A ring with an 18mm diameter falls off a scientist's finger into the solenoid in the lab. The solenoid is 25 cm long, 5.0 cm in diameter and has 1500 turns. When turned on, the current in the solenoid is increases linearly to 20 A in 1 second. What is the induced emf in the ring?
a) 2.0 x 10-5 v
b) 3.8 x 10-5 v
c) 1.2 x 10-3 v
d) 1.9 x 10-4 v

Answers

Answer 1

Answer:

the answer should be b) 3.8 x 10-5 v


Related Questions

Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said

Answers

Answer:

D

Explanation:

Anyone could be leaning forward toward the speaker but be distracted and I believe if you're paying attention to the speaker, you would ask questions to make sure you're understanding what they are speaking

Answer:

A

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Describe how the words Science and optics would appear when viewed in a plane mirror?

Answers

Answer:

Lateral inversion will occur in a plane mirror.

Explanation:

When words are displayed in a plane or flat mirror, the result is that if the words are displayed left, they change to right and if they were normally displayed right, they change to left. This phenomenon is known as lateral inversion. So, this will apply to the words, Science and optics. Only the sides will be interchanged.

A plane mirror reflects light, therefore, the image that is produced by it remains the same size. The image produced will not appear upside down. Only the sides will be interchanged.

How can I solve the following statement?

What is the magnitude of the electric field at a point midway between a −8.3μC and a +7.8μC charge 9.2cm apart? Assume no other charges are nearby.

Answers

Answer:

The net electric field at the midpoint is 6.85 x 10^7 N/C.

Explanation:

q = − 8.3 μC

q' = + 7.8 μC

d =  9.2 cm

d/2 = 4.6 cm

The electric field due to the charge q at midpoint is

[tex]E = \frac{k q}{r^2}\\\\E = \frac{9\times 10^9\times 8.3\times 10^{-6}}{0.046^2}\\\\E = 3.53\times 10^7 N/C[/tex] leftwards

The electric field due to the charge q' at midpoint is

[tex]E' = \frac{k q}{r^2}\\\\E' = \frac{9\times 10^9\times 7.8\times 10^{-6}}{0.046^2}\\\\E' = 3.32\times 10^7 N/C[/tex]

The resultant electric field at mid point is

E'' = E + E' = (3.53 + 3.32) x 10^7 = 6.85 x 10^7 N/C

The spaceship Enterprise 1 is moving directly away from earth at a velocity that an earth-based observer measures to be 0.66c. A sister ship, Enterprise 2, is ahead of Enterprise 1 and is also moving directly away from earth along the same line. The velocity of Enterprise 2 relative to Enterprise 1 is 0.34c. What is the velocity of Enterprise 2, as measured by the earth-based observer

Answers

Answer:

The answer is "0.82 c".

Explanation:

Given:

Spacecraft speed 1 is [tex]u = + 0.66 \ c[/tex]

Space velocity 2 relative to spacecraft 1 is [tex]v = + 0.34\ c[/tex]

The spacecraft velocity 2 measured by the Earth observation

   [tex]\to u' = \frac{u +v}{1 + ( \frac{uv}{c^2})}[/tex]

            [tex]= \frac{0.66 \ c +0.34\ c}{ 1+ (\frac{0.66\ c \times 0.33\ c }{c^2})}\\\\ = \frac{1 \ c }{ 1+ (\frac{0.2178\ c^2 }{c^2})}\\\\ = \frac{1 \ c }{ 1+ (0.2178 )}\\\\ = \frac{1 \ c }{ 1.2178 }\\\\=0.82\ c[/tex]

A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 ksi. The bar is subjected to a steady torsional stress of 15 kpsi and an alternating bending stress of 25 ksi. Find the factor of safety guarding against a static failure, and either the factor of safety guarding against a fatigue failure or the expected life of the part. For the fatigue analysis use Modified Goodman criterion.

