In a certain standing wave pattern. The distance from one node to the next is 2.0 m. What is the wavelength of one of the standing waves?

Answers

Answer 1

Given that the distance between 2 consecutive nodes is 2m

We have to find the wavelength

\(\lambda\)

The distance between 2 nodes is half the wavelength,

\(\begin{gathered} \frac{\lambda}{2}=2 \\ \lambda=\text{ 4 m} \end{gathered}\)

Thus, the wavelength of the standing wave is 4 m.


Related Questions

Type your response in the box.
Different kinds of substances have different properties. Compare and contrast the electrical properties of salts, acid , metals

Answers

Answer:

salts do not conduct electricity. unless u try to dissociate its ions,it cannot.

metals are good conductors of electricity.

acids also conduct electricity if you dissociate them into ions.

A continental polar air mass forms in
a. the Pacific Ocean.
b. northern Canada.
c.
the Gulf of Mexico.
the desert Southwest.
d.
Please select the best answer from the choices provided
А
B
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my uq xbbbnxnjjxjxusjhhhwhhhnn he c x. Yes suhsjjdhhehy yes eirui
M I was going ask m
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Answers

Answer:

B. Northern Canada

Explanation:

A continental polar air mass can form over the land during the winter months. In the Northern Hemisphere, it originates in northern Canada or Alaska. As it moves southward, it brings dry weather conditions to the United States. Temperature and humidity levels are both low. Hope this helps :)

1. A charge of 6.4 C passes through a cross-sectional area or conductor in 2s. How much charge will pass through a cross sectional area of the conductor in 1 min?​

Answers

The amount of charge that will pass through the cross-sectional area of the conductor in 1 min is 192 C.

What is the  amount of charge?

We can use the formula Q = I * t,

where;

Q is the amount of charge, I is the current, and t is the time.

Given that a charge of 6.4 C passes through a cross-sectional area of the conductor in 2 s, we can find the current using the formula:

I = Q / t = 6.4 C / 2 s = 3.2 A

So, the current through the conductor is 3.2 A.

To find the amount of charge that will pass through the cross-sectional area of the conductor in 1 min (60 s), we can use the same formula:

Q = I * t = 3.2 A * 60 s = 192 C

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The speed of sound is measured to be 340 m/s on a certain day.
What is this in Kilometers per hour?? s/km/h=


Please help and explain how to do these types of problems in very confused!!!

Answers

Answer: 1,224 km/h

Explanation:

To do this, we pick the first unit and convert
Picking m first and converting to km:
Since we're converting from a non-prefix to a prefix, we divide the value by the prefix were taking it to. In this case, kilo = 10³ which means we're going to divide our value by 1000 to convert it from m to km
340 m/s ÷ 1000 = 0.34 km/s
Now, let's convert our seconds to hour:
We'll need to calculate how many hours is equivalent to one second first;
1 hr = 60×60 seconds
X hr = 1 second
*Cross multiply*
1 × 1 = X × 60 × 60
1 = 3,600 X
X = 1 / 3,600
X = 2.778×10⁻⁴ hour
So, in the place of "1 Second", we're going to be inserting 2.778×10⁻⁴ hour instead
0.34 km / s = 0.34 km / 2.778×10⁻⁴ hour
(0.34 / 2.778×10⁻⁴) km/hour
1,224 km/h.
340 m/s = 1,224 km/h

Pls quickly brainliest to the first to anwser

Pls quickly brainliest to the first to anwser

Answers

Answer:

8m/s^2

Explanation:

hope it helps........

Pls quickly brainliest to the first to anwser

Explanation:

you're supposed to know the formula of acceleration which is velocity of a time then you can solve the question

Mars Rover When the Mars rover was deployed on the surface of Mars in July 1997, radio signals took about 12 minmin to travel from Earth to the rover.
How far was Mars from Earth at that time?

Answers

Answer:

s = 2.16 x 10¹¹ m

Explanation:

Since, the waves travelling from Earth to the Mars rover are electromagnetic. Therefore, there speed must be equal to the speed of light. So, from the equation given below:

s = vt

where,

s = the distance between Earth and Mars = ?

v = speed of the wave = speed of light = 3 x 10⁸ m/s

t = time taken by the radio signals to reach the rover from Earth

t = (12 min)(60 s/1 min) = 720 s

Therefore,

s = (3 x 10⁸ m/s)(720 s)

s = 2.16 x 10¹¹ m

A sports car accelerates at a constant rate from rest to a speed of 90 km/hr in 8 s. What is its acceleration?

