9} \times 8 \times 10 ^{ - 9} }{9 \times 10 ^{ - 4} } \)

\(F _{1} = 52.8 \times 10 ^{ - 5} \: N\)

\(F _{1} = F _{1} \: cos(60°)i + F _{1} \: sin(60°)j\)

\(= ( - 26.4 \: i \: + 45.7 \: j \: ) ×10 ^{ - 5} \)

The force acting on particle 2 is,

\( = \frac{9 \times 10 ^{9} \times 3.2 \times 10 ^{ - 9} \times 8 \times 10 ^{ - 9} }{9 \times 10 ^{ - 4} } \)

\( = - 105.6 \times 10 ^{ - 5} \: j\)

The net force acting on particle 3 is,

\(F_{Net} =F _{1} + F _{2}\)

\( = ( - 132 \times 10 ^{ - 5} \: i + 45.7 \times 10 ^{ - 5} \: j)\)

\(F_{Net} =139.68 \times \: 10 ^{ - 5} \: N\)

Thus, the net force acting on particle 3 is 139.68 × 10—5 N.

Let the angle made by it with at the +x axis be θ.

\(cos \: θ = \frac{ - 132 \times 10 ^{ - 5} }{139.6 \times 10 ^{ - 5} } \)

θ = 19.1°

Therefore, the net force acting on particle 3 is 139.68 ×

10—5 N and the angle made it by with at the +x axis is 19.1°.

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Related Questions

Someone just help me

Someone just help me

Answers

C according to my calculations

should nuclear energy be part of sustainable energy future? explain your answer

Answers

Answer:

Nuclear power is presently a sustainable energy source, but could become completely renewable if the source of uranium changed from mined ore to seawater. Since U extracted is continuously replenished through geologic processes, nuclear would become as endless as solar.

Which of the following materials could be used to make an inactive electrode? (Select all that apply) a) a plastic rod b) a rubber policeman c) a carbon rod d) a glass stir rod e) a platinum wire

Answers

An inactive electrode can be made from a plastic rod, a rubber policeman, and a glass stir rod.

Inactive electrodes are used in electrochemical reactions to complete the electrical circuit with the active electrode. These electrodes do not participate in the reaction and are typically made of materials that do not react with the solution or produce any unwanted products. Platinum wire and carbon rod are examples of active electrodes that can participate in the reaction.

Plastic rods, rubber policemen, and glass stir rods are all non-conductive materials that can be used to make inactive electrodes. They do not conduct electricity and do not react with the solution, making them suitable for use as electrodes in electrochemical reactions. Plastic and rubber are particularly useful as they can be easily shaped into different forms to suit the requirements of the experiment.

In conclusion, a plastic rod, a rubber policeman, and a glass stir rod can be used to make inactive electrodes. These materials are non-conductive and do not react with the solution, making them suitable for use in electrochemical reactions. Platinum wire and carbon rods should be avoided as they are active electrodes that can participate in the reaction.

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Which applications, either for diagnostic purposes or for therapeutic purposes, do not involve ionizing radiation? Check all that apply.

Answers

Answer: I do not know (is this an RP question? ;-;)

Explanation:

Answer:

Applications in which ionizing radiation are not used are  

MRI

ultrasound

laser surgery

Explanation:

hope its right

bestfriend

When you pump a bicycle tire, what is happening to the particles inside the tire?

A:Nothing, because pumping in more air does not affect the particles inside.
B:They are moving closer together and contracting, filling the tire and making it more firm.
C:They are moving farther and farther apart, which is what expands the tire.
D:They are moving faster and faster, making the tire feel more full.

Answers

collisions of particles with the inside walls of the tire cause the pressure that is exerted by the enclosed gas. because of the increasing the number of air particles increases the number of collisions, which then increased the pressure of the tire.

Answer:B

Explanation: Just did it

what should scientists do when they see that the data collection or analysis from their experiment phyhas limitations APEX

A. describe the limitations in detail in thier final report.m
B. ignore the limitations when they draw conclusions.
C. repeat the experiment to see if it still has limitations.
D. decide not to report any of the expromental results.

Answers

Answer:

C. Describes the limitations in detail in their final report.

Explanation:

A. Describe the limitations in detail in their final report

what is the speed a rock needs to be given at the surface of the earth in order for it to have a residual speed of 2.5 km/s ?

Answers

The rock needs to be given a horizontal speed of approximately 318.6 kilometers per second at the surface of the earth in order to have a residual speed of 2.5 km/s.