Answers

Answer:

The correct solution is:

(a) 1.66

(b) 1.05

Explanation:

Given:

Bending stress,

[tex]\sigma_b = 25 \ kpsi[/tex]

Torsional stress,

[tex]\tau= 15 \ kpsi[/tex]

Yield stress of steel bar,

[tex]\delta_y = 60 \ kpsi[/tex]

As we know,

⇒ [tex]\sigma_{max}^' \ = \sqrt{\sigma_b^2 + 3 \gamma^2}[/tex]

        [tex]= \sqrt{(25)^2+3(15)^2}[/tex]

        [tex]=36.055 \ kpsi[/tex]

(a)

The factor of safety against static failure will be:

⇒ [tex]\eta_y = \frac{\delta_y}{\sigma_{max}^'}[/tex]

By putting the values, we get

        [tex]=\frac{60}{36.055}[/tex]

        [tex]=1.66[/tex]

(b)

According to the Goodman line failure,

[tex]\sigma_a = \sigma_b = 25 \ kpsi[/tex]

[tex]S_e = 40 \ kpsi[/tex]

[tex]\sigma_m = \sqrt{3} \tau[/tex]

     [tex]=\sqrt{3}\times 15[/tex]

     [tex]=26 \ kpsi[/tex]

[tex]Sut = 80 \ kpsi[/tex]

⇒ [tex]\frac{\sigma_a}{S_e} +\frac{\sigma_m}{Sut} =\frac{1}{\eta_y}[/tex]

      [tex]\frac{25}{40}+\frac{26}{80}=\frac{1}{\eta_y}[/tex]

              [tex]\eta_y = 1.05[/tex]

12. A concave lens has a focal length of 10 cm. An object 2.5 cm high is placed 30 cm from the lens. Determine the position and size of the image. (3)​

Answers

Answer:

I think 9.5

Explanation:

............

What is the volume of a metal block 3cm long by 2cm wide by 4cm high? What would be the volume of a block twice as long, wide, and high?

Answers

Answer:

Volume of a metal block = 24 cm^3

Volume of a block twice as long, wide and high = 192 cm^3

Explanation:

Volume of a block is measured in l*w*h and in the first block, the sides are 3, 2 and 4 and 3*2*4 = 24

Second block, just double each of the lengths to get 6*4*8 = 192

Help! xoxo thank you

Answers

Like charges repel and opposite charges attract.

what are the two main types of sound like soundwave​

Answers

Answer:

acoustic energy and mechanical energy

Explanation:

each type of sounds has to be tackled in their own way.

A lightning bolt has a current of 56,000 A and lasts for 80 x 10-6 seconds (80 μs). How much charge (in Coulombs) has flowed in this bolt?

Answers

Answer:

A cloud can discharge as much as 20 coulombs in a lightning bolt.

if C is the vector sum of A and B C=A+B what must be true about directions and magnitude of A and B if C=A+B? what must be true about the directions and magnitude of A and B if C=0​

Answers

The vector sum is the algebraic sum if the two vectors have the same direction.

The sum vector is zero if the two vectors have the same magnitude and opposite direction

Vector addition is a process that can be performed graphically using the parallelogram method, see  attached, where the second vector is placed at the tip of the first and the vector sum goes from the origin of the first vector to the tip of the second.

There are two special cases where the vector sum can be reduced to the algebraic sum if the vectors are parallel

case 1. if the two vectors are parallel, the sum vector has the magnitude of the sum of the magnitudes of each vector

case 2. If the two vectors are antiparallel and the magnitude of the two vectors is the same, the sum gives zero.

In summary in the sum of vectors If the vectors are parallel it is reduced to the algebraic sum, also in the case of equal magnitude and opposite direction the sum is the null vector

a) Magnitudes: [tex]\| \vec A\| \ge 0[/tex], [tex]\|\vec B\| \ge 0[/tex], [tex]\|\vec C\| \ge 0[/tex]; Directions: [tex]\theta_{A} \in (-\infty, +\infty)[/tex] for [tex]\|\vec A\|\ne 0[/tex]. Undefined for [tex]\|\vec A\| = 0[/tex], [tex]\theta_{B} \in (-\infty, +\infty)[/tex] for [tex]\|\vec B\|\ne 0[/tex]. Undefined for [tex]\|\vec B\| = 0[/tex], [tex]\theta_{C} \in (-\infty, +\infty)[/tex] for [tex]\|\vec C\|\ne 0[/tex]. Undefined for [tex]\|\vec C\| = 0[/tex].

b) Magnitudes: [tex]\|\vec A\| \ge 0[/tex], [tex]\|\vec B\| \ge 0[/tex], [tex]\|\vec C\| = 0[/tex]; Directions: [tex]|\theta_{A}-\theta_{B}| = 180^{\circ}[/tex], [tex]\theta_{C}[/tex] is undefined.

a) Let suppose that [tex]\vec A \ne \vec O[/tex], [tex]\vec B \ne \vec O[/tex] and [tex]\vec C \ne \vec O[/tex], where [tex]\vec O[/tex] is known as Vector Zero. By definitions of Dot Product and Inverse Trigonometric Functions we derive expression for the magnitude and directions of [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex]:

Magnitude ([tex]\vec A[/tex])

[tex]\|\vec A\| = \sqrt{\vec A\,\bullet\,\vec A}[/tex]

[tex]\| \vec A\| \ge 0[/tex]

Magnitude ([tex]\vec B[/tex])

[tex]\|\vec B\| = \sqrt{\vec B\,\bullet\,\vec B}[/tex]

[tex]\|\vec B\| \ge 0[/tex]

Magnitude ([tex]\vec C[/tex])

[tex]\|\vec C\| = \sqrt{\vec C\,\bullet \,\vec C}[/tex]

[tex]\|\vec C\| \ge 0[/tex]

Direction ([tex]\vec A[/tex])

[tex]\vec A \,\bullet \,\vec u = \|\vec A\|\cdot \|u\|\cdot \cos \theta_{A}[/tex]

[tex]\theta_{A} = \cos^{-1} \frac{\vec A\,\bullet\,\vec u}{\|\vec A\|\cdot \|u\|}[/tex]

[tex]\theta_{A} = \cos^{-1} \frac{\vec A\,\bullet\,\vec u}{\|\vec A\|}[/tex]

[tex]\theta_{A} \in (-\infty, +\infty)[/tex] for [tex]\|\vec A\|\ne 0[/tex]. Undefined for [tex]\|\vec A\| = 0[/tex].

Direction ([tex]\vec B[/tex])

[tex]\vec B\,\bullet \, \vec u = \|\vec B\|\cdot \|\vec u\| \cdot \cos \theta_{B}[/tex]

[tex]\theta_{B} = \cos^{-1} \frac{\vec B\,\bullet\,\vec u}{\|\vec B\|\cdot \|\vec u\|}[/tex]

[tex]\theta_{B} = \cos^{-1} \frac{\vec B\,\bullet\,\vec u}{\|\vec B\|}[/tex]

[tex]\theta_{B} \in (-\infty, +\infty)[/tex] for [tex]\|\vec B\|\ne 0[/tex]. Undefined for [tex]\|\vec B\| = 0[/tex].

Direction ([tex]\vec C[/tex])

[tex]\vec C \,\bullet\,\vec u = \|\vec C\|\cdot\|\vec u\|\cdot \cos \theta_{C}[/tex]

[tex]\theta_{C} = \cos^{-1}\frac{\vec C\,\bullet\,\vec u}{\|\vec C\|\cdot\|\vec u\|}[/tex]

[tex]\theta_{C} = \cos^{-1} \frac{\vec C\,\bullet\,\vec u}{\|\vec C\|}[/tex]

[tex]\theta_{C} \in (-\infty, +\infty)[/tex] for [tex]\|\vec C\|\ne 0[/tex]. Undefined for [tex]\|\vec C\| = 0[/tex].

Please notice that [tex]\vec u[/tex] is the Vector Unit.

b) Let suppose that [tex]\vec A \ne \vec O[/tex] and [tex]\vec B \ne \vec O[/tex] and [tex]\vec C = \vec O[/tex]. Hence, [tex]\vec A = -\vec B[/tex]. In other words, we find that both vectors are antiparallel to each other, that is, that angle between [tex]\vec A[/tex] and [tex]\vec B[/tex] is 180°. From a) we understand that [tex]\|\vec A\| \ge 0[/tex], [tex]\|\vec B\| \ge 0[/tex], but [tex]\|\vec C\| = 0[/tex].

Then, we have the following conclusions:

Magnitude ([tex]\vec A[/tex])

[tex]\|\vec A\| \ge 0[/tex]

Magnitude ([tex]\vec B[/tex])

[tex]\|\vec B\| \ge 0[/tex]

Magnitude ([tex]\vec C[/tex])

[tex]\|\vec C\| = 0[/tex]

Directions ([tex]\vec A[/tex], [tex]\vec B[/tex]):

[tex]|\theta_{A}-\theta_{B}| = 180^{\circ}[/tex]

Direction ([tex]\vec C[/tex]):

Undefined

An object moving with initial velocity 10 m/s is subjected to a uniform acceleration of 8 m/s ^² . The displacement in the next 2 s is: (a) 0m (b) 36 m (c) 16 m (d) 4 m​

Answers

365 Everyday Value, Organic Creamy Peanut Butter. Net Carbs: 4 grams per serving. ...
Classic Peanut Butter by Justin's. Net Carbs: 5 grams. ...