3.13 m/s2

4.22 m/s2

5.31 m/s2

6.67 m/s2

none of the above

Answers

First convert 90km/hr to m/s.

Initiate velocity = 0m/s (car was at rest)

Final velocity is 25m/s (90km/hr converted)

25m/s - 0m/s / 8s = 3.125 m/s^s

Therefore the answer is option A (3.13m/s^2)

The Gift of the Magi
by O Henry

After Della counted her money she flopped down on the couch and began to scream and cry. Sobs, sniffles and smiles seem to be a progression from sadness to satisfaction.

Read the passage closely and answer the following question:

On reflection, what did Della (Mrs. James Dillingham Young) decide that life was made up of?

Answers

On reflection, what did Della (Mrs. James Dillingham Young) decide that life was made up of happiness.

In the context of mental or emotional states, happiness refers to good or pleasant emotions ranging from satisfaction to profound delight. Life satisfaction, well-being, subjective well-being, flourishing, and eudaimonia are some of the other types.

Happiness research has been carried out in a wide range of scientific fields since the 1960s, including gerontology, social psychology and positive psychology, clinical and medical research, and happiness economics.

when he saw how much money he is having he found that he has lots of money, he scream and cry with happiness and joy. Then he decided that the life is made up of happiness.

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220 g of water at 90 °C is added to a certain unknown mass of water at 10 °C The final temperature of the mixture is 33 °C. Calculate the unknown mass of the water.​

Answers

The unknown mass of water is 545.21

What is mass?

mass is a quantitative measure of inertia , a fundamental property of all matter .

mass depends on the number and kind of atoms.

It is a dimensionaless quantity.

Sol-

As per the given question

220 g of water added to 90°c

Mass of water=10°C

Tempreture of the mixture =33°C

Unknown mass

m1 (n-t)= m2(t-b)

220(90-33)=m2(33-10)

:- (we can also do multiple of cp but as both side of the cp fluid unit  are same so it's not needed)

220×57=m2 (23)

m2= 220×57/23

m2 =545.21

Thus the unknown mass of water is 545.21 .

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how is newtons first law of motion related to the concept of inertia?​

Answers

The focus of Lesson 1 is Newton's first law of motion - sometimes referred to as the law of inertia. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Hope this helps :)

. Acylinder contains 1 mole of oxygen at
a temperature of 27 °C. The cylinder
is provided with a frictionless piston
which maintains a constant pressure
of 1 atm on the gas. The gas is heated
until its temperature rises to 127 °C.
(a) How much work is done by the
piston in the process?
(b) What is the increase in internal
energy of the gas?
(c) How much heat was supplied
to the gas?
(C = 7.03 calmol-¹°C¯¹;
R = 1.99 calmol-¹°C-¹;
1cal = 4.184 J)

Answers

a}The work is done by the piston in the process is 199 cal.

b) The increase in internal energy of the gas is  703 cal

c) The heat was supplied to the gas is  3771 J

(a) To calculate the work done by the piston, we can use the formula:

Work = P * ΔV

Where P is the constant pressure and ΔV is the change in volume. Since the pressure is constant, the work done is given by:

Work = P * (\(V_2 - V_1\))

Since the amount of gas is constant (1 mole), we can use the ideal gas law to calculate the initial and final volumes:

PV = nRT

\(V_1 = (nRT_1) / P_1\)

\(V_2 = (nRT_2) / P_2\)

Here, n is the number of moles (1 mole), R is the gas constant (1.99 cal/mol·°C), T1 is the initial temperature (27 °C + 273 = 300 K), T2 is the final temperature (127 °C + 273 = 400 K), and P1 and P2 are the initial and final pressures, respectively (both 1 atm).

Substituting the values into the equation, we have:

V1 = (1 mol * 1.99 cal/mol·°C * 300 K) / (1 atm) ≈ 597 cal

V2 = (1 mol * 1.99 cal/mol·°C * 400 K) / (1 atm) ≈ 796 cal

Therefore, the work done by the piston is:

Work = 1 atm * (796 cal - 597 cal) = 199 cal

(b) The increase in internal energy of the gas can be calculated using the equation:

ΔU = n * C * ΔT

Where ΔU is the change in internal energy, n is the number of moles (1 mole), C is the molar heat capacity (7.03 cal/mol·°C), and ΔT is the change in temperature (127 °C - 27 °C = 100 °C).