To determine the initial speed a rock needs at the surface of Earth to have a residual speed of 2.5 km/s, we need to consider the forces acting on the rock and the speed it will gain or lose due to those forces. The two main forces acting on the rock are gravity and air resistance. Gravity will tend to pull the rock back towards Earth, decreasing its speed as it moves away from the surface. Air resistance will also oppose the motion of the rock, further reducing its speed. To overcome these forces and achieve a residual speed of 2.5 km/s, the rock must be given an initial speed that is greater than the sum of the speeds it will lose due to gravity and air resistance. This initial speed will depend on specific conditions, such as the mass of the rock, the density of the atmosphere, and the altitude from which the rock is launched. Calculating the exact initial speed required would involve solving a system of equations that account for these factors. However, without specific details about the rock and the environment, it's not possible to provide a precise value for the required initial speed. In summary, the initial speed a rock needs at Earth's surface to have a residual speed of 2.5 km/s will depend on various factors, such as the rock's mass and the atmospheric conditions. To find this speed, a more detailed analysis would be needed.

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answer please in comment what i am typing​

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Answer:

Hiiiiiiii........where r u frm??

a force pair is created when you push on a large crate that rests on the floor. the crate does not move when pushed. which free-body diagram correctly represents the forces acting on the crate?

Answers

The free-body diagram for the crate  shows all the forces acting on the crate like the force applied by the person pushing the crate, the force of friction between the crate and the floor, and the force of gravity acting on the crate.

The free-body diagram for the crate should show all the forces acting on the crate, including the force applied by the person pushing the crate, the force of friction between the crate and the floor, and the force of gravity acting on the crate.

Since the crate is not moving, the force applied by the person pushing the crate must be equal in magnitude and opposite in direction to the force of friction acting on the crate.

This means that the net force on the crate is zero, and the free-body diagram should reflect this.

Here is a description of the forces acting on the crate and a corresponding free-body diagram:

   Force applied by person pushing crate (to the right)    Force of friction between crate and floor (to the left)    Force of gravity acting on crate (downwards)

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please help me! Fill in all the blanks using the highlighted words. All 23 please. Thank you!!

please help me! Fill in all the blanks using the highlighted words. All 23 please. Thank you!!

Answers

Blood travels throughout the body as follows:

oxygen inhale   red blood cellsblood   vena cavaright atriumright ventriclelungs   pulmonary    deoxygenated      lungs  Gas exchangecapillaries     oxygenated   pulmonaryleft  oxygenated    heart  left atrium ventricle   aortaupper lower

How does circulation work?

Circulation is the continuous movement of blood throughout the body by the circulatory system. It consists of the heart, blood vessels (arteries, veins, and capillaries), and blood. The heart acts as a pump, sending oxygen-rich blood through the arteries to the body's cells, and then returning oxygen-depleted blood through the veins back to the heart.

The exchange of oxygen, nutrients, and waste products between the blood and cells occurs through the capillaries. This continuous flow of blood helps to maintain the body's functions and overall health.

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name the sections of the electromagnetic spectrum from highest frequency to lowest.

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The sections of the electromagnetic spectrum from highest frequency to lowest are gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, microwaves, and radio waves.

The electromagnetic spectrum is a range of frequencies, wavelengths and photon energies covering frequencies from below 1 hertz to above 1025 Hz, corresponding to wavelengths which are a few kilometres to a fraction of the size of an atomic nucleus in the spectrum of electromagnetic waves.

In a vacuum, electromagnetic waves tend to travel at speeds which is similar to that of light. However, they do so at a wide range of wavelengths, frequencies and photon energies.

The electromagnetic spectrum consists of a span of all electromagnetic radiation which further contains many subranges, which are commonly referred to as portions. These can be further classified as infrared radiation.

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f) if the red laser has a wavelength of 633 nm, what is the speed and wavelength of the red light in the plastic?

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The speed of light in a medium, such as plastic, is given by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3 x 10^8 m/s), and n is the refractive index of the medium. To determine the speed of red light in plastic, the refractive index of the specific plastic material must be known.

The wavelength of light in a medium can be determined using the equation λ = λ0/n, where λ is the wavelength of light in the medium, λ0 is the wavelength of light in vacuum, and n is the refractive index of the medium. Given that the red laser has a wavelength of 633 nm (633 x 10^-9 m) in vacuum, the wavelength of red light in plastic can be calculated using the refractive index of the plastic material.

In conclusion, to determine the speed and wavelength of red light in plastic, the specific refractive index of the plastic material needs to be known.