Choose the appropriate explanation how such a low value is possible given Saturn's large mass - 100 times that of Earth.

a. This low value is possible because the magnetic field of Saturn is so strong.
b. This low value is possible because the magnetic field of Saturn is so weak.
c. This low value is possible because the density of Saturn is so high.
d. This low value is possible because the density of Saturn is so low.

Answers

Answer:

Explanation:

That is an amazing fact.

The minus sign is what you have to pay attention to. The earth has a mass of 100 times that of Saturn. As someone on here once noted, Saturn has such a low density that it would float in water.

The answer is D

Joule is a SI unit of power
Measuring cylinder is used to measure the volume of a liquid

Answers

Answer:

The SI unit of power is watt

Define wave length as applied to wave motion​

Answers

Answer: Wavelength can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave.

Explanation:

Wavelength refers to the length or distance between two identical points of neighboring cycles of a wave signal traveling in space or in any physical medium. ... The wavelength of a signal is inversely proportional to its frequency, that is, the higher the frequency, the shorter the wavelength.

answer bhejo please please please​

Answers

Answer:

Various uses of water :

1. Water is used for daily purpose like cooking , bathing , cleaning and drinking.

2. Water used as a universal solvent.

3. water maintains the temperature of our body.

4. Water helps in digestion in our body.

5 .water is used in factories and industries.

6. Water is used to grow plants , vegetables and crops.

We do not use water instead of mercury in a barometer​

Answers

Answer:

Because

1)Water is relatively less dense. Mercury is 13.6 times more dense than water. SO, If you use water, you have to have the length of barometer of length (or height) 13.534 times the length of mercury barometer, which may be more than 11 meter in length.

2)Also mercury as compared to water, has comparatively less specific heat and good conductor of heat, could come to the same temperature of the atmosphere more quickly.

Answer:

The atmospheric pressure at sea level 76 cm of Hg=1.013× 10⁵ pascal .

Explanation:

That is if water is used in barometer tube instead of mercury the length of the tube must be greater than 10.326 cm.so we cannot replace mercury by water in the barometer.

Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific instruments, including a meter stick. Now that Jill is underway, how long does she measure the meter stick to be?
A) 0.280 m
B) 1.00 m
C) 0.960 m
D) 1.28 m
E) 1.04 m

Answers

(B) 1.00 m

Explanation:

Since the meter stick is traveling with Jill, it will have the same speed as she does so relative to Jill, the meter stick is stationary so its length remains 1.00 m as measured by her.

When astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c and measure the meter stick to be 1 meter. Hence, option B is correct.

What is length contraction?

Length contraction is defined as the phenomenon of the moving object being shorter than its appropriate length, measured in the object's rest frame.

When the object travels with the speed of light, the length of the object gets more contracted than its original length, relative to the observer. It is also known as the Lorentz-Fitgerald contraction.

Length contraction, L = L₀√(1-v²/c²), where L is the original length, L₀ is the contracted length. c² is known as the velocity of light. v² is the velocity of the speed of the object.

From the given,

speed of the spaceship = 0.280c      (c is the speed of the light)

Length contraction, L = L₀ √(1-v²/c²)

The stick also travels in the spaceship. Hence, the length of the meter stick does not change. It remains at its original length of one meter.  Thus, the ideal solution is option B.

To learn more about length contraction:

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Polarized sunglasses:

a. block most sunlight because sunlight is polarized
b. are better but work the same way as non-polarized sunglasses
c. are polarized to filter out certain wavelengths of light
d. block reflected light because reflected light is partially polarized.

Answers

Polarized sunglasses creates filter of vertical openings for light. The light rays will reach the eyes of human vertically only.

The sun rays will not reach human eye directly which will create a shield for sun light burden on human eye.

Polarized sunglasses are best used for blocking and eliminating certain wavelengths of light.

Therefore the correct answer is option C. Polarizes Sunglasses are polarized and it filter out certain wavelengths of light.

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What is the magnitude of the force between a 25μC charge exerts on a -10μC charge 8.5cm away?

Answers

Answer:

Force,

[tex]F = \frac{kQ_{1} Q_{2} }{ {r}^{2} } \\ F = \frac{(9 \times {10}^{9}) \times (25 \times {10}^{ - 6}) \times (10 \times {10}^{ - 6} ) }{ {(0.85)}^{2} } \\ \\ F = 3.114 \: newtons[/tex]

The magnitude of the force between a 25μC charge exerts on a -10μC charge 8.5cm away would be 311.4 N.

What is Coulomb's Law?