Substituting the values into the equation, we have:

ΔU = 1 mol * 7.03 cal/mol·°C * 100 °C = 703 cal

(c) The heat supplied to the gas can be calculated using the equation:

Q = ΔU + Work

Substituting the values calculated in parts (a) and (b), we have:

Q = 703 cal + 199 cal = 902 cal

Since 1 cal = 4.184 J, the heat supplied to the gas is:

Q = 902 cal * 4.184 J/cal ≈ 3771 J

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Could someone explain to me how to got the answer B, thank you very much​

Could someone explain to me how to got the answer B, thank you very much

Answers

Answer:

since -6 lasted for 5 seconds, multiplying both would result in -30

3 lasted for 10 seconds, so multiplying both would give +30

average = ( 30 + (-30) ) / 2

30 -30 is already equal to zero, so the answer should be 0

the earth's moon has a gravitational field strength of about 1.6 n/kg near its surface. the moon has a mass of 7.35x10^22 kg. what is the radius of the moon? please show work.​

Answers

Answer:

1737 kilometers

4. Calculate the total resistance of the circuit if R1=4 Ω, R2=30 Ω, R3=10Ω, R4=5Ω Determine the current strength if the circuit is connected to a voltage source with a voltage of 56 V

4. Calculate the total resistance of the circuit if R1=4 , R2=30 , R3=10, R4=5 Determine the current

Answers

The total resistance of the circuit is 49 Ω. The current strength in the circuit, when connected to a voltage source of 56 V, is approximately 1.14 A.

To calculate the total resistance of the circuit, we need to determine the equivalent resistance of the resistors connected in a series.

Given:

R1 = 4 Ω

R2 = 30 Ω

R3 = 10 Ω

R4 = 5 Ω

Calculate the equivalent resistance (RT) of R1 and R2, as they are connected in series:

RT1-2 = R1 + R2

RT1-2 = 4 Ω + 30 Ω

RT1-2 = 34 Ω

Calculate the equivalent resistance (RTotal) of RT1-2 and R3, as they are connected in parallel:

1/RTotal = 1/RT1-2 + 1/R3

1/RTotal = 1/34 Ω + 1/10 Ω

1/RTotal = (10 + 34) / (34 * 10) Ω

1/RTotal = 44 / 340 Ω

1/RTotal ≈ 0.1294 Ω

RTotal ≈ 1 / 0.1294 Ω

RTotal ≈ 7.74 Ω

Calculate the equivalent resistance (RTotalCircuit) of RTotal and R4, as they are connected in series:

RTotalCircuit = RTotal + R4

RTotalCircuit = 7.74 Ω + 5 Ω

RTotalCircuit ≈ 12.74 Ω

Therefore, the total resistance of the circuit is approximately 12.74 Ω.

To determine the current strength (I) when connected to a voltage source of 56 V, we can use Ohm's Law:

I = V / RTotalCircuit

I = 56 V / 12.74 Ω

I ≈ 4.39 A

Therefore, the current strength in the circuit, when connected to a voltage source of 56 V, is approximately 4.39 A (or 1.14 A, considering significant figures).

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What force pushes the plane upwards

Answers

Answer: The force that pushes a plane upwards is the lift generated by the wings as the plane moves through the air. The lift force is created by the difference in air pressure above and below the wings, which creates an upward force that opposes the weight of the plane.

A 2.3 kg block on a frictionless incline of 27 degrees. The acceleration of gravity is 9.8 m/s2. Answer in units of ms. What is the normal force on the block...

Answers

The normal force on the block is approximately 20.05 N.

What is force acting on a body?

Force describes the interaction between objects or between an object and its environment. It causes a change in the motion of the body it acts upon.

The normal force, which counteracts the force of gravity dragging the block downward, is the force generated by the slope acting perpendicular to its surface. As the incline has no friction, there is no force acting parallel to its surface.

To ascertain the parts of the force of gravity pulling on the block, we can apply trigonometry. There are two parts to the force of gravity: one that is parallel to the incline's surface and the other that is perpendicular to it. The weight of the block, mg, where m is its mass and g is its gravitational acceleration, is equal to the component of gravity perpendicular to the inclination. mg sin θ, where is the angle of the incline, is the component of gravity that is parallel to the incline.