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The speed of light is around 3.000E5 km/s. It takes approximately 9.221 seconds for light reflected from the moon Vega to reach planet Xartan. What is the average distance from the moon Vega to the planet Xartan?

Answers

Answer:

\(d=2.77\cdot 10^6\ Km\)

Explanation:

Speed

The speed is calculated as the ratio of the distance d by the time t:

\(\displaystyle v=\frac{d}{t}\)

If we need to calculate the distance, the equation is solved for d:

d=v*t

The speed of light is

\(v=3\cdot 10^5\ Km/s\)

It takes t=9.221 seconds for light reflected from the moon Vega to reach planet Xartan.

We can calculate the average distance the light traveled:

\(d=3\cdot 10^5\ Km/s*9.221\)

\(d=2,766,300\ Km\)

Or, in scientific notation:

\(\mathbf{d=2.77\cdot 10^6\ Km}\)

a 627n woman dives from a 10m platform.a. what is her potential energy 7m into the dive in [j]? assume no external forcesare applied during the dive.

Answers

The potential energy is 4389 J.

Potential energy saved energy that relies upon the relative position of numerous components of a gadget. A spring has greater potential energy when it is compressed or stretched. A steel ball has extra capability strength raised above the ground than it has after falling to Earth.

Potential energy = mgh

m = mass

g = acceleration due to gravity

Here, mg = 627 N

h = height, given = 7 m

Put the values in the formula, mgh

potential energy = mgh

potential energy = 627 × 7

potential energy = 4389 J

Hence, the potential energy is 4389 J.

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A toy boat moves horizontally in a pond. The horizontal position of the boat in meters over time is shown below.

Answers

Displacement=-21
Distance=39


(Sorry if this didn’t help)

The wavelengths in the hydrogen spectrum with m = 1 form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the series.

Answers

the wavelengths in the hydrogen spectrum of the first four members of the series where m=1, the first four members have the wavelength of \(1.464 * 10^7 m,\) \(1.231 * 10^7 m,\) \(1.164 * 10^7 m,\) and \(1.097 * 10^7 m.\)

The wavelengths of the spectral lines in the Lyman series of the hydrogen spectrum can be calculated using the Rydberg formula:

1/λ = \(R * (1/n1^2 - 1/n2^2)\)

Where λ is the wavelength of the spectral line, R is the Rydberg constant (approximately \(1.097 * 10^7 m^-^1)\), and n1 and n2 are positive integers representing the energy levels of the electron in the hydrogen atom.

For the Lyman series, we have m = 1, which means the electron transitions from higher energy levels (n2) to the first energy level (n1 = 1).

Let's calculate the wavelengths for the first four members of the Lyman series:

For n2 = 2:

1/λ = \(R * (1/1^2 - 1/2^2)\)

1/λ = \(R * (1 - 1/4)\)

1/λ = \(R * (3/4)\)

λ = \(4/3R\)

Substituting the value of the Rydberg constant:

λ = \((4/3) * (1.097 × 10^7 m^-^1)\)

λ ≈ \(1.464 * 10^7 m\)

For n2 = 3:

1/λ = \(R * (1/1^2 - 1/3^2)\)

1/λ = \(R * (1 - 1/9)\)

1/λ = \(R * (8/9)\)

λ = \(9/8R\)

Substituting the value of the Rydberg constant:

λ = \((9/8) * (1.097 * 10^7 m^-1)\)

λ ≈ \(1.231 * 10^7 m\)

For n2 = 4:

1/λ = \(R * (1/1^2 - 1/4^2)\)

1/λ = \(R * (1 - 1/16)\)

1/λ = \(R * (15/16)\)

λ = \(16/15R\)

Substituting the value of the Rydberg constant:

λ = \((16/15) * (1.097 * 10^7 m^-^1)\)

λ ≈ \(1.164 * 10^7 m\)

For n2 = 5:

1/λ = \(R * (1/1^2 - 1/5^2)\)

1/λ = \(R * (1 - 1/25)\)

1/λ = \(R * (24/25)\)

λ = \(25/24R\)

Substituting the value of the Rydberg constant:

λ = \((25/24) * (1.097 * 10^7 m^-^1)\)

λ ≈ \(1.097 * 10^7 m\)

Therefore, the wavelengths of the first four members of the Lyman series are approximately:

\(1.464 * 10^7 m,\)

\(1.231 * 10^7 m,\)

\(1.164 * 10^7 m,\)

and \(1.097 * 10^7 m.\)

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Which one of these is not a physical charge

A melting and ice cube
B crushing a can
C chopping wood
D metal resting

Answers

Answer:

the answer is D metal resting

Explanation:

I just think that because if you treasure can that's physical charge by dropping where you create a physical charge melting and Ice Cube might be 1 but I feel like metal resting is more likely

A force of 3kN acts on a car to make it accelerate by 1.5m/s/s. What is the mass of the car?