Coulomb's law can be stated as the product of the charges and the square of the distance between them determine the force of attraction or repulsion acting in a straight line between two electric charges.

The math mathematical expression for the coulomb's law given as

F= k Q₁Q₂/r²

where F is the force between two charges

k is the electrostatic constant which is also known as the coulomb constant,it has a value of 9×10⁹

Q₁ and Q₂ are the electric charges

r is the distance between the charges

As given in the problem two charges a 25μC charge exerts on a -10μC charge 8.5cm away

By substituting the respective values in the above formula of Coulomb law

F =9×10⁹×(25×10⁻⁶)×(-10×10⁻⁶)/(8.5×10⁻²)²

F= -311.4 N

A negative sign represents that the force is attractive in nature

Thus, the magnitude of the force is 311.4 N.

Learn more about Coulomb's law from here

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Which was a major effect of Pope Leo III crowning Charlemagne emperor of the Romans ?

Answers

Answer:

The crowning of Charlemagne by Pope Leo III was significant in a number of ways. For Charlemagne, it was necessary because it encouraged to give him higher reliability. It gave him the rank of a dictator, giving him the only ruler in Europe west of the Byzantine emperor in Constantinople.

A cylindrical swimming pool has a radius 2m and depth 1.3m .it is completely filled with salt water of specific gravity 1.03.The atmospheric preassure is 1.013 x 10^5 Pa.

a.calculate the density of salt water.

Answers

Answer:

the density of the salt water is 1030 kg/m³

Explanation:

Given;

radius of the cylindrical pool, r = 2 m

depth of the pool, h = 1.3 m

specific gravity of the salt water, γ = 1.03

The atmospheric pressure, P₀ = 1.013 x 10⁵ Pa

Density of fresh water, [tex]\rho _w[/tex] = 1000 kg/m³

The density of the salt water is calculated as;

[tex]Specific \ gravity \ of \ salt\ water \ (\gamma _s_w) = \frac{density \ of \ salt \ water \ (\rho_{sw})}{density \ of \ fresh \ water \ (\rho_{w})} \\\\1.03 = \frac{\rho_{sw}}{1000 \ kg/m^3}\\\\\rho_{sw} = 1.03 \times 1000 \ kg/m^3\\\\\rho_{sw} = 1030 \ kg/m^3[/tex]

Therefore, the density of the salt water is 1030 kg/m³

A uniform disk turns at 3.6 rev/s around a frictionless spindle. A non rotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk . They then both turn around the spindle with their centers superposed.
What is the angular frequency in rev/s of the combination?
please express answer in proper significant figures and rounding.

Answers

Answer:

ω₁ = 2.2 rev/s

Explanation:

Conservation of angular momentum

moment of inertia uniform disk is ½mR²

moment of inertia uniform rod about an end mL²/3

We can think of our rod as two rods of mass m/2 and length R

L = ½mR²ω₀

L = (½mR² + 2(m/2)R²/3)ω₁

ω₁ = ω₀(½mR² / (½mR² + mR²/3))

ω₁ = ω₀(½  / (½  + 1/3))

ω₁ = 0.6ω₀

ω₁ = 2.16

Kelsey the triathelete swims 1.5 km east, then bikes 40 km north, and then runs 10 km west. Which choice gives the
correct solution for the resultant?
R2 = 402 – 8,52
R2 = 402 - 102 - 2(40)(1.5) cos 10
R2 = 102 - 40
R2 = 10- - 402 – 2(1.5)(10) cos 40

Answers

Answer:

Hey,. its a simple question. hope you learn from the solution. check attached picture

Explanation:

Why are scientific models important?

Answers

Answer:

Scientific models are representations of objects, systems or events and are used as tools for understanding the natural world. Models use familiar objects to represent unfamiliar things. Models can help scientists communicate their ideas, understand processes, and make predictions.

In part B of the lab, when the current flows through the orange part of the wire from right to left, the wire deflects (or moves) ____. This is in accordance with the right-hand-rule.

Answers

This seems to be incomplete, as we do not have any information about the magnetic field surrounding the wire, but we can answer in a general way.

We know that for a wire of length L, with a current I, and in a magnetic field B, the force can be written as:

F = L*(IxB)

if we define the right as the positive x-axis, and knowing that the current flows to the right, we can write:

I = i*(1, 0, 0)

And the field will be some random vector that can't be parallel to the current because in that case, we do not have any force.

To find the direction of the force, which will tell us the direction in which the wire deflects or moves, first, we need to point with our thumb in the direction of the current, in this case, to the right.