To calculate the acceleration of the block moving down the incline, we can apply Newton's second law, F = ma. The component of gravity parallel to the inclination, or mg sin θ, represents the net force exerted on the block. As a result, we have:

\(mg sin(theta) = ma\)

To solve for a, we obtain:

\(a = g sin(theta)\)

Substituting the given values, we get:

\(a = 9.8 m/s^2 * sin(27°)\) ≈ \(4.69 m/s^2\)

Now that we know the normal force acting on the block, we can use Newton's second law once more. The component of gravity's force perpendicular to the incline is equal in magnitude to the normal force and moves in the opposite direction. As a result, we have:

\(mg cos(theta) = N\)

Inputting the values provided yields:

\(N = 2.3 kg * 9.8 m/s^2 * cos(27°)\) ≈ \(20.05 N\)

Therefore, the normal force on the block is approximately 20.05 N.

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Analyze the data on the plot below. Determine the speed of the hawksbill sea turtle during each interval listed below.

HELP PLEASE!!!

Analyze the data on the plot below. Determine the speed of the hawksbill sea turtle during each interval

Answers

Answer:

Day 0 to day 2: 5km/day

Day 2 to day 3: 2km/day

Explanation:

Day 0 to day 2: 10/2 = 5

Day 2 to day 3: 12 - 10 = 2

To Calculate:

The x-axis, or the days from 0 to 6, line up with the y-axis, or the distance from 0 to 24.  The point in the graph means that on that day, the turtle traveled that much distance.  For example, on the third point (2, 10), the day is 2 and the distance is 10.  To find the distance over multiple days, catalog the days in your mind and look for the points.  Then, find the difference.  For example, from day 2 (2, 10) to day 5 (5, 18), this would look like: 5 - 2 = 3, and 18 - 10 = 8, so this means that over 3 days, the turtle traveled 8 km.

a rock falls off a 25 m high building. after 2s, how fast is it moving?

Answers

Answer:

99 MPH

Explanation:

Because when something falls gravity pulls it down while it is coming down making it faster.

Answer:

5m high

Explanation:

Because it has fallen off

Can someone help me with my physics sheet? I don’t understand it.. thank you

Can someone help me with my physics sheet? I dont understand it.. thank you

Answers

Acceleration of the skydiver during the free fall is 4.13 m/s².

1) Mass of the skydiver, m = 83 kg

Weight, W = mg = 83 x 9.8

W = 813.4 N

Free fall acceleration is the acceleration that a body travelling in free fall experiences due to only the gravitational pull of the earth. This is the acceleration brought on by gravity.

Since there is no air resistance, the acceleration of the skydiver during the free fall is the acceleration due to gravity, g.

Freebody diagram is given in Fig.1.

2) Mass of the skydiver, m = 78 kg

Air resistance acting on him, F' = 470 N

mg - 470 = ma

813.4 - 470 = ma

a = 343.4/83

a = 4.13 m/s²

Freebody diagram is given in fig.2.

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Can someone help me with my physics sheet? I dont understand it.. thank you

A water tank measures 2 m X 4m x 5 m.
What mass of water will it contain?

Answers

Answer:

1 L = 1000 cm^3

1 m^3 = 1000 L = 10^6 cm^3

1 m^3 = 10^6 g = 10^3 kg  density of water

M = Density * Volume

V = 2 * 4 * 5 = 40 m^3

M = 10^3 kg / m^3 * 40 m^3 = 4.0 * 10^4 kg

Where is the near point of an eye for which a spectacle lens of power +2 D is prescribed for reading purpose?

Answers

The near point of a human eye is about a distance of 25 cm.

The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.

This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.

The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.

In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.

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A child blows a leaf from rest straight up in the air. the leaf has a constant upward acceleration of magnitude 1.0 m by s square. how much time does it take the leaf to displace 1.0m upwards?

Answers

Answer:

√2

Explanation:

From the question, we're given that the

Acceleration of the leaf is 1 m/s²

Change in displacement of the leaf is 1 m/s.

Again, from the question, we can tell that the initial velocity u = 0, since the object starts at rest

Now, to solve this, we don't the equation of motion to ur

S = ut + 1/2at², substituting the whole parameters, we then have

1 = 0 * t + 1/2 * 1 * t²

1 = 1/2 * t²

t²/2 = 1

t² = 2

t = √2 seconds

Therefore the time it takes the leaf to dislodge is 2 seconds

If a force of 20kn acts on a circular rod of a diameter 10mm, calculate the stress of the rod

Answers

σ = F/A = F/ (πD²/4) = 20000 / (π0.10²/4) = 2.55 MN/m²

Calculate the energy changes corresponding to the transitions of the hydrogen atom. From n = 3 to n = ∞.