Answers

Answer:

2

Explanation:

To find force it's force = mass times acceleration so to find mass you would divide force by acceleration

kinetic energetic plus potential energy is called

Answers

Object mechanical energy

if our sun were twenty-four times as massive as it is, how many times faster or slower should the earth move in order to remain in the same orbit?

Answers

if our sun were twenty-four times as massive as it is, 4.4721Vο  times faster or slower should the earth move in order to remain in the same orbit.

Given m= 20 m

Vо = √GM/R

     =√20Vo

      =4.47214 Vo

Depending on how far away from the Sun a planet is, its orbital speed varies. A planet's gravitational attraction is stronger and it moves more quickly the closer it is to the Sun. If the Sun's mass doubled without pushing or pulling on the Earth, the Earth's orbit would change to an ellipse, bringing it out to our current radius but spending most of the time closer to the Sun. The farther it is from the Sun, the weaker the Sun's gravitational pull is, and the slower it moves in its orbit. When our orbit brings us closer to the sun, the tides would likely get considerably greater. The sun's gravity controls the orbital distance and speed.

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Which processes require the input of energy to overcome intermolecular forces?

Answers

Endothermic reactions like melting, evaporation, and sublimation need heat to escape intermolecular forces.

What is the easiest way to define energy?

Energy is referred to by scientists as the capacity for work. People have figured out how to transform transformed from one medium to the next and then use it to accomplish tasks, making modern civilization possible.

What are energy and its measure?

The capacity to perform labor is referred to as energy. A body's capacity for energy is determined by how much work it can accomplish when it is released. A scalar quantity, energy. The SI unit for energy is called a joule. One joule of energy is the amount of energy needed to perform one joule of work.

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How long will it take a runner to complete a marathon race of 42. 2 km if that runner can maintain an average speed of 4. 1 m/s?

Answers

 It would take the runner approximately 10,268.29 seconds (or about 2 hours, 51 minutes, and 8 seconds) to complete a marathon race of 42.2 km, maintaining an average speed of 4.1 m/s.

We can use the formula:

time = distance ÷ speed

to calculate the time it would take the runner to complete a marathon race of 42.2 km, given an average speed of 4.1 m/s.

First, we need to convert the distance to meters, as the speed is given in meters per second:

42.2 km = 42,200 m

Now, we can substitute the values into the formula:

time = distance ÷ speed

time = 42,200 m ÷ 4.1 m/s

time ≈ 10,268.29 s

Thus the time that the runner would take is  10,268.29 seconds  to complete a marathon race.

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Mass m1 on the frictionless table of the figure is connected by a string through a hole in the table to a hanging mass m2

Answers

For a mass m1 on the frictionless table, the speed m1 must rotate a with radius r if m2 is to remain hanging at rest is mathematically given as

\(v=\sqrt{m1/m2*xg}\)

What speed must m1 rotate in a circle of radius r if m2 is to remain hanging at rest?

Generally, the equation for the Force  is mathematically given as

Fc=Fw

Therefore

\(\frac{m1v1}{x}=m2g\)

\(v=\sqrt{m1/m2*xg}\)

In conclusion,  if m2 is to remain hanging at rest the speed of ratio of m1 is calcuylated using

\(v=\sqrt{m1/m2*xg}\)

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The value of the velocity for the mass m₁ on the frictionless table will be \(\rm v = \sqrt{\frac{m_1}{m_2 xg} }\). Velocity is a time-based component. Its unit is m/sec.

What is velocity?

The change of distance with respect to time is defined as speed. Speed is a scalar quantity.

The given data in the problem is

m is the mass

g is the acceleration of free fall =10m/sec²

v is the velocity

From the balancing equation of force the centripetal force is equal to the weight;

\(\rm F_c= m_2 g \\\\ \rm \frac{m_1v_1^2}{x} = m_2 g \\\\ v= \sqrt{\frac{m_1}{m_2xg} } \\\\\)

Hence the value of the velocity for the mass m₁ on the frictionless table will be \(\rm v = \sqrt{\frac{m_1}{m_2 xg} }\).