Now, with the hand open, using the tip of our other fingers we point in the direction of the magnetic field.

For example, if the magnetic field is in the positive z-axis, we will point upwards.

Now the palm of our hand tells us in which direction the force is applied.

This is the right-hand rule.

For example, in the case that the current goes to the right and the magnetic field is upwards, we could see that the force is to the front.

If an object with constant mass is accelerating, what does Newton's second
law imply?
A. It will continue to accelerate until it meets an opposing force.
B. The object is exerting an opposite but equal force.
C. A force must be acting on the object.
D. The object will be difficult to decelerate.

Answers

Answer:

C. A force must be acting on the object.

Explanation:

This is due to the action of its momentum direction.

[tex].[/tex]

Use the values from PRACTICE IT to help you work this exercise. If the current in each wire is doubled, how far apart should the wires be placed if the magnitudes of the gravitational and magnetic forces on the upper wire are to be equal

Answers

Which behavior would best describe someone who has good communication skills with customers ? a) Following up with some customers b) Talking to customers more than listening to them c) Repeating back what the customer says d) Interrupting customers frequently

When you are standing on Earth, orbiting the Sun, and looking at a broken cell phone on the ground, there are gravitational pulls on the cell phone from you, the Earth, and the Sun. Rank the gravitational forces on the phone from largest to smallest. Assume the Sun is roughly 109 times further away from the phone than you are, and 1028 times more massive than you. Rank the following choices in order from largest gravitational pull on the phone to smallest. To rank items as equivalent, overlap them.

a. Pull phone from you
b. Pull on phone from earth
c. Pull on phone from sun

Answers

Answer:

The answer is "Option b, c, and a".

Explanation:

Here that the earth pulls on the phone, as it will accelerate towards Earth when we drop it.

We now understand the effects of gravity:

[tex]F \propto M\\\\F\propto \frac{1}{r^2}\\\\or\\\\F \propto \frac{M}{r^2}\\\\Sun (\frac{M}{r^2}) = \frac{10^{28}}{(10^9)^2} = 10^{10}[/tex]

The force of the sun is, therefore, [tex]10^{10}[/tex] times greater and the proper sequence, therefore, option steps are:

b. Pull-on phone from earth

c. Pull-on phone from sun

a. Pull phone from you

An electron is released from rest at a distance of 9.00 cm from a fixed proton. How fast will the electron be moving when it is 3.00 cm from the proton

Answers

Answer:

the  speed of the electron at the given position is 106.2 m/s

Explanation:

Given;

initial position of the electron, r = 9 cm = 0.09 m

final position of the electron, r₂ = 3 cm = 0.03 m

let the speed of the electron at the given position = v

The initial potential energy of the electron is calculated as;

[tex]U_i = Fr = \frac{kq^2}{r^2} \times r = \frac{kq^2}{r} \\\\U_i = \frac{(9\times 10^9)(1.602\times 10^{-19})^2}{0.09} \\\\U_i = 2.566 \times 10^{-27} \ J[/tex]

When the electron is 3 cm from the proton, the final potential energy of the electron is calculated as;

[tex]U_f = \frac{kq^2}{r_2} \\\\U_f = [\frac{(9\times 10^9)\times (1.602 \times 10^{-19})^2}{0.03} ]\\\\U_f = 7.669 \times 10^{-27} \ J \\\\\Delta U = U_f -U_i\\\\\Delta U = (7.699\times 10^{-27} \ J ) - (2.566 \times 10^{-27} \ J)\\\\\Delta U = 5.133 \times 10^{-27} \ J[/tex]

Apply the principle of conservation of energy;

ΔK.E = ΔU

[tex]K.E_f -K.E_i = \Delta U\\\\initial \ velocity \ of \ the \ electron = 0\\\\K.E_f - 0 = \Delta U\\\\K.E_f = \Delta U\\\\\frac{1}{2} mv^2 = \Delta U\\\\where;\\\\m \ is \ the \ mass \ of\ the \ electron = 9.1 1 \times 10^{-31} \ kg\\\\v^2 = \frac{ 2 \Delta U}{m} \\\\v = \sqrt{\frac{ 2 \Delta U}{m}} \\\\v = \sqrt{\frac{ 2 (5.133\times 10^{-27})}{9.11\times 10^{-31}}}\\\\v = \sqrt{11268.935} \\\\v = 106.2 \ m/s[/tex]

Therefore, the  speed of the electron at the given position is 106.2 m/s

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