Answers

Answer: ΔE = -2.42 × 10^-19 J

Explanation:

The energy of an electron in the nth energy level of a hydrogen atom is given by the following formula:

E = (-2.18 × 10^-18 J) × (Z^2 / n^2)

where Z is the atomic number (1 for hydrogen) and n is the principal quantum number.

The energy change corresponding to a transition from energy level n1 to energy level n2 is given by the formula:

ΔE = E2 - E1 = (-2.18 × 10^-18 J) × Z^2 (1/n2^2 - 1/n1^2)

Given that the electron transitions from n = 3 to n = ∞, we can substitute n1 = 3 and n2 = ∞ in the above formula to obtain:

ΔE = (-2.18 × 10^-18 J) × 1^2 (1/∞^2 - 1/3^2)

ΔE = (-2.18 × 10^-18 J) × (1/9)

ΔE = -2.42 × 10^-19 J

Therefore, the energy change corresponding to the transition of the hydrogen atom from n = 3 to n = ∞ is -2.42 × 10^-19 J.

The energy change for the transition of a hydrogen atom from n = 3 to n = ∞ is 1.511 eV. This transition represents the electron moving to an energy level where it is essentially unbound from the nucleus, resulting in an energy increase.

The energy changes corresponding to the transitions of a hydrogen atom can be calculated using the formula for energy levels in hydrogen:

E = -13.6 eV * (Z² / n²)

Where:

E is the energy of the electron in electronvolts (eV).

Z is the atomic number, which is 1 for hydrogen.

n is the principal quantum number, representing the energy level.

Given the transition from n = 3 to n = ∞, we can calculate the energy change:

Calculate the initial energy (n = 3):

Einitial = -13.6 eV * (1² / 3²) = -13.6 eV * (1/9) = -1.511 eV

Calculate the final energy (n = ∞):

Efinal = -13.6 eV * (1² / ∞²)

In the final state, as n approaches infinity, the energy becomes zero.

Calculate the energy change (ΔE):

ΔE = Efinal - Einitial = 0 - (-1.511 eV) = 1.511 eV

So, the energy change corresponding to the transition of a hydrogen atom from n = 3 to n = ∞ is 1.511 electronvolts (eV).

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how liquid state is change into solid state?

Answers

Answer:

The change from the liquid state to the solid state is called freezing. As the liquid cools, it loses thermal energy. ... For example, solid water melts at 0°C and liquid water freezes at 0°C. During freezing, the temperature of a substance remains constant while the particles in the liquid form a crystalline solid.

Explanation:

When the liquid state freezes, it changes into solid state.

Example,

When you freeze water, it changes into ice, ice is a solid.

Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph.Can you draw the shapes for each type ?

Answers

Explanation:

Yes, there are differences in the shapes of position-time graphs for uniform acceleration and uniform deceleration in different directions. Let's consider each case separately:\(\hrulefill\)

(1) - Uniform acceleration towards the positive direction:

In this case, the object is moving in the positive direction with a constant acceleration. The displacement-time graph will typically be a curve that starts from an initial position and shows a steady increase in displacement over time. The shape of the graph will depend on the specific acceleration value.

(2) - Uniform acceleration towards the negative direction:

In this case, the object is moving in the negative direction with a constant acceleration. The displacement-time graph will also be a curve, but it will show a steady decrease in displacement over time.

(3) - Uniform deceleration towards the positive direction:

In this case, the object is initially moving in the positive direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a positive slope and gradually levels off.

(4) - Uniform deceleration towards the negative direction:

In this case, the object is initially moving in the negative direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a negative slope and gradually levels off.

Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform

A student is using two circuits to investigate power consumption. She connects two identical light bulbs in series in one circuit and in parallel in the second circuit. What should she measure to calculate which configuration uses more power?
Responses
A The resistance of the bulbs and the potential difference of the battery.The resistance of the bulbs and the potential difference of the battery.
B The current flowing into each bulb and the potential difference across each bulb.The current flowing into each bulb and the potential difference across each bulb.
C The current flowing out of the battery and the resistance of each bulb.The current flowing out of the battery and the resistance of each bulb.
D The potential difference of the battery and the resistance of the battery.