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Based on what you know about the intrinsic brightness of stars, select all of the correct statements from the following list.

Answers

The intrinsic brightness of a star can vary greatly from star to star, depending on factors such as its size, temperature, and age. These variations in intrinsic brightness are used to classify stars into different types or spectral classes, such as supergiants and dwarfs.

Based on what you know about the intrinsic brightness of stars, select all of the correct statements from the following list:
1. The intrinsic brightness of a star is also known as its absolute magnitude. This magnitude measures the actual amount of light that a star emits.
2. The intrinsic brightness of a star is independent of its distance from Earth. This means that even if a star is far away, its intrinsic brightness remains the same.
3. The intrinsic brightness of a star can be determined by measuring its apparent magnitude and knowing its distance from Earth. The apparent magnitude is how bright a star appears to us from Earth, while the distance is the actual physical distance between the star and Earth.
4. The intrinsic brightness of a star can be used to classify stars into different types or spectral classes. For example, stars with high intrinsic brightness are classified as "supergiants," while stars with low intrinsic brightness are classified as "dwarfs."
5. The intrinsic brightness of a star can vary greatly from star to star. Some stars are much brighter than others due to factors like their size, temperature, and age.
6. The intrinsic brightness of a star can be calculated using the formula: Intrinsic Brightness = (Apparent Brightness * 4π * (Distance)²) / (Luminosity Constant)
The intrinsic brightness of a star, also known as its absolute magnitude, is a measure of the actual amount of light that a star emits. It is important to note that the intrinsic brightness of a star is independent of its distance from Earth. This means that even if a star is far away, its intrinsic brightness remains the same.

However, in order to determine the intrinsic brightness of a star, we need to measure its apparent magnitude (how bright it appears to us from Earth) and know its distance from Earth. The apparent magnitude is measured on a logarithmic scale, with smaller numbers indicating brighter stars. By comparing the apparent magnitude and distance of a star, we can calculate its intrinsic brightness using the formula: Intrinsic Brightness = (Apparent Brightness * 4π * (Distance)²) / (Luminosity Constant).

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Which best describes a radio wave?
A. an electromagnetic wave at very long wavelength (low
frequency)
B. a pressure wave at very long wavelength (low frequency)
C. a pressure wave at very short wavele

Answers

Option A. An electromagnetic wave at very long wavelength (low frequency) best describes a radio wave.

A radio wave is best described as an electromagnetic wave at a very long wavelength or low frequency. It is not a pressure wave. Radio waves are a type of electromagnetic radiation, which also includes other forms such as visible light, infrared, and X-rays. The term "wavelength" refers to the distance between two consecutive points in a wave, such as from one crest to the next. In the case of radio waves, the wavelength is quite long, ranging from several millimeters to hundreds of meters. This long wavelength allows radio waves to travel long distances and pass through obstacles such as buildings and trees. Radio waves are used for various purposes, including communication, broadcasting, and radar systems. For example, when you listen to the radio, the sound is encoded onto a carrier wave, which is a specific radio wave frequency. The receiver then extracts the sound from the carrier wave, allowing you to hear it. Similarly, radar systems use radio waves to detect and track objects like airplanes or weather patterns. To summarize, a radio wave is an electromagnetic wave at a very long wavelength or low frequency. It is not a pressure wave. Radio waves are used for communication, broadcasting, and radar systems due to their ability to travel long distances and pass through obstacles. They play a crucial role in everyday life, allowing us to enjoy wireless communication and entertainment.

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A tennis ball moving with velocity v₁ hits a stationary tennis ball. The collision is inelastic and the two balls start travelling
together, as shown in the picture. What is the velocity of the two tennis balls moving
together?

A. 2v1
B. 1/2v1
C. 1/3v1
D. V1

Answers

Answer:

B.1/2v1 that's the answer

6.(2) When X = 0.70, Y = 0.30, Z = 0.00, calculate the mean atomic mass, μ and He

Answers

To calculate the mean atomic mass, μ and He when X = 0.70, Y = 0.30, Z = 0.00, the following steps should be taken. The first step is to calculate the average atomic mass of the element.