Answers

The potential difference across the each bulb and the current entering each bulb.

What occurs if you connect two light bulbs in series?

Each bulb in a straightforward parallel circuit receives the entire battery power. This is explains why the parallel circuit's lights will shine stronger than the series circuit's. The parallel circuit also has the benefit of maintaining an electricity even if one loop is disconnected.

When are two identical bulbs linked in both series and parallel?

The same brightness is produced when two identical bulbs are linked in parallel as it is when they are connected in a series, which is why.

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What are the four most important characteristics of an electric circuit?

Answers

Answer:

an energy source (AC or DC), a conductor (wire), an electrical load (device), and at least one controller (switch).

Explanation:

mark as brainliest please

The 4 most important characteristics of an electric circuit are discussed below.

We have a electric circuit.

We have to mention its 4 important characteristics.

What is an Electric circuit ?

Electrical circuit is a closed path which acts as a medium for the flow of current when there is a potential difference between two points in the path.

According to the question -

The important characteristics of electric circuit are -

It must contain at least one source of energy.It is a combination of both active and passive elements.It always exist in the form of closed loop for regular flow of current.The flow of electrons take place from negative terminal to positive terminal

Hence, the 4 most important characteristics of an electric circuit are mentioned above.

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quá trình nào entropi của hệ không đổi

Answers

Answer:

I don speak communism. Could you answer in English?

Explanation:

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.0900 N when their center-to-center separation is 48.5 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0528 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)

Answers

Answer:

(a)\(-0.75\mu\) Coulomb

(b) \(3.1 \mu\) Coulomb

Explanation:

Let \(q_1\) be the positive charge, in Coulumb, on the one sphere and \(q_2\) be the negative charge, in Coulumb, on the other sphere, where \(q_{1} > q_2\).

The center-to-center distance between the spheres is,

\(d=48.5 cm=0.485 m\).

From Coulomb's law, the magnitude of the force, \(F\), between two point charges having magnitudes \(q_1 \& q_2\), separated by distance,\(d\), is

\(F=\frac {1}{4\pi\epsilon_0}\frac{q_1q_2}{d^2}\;\cdots(i)\)

where, \(\epsilon_0\) is the permittivity of free space and

\(\frac {1}{4\pi\epsilon_0}=9\times 10^9\) in SI units.

So, using equation (i), the attractive force between both the spheres is

\(9\times 10^9\frac{q_1q_2}{(0.485)^2}=0.09\)

\(\Rightarrow q_1q_2=2.35225\times 10^{-12}\)

\(\Rightarrow q_1q_2= 2.35225 \mu^2\) [as \(\mu=10^{-6\)]

\(\Rightarrow q_2=\frac{\mu^2 2.35225}{q_1}\;\cdots (ii)\)

When both the sphere is connected by a thin conducting wire, then redistribution of charge take place and net charge , on combining both the spheres, is \(q_1-q_2\) ( as \(q_1>q_2\)).

Finally, the charge density on both the sphere will be the same.

Given that, both the sphere are identical, so, the quantity of charges on of charged on both the conducting spheres, after removing the conduction wire, will be the same.

So, the net charge on the individual sphere is

\(\frac {q_1-q_2}{2}\) which is positive in nature.

From equation (i), the repulsive force between the spheres is

\(9\times 10^9\times \frac{(q_1-q_2)(q_1-q_2)}{4\times 0.485^2}=0.0528\)

\(\Rightarrow (q_1-q_2)^2=5.52\mu^2\) [ as \(\mu=10^{-6}\)]

\(\Rightarrow q_1-q_2=2.35\mu\;\cdots(iii)\)

\(\Rightarrow q_1 - \frac{\mu^2 2.35225}{q_1}= 2.35\mu\) [using equation (ii)]

\(\Rightarrow q_1^2- 2.35\mu q_1- 2.35225\mu^2=0\)

\(\Rightarrow q_1=3.1 \mu\) or \(-0.76 \mu\)

Taking positive sign as \(q_1\) is the magnitude of charge.

So, for \(q1=3.1 \mu\)

\(q_2=3.1- \mu- 2.35\mu=0.75 \mu\) [from equation (iii)]

Hence,

(a) Negative charge on one of the spheres is,

\(q_2=-0.75 \mu\) Coulomb.

(b) Positive charge on the other sphere is,

\(q_1=3.1 \mu\) Coulomb.

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