This can be calculated using the following equation:μ = (X × mX) + (Y × mY) + (Z × mZ)where:X = the mass fraction of the first isotope Y = the mass fraction of the second isotopeZ = the mass fraction of the third isotopem X = the mass of the first isotope in atomic mass units (amu)mY = the mass of the second isotope in amumZ = the mass of the third isotope in amu The second step is to calculate the mass of He produced in the reaction. This can be done using the following equation:Mass of He = (Y × mHe) / 2where:mHe = the mass of helium in amuTo calculate the mean atomic mass, μ and He when X = 0.70, Y = 0.30, Z = 0.00, we can use the following values:X = 0.70Y = 0.30Z = 0.00mX = 12.00 amumY = 13.01 amumZ = 14.01 amumHe = 4.00 amu Using the equation above, we can calculate the average atomic mass as follows:μ = (0.70 × 12.00) + (0.30 × 13.01) + (0.00 × 14.01)= 8.40 + 3.90 + 0= 12.30 amu The mass of He produced can be calculated as follows:Mass of He = (0.30 × 4.00) / 2= 0.60 / 2= 0.30 amu Therefore, when X = 0.70, Y = 0.30, Z = 0.00, the mean atomic mass is 12.30 amu and the mass of He produced is 0.30 amu.

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The photograph shows matter going through a physical change. Which characteristic of the matter changes?

A. shape.

B. shininess.

C. state.

D. type of atoms

The photograph shows matter going through a physical change. Which characteristic of the matter changes?

Answers

Answer:

Possibly shape.

Explanation:

Because it is ripped in half. As you guys and the questioner can see that there is a wiggly strip down the middle. That also cause of a shape change.

I really hope my answer is right ^_^  

The characteristic of matter which is undergoing change in the picture is it's shape as it is being teared apart.

What is matter?

Matter in chemistry, is defined as any kind of substance that has mass and occupies space that means it has volume .Matter is composed up of atoms which may or not be of same type.

Atoms are further made up of sub atomic particles which are the protons ,neutrons and the electrons .The matter can exist in various states such as solids, liquids and gases depending on the conditions of temperature and pressure.

The states of matter are inter convertible into each other by changing the parameters of temperature and pressure.Matter possesses both particle and wave characteristics.Phase is a form of matter having uniform composition as well as physical properties.

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at what values of theta is the vertical component ay of the acceleration vector greatest in magnitude

Answers

The values of theta is the vertical component ay of the acceleration vector greatest in magnitude at  90° and 270°.

Multidimensional stir with constant acceleration can be treated the same way as shown in the former chapter for one- dimensional stir. before we showed that three- dimensional stir is original to three one- dimensional movements, each along an axis vertical to the others.

To develop the applicable equations in each direction, let’s consider the two- dimensional problem of a flyspeck moving in the xy aeroplane with constant acceleration, ignoring the z- element for the moment.

Thinking of circles as parametric equations:

ry=sinθ

rx=cosθ

Note that I have limited θ:     0° <=θ < 360°

Also note that the greatest magnitude of sine and cosine functions is1.

This problem is based only on the y-component, so just consider ry=sinθ.

It hast he greatest magnitude (vertical distance from the center) at90° (and 270°).

Takethe derivative for velocity.

vy=cosθ

It has the greatest magnitudes at 0° and 180°.

Take the derivative for acceleration

ay=-sinθ

It has the greatest magnitudes at 90° and 270°

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Complete question:

At what value(s) of is the vertical component ay of the acceleration vector greatest in magnitude? (Several choices may be correct.) 0° 90° 180° 270°

Two identical blocks are attached to the same massless rope, which is strung around two massless, frictionless pulleys. A massless scale is connected to the same rope and measures the tension in the rope. The two identical blocks are released from the rest. The experiment is then repeated with two new blocks, with masses m1 and m2. When they are released from rest, the system remains at rest, and the scale measures the same tension as in the previous experiment. Find m1 and m2 in terms of m.

Answers

Answer:

The value of mass 1, m1= 6/5m

The value of mass 2, m2= 3/5m

Explanation:

case 1:

here tension and the acceleration will be:

for m1;

mg-T=ma2mg - 2T = 2ma  .....1.

for m2:

2T-mg = ma/2 ..... 2.

adding the both equations,

2mg - 2T + 2T-mg = 2ma + ma/2

a = 2/5 g

putting the value of a into the equation 1.

mg - T = m* (2/5)g

T = 3/5 ( mg )

now

case 2:

The two identical blocks are released from the rest, the tension remains the same as the case 1.

so,

for m1:

2T-m2g=0

for m2:

2m2g - 2T =0

adding both equations we get,

2T-m2g + 2m2g - 2T = 0

m2 = m1 / 2

T = m1*g / 2

here we know that

T (case1) = T (case2)

3/5 ( mg ) = m1*g / 2

m1 = 6/5 m

hence

m2 = 3/5 m

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