Answer:
* I will look at the range of both, such as 100-5 = 95 and 94+4=98. Since the ranges overlap, I can conclude that they are the same within uncertainty.
* I willl draw a dot-and-whisker plot for both. Since they overlap, I can conclude that they are equal within the uncertainty
Explanation:
The value of all physical measurement has an uncertainty, so it is within a range of values, in this case we must compare the range of values of the resistors
The nominal value is 100 ± 5 Ω
therefore its range of possible values is between
95 <= R <= 105
For the experimentally measured value
88 <= R <= 96
as the values overlap we must conclude that they are the same.
When reviewing the different options we have two statements that are correct
* I will look at the range of both, such as 100-5 = 95 and 94+4=98. Since the ranges overlap, I can conclude that they are the same within uncertainty.
* I willl draw a dot-and-whisker plot for both. Since they overlap, I can conclude that they are equal within the uncertainty
A person makes ice tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0.00°C, are required to bring the mixture to 10°C? The heat of fusion of ice is 334 kJ/kg, and we can assume that tea has essentially the same thermal properties as water, so its specific heat is 4190 J/(kg·K).
Answer:
The required mass of ice is 12.5 kg.
Explanation:
Mass of hot tea, [tex]m_{t}[/tex] = 1.8 kg
Initial temperature of hot tea = 80°C = 353 K
Initial temperature of ice = 0.00°C = 273 K
Final temperature of mixture = 10°C = 283 K
Heat of fusion of ice, L = 334 kJ/kg
Specific heat capacity of tea, [tex]c_{t}[/tex] = Specific heat capacity of water = 4190 J/kg/K
Heat lost tea = Heat gained by ice
[tex]m_{t}[/tex][tex]c_{t}[/tex]Δ[tex]T_{t}[/tex] = [tex]m_{i}[/tex]L + [tex]m_{i}[/tex][tex]c_{i}[/tex]Δ[tex]T_{t}[/tex]
[tex]m_{t}[/tex][tex]c_{t}[/tex]Δ[tex]T_{t}[/tex] = [tex]m_{i}[/tex] (L + [tex]c_{i}[/tex]Δ[tex]T_{t}[/tex])
1.8 x 4190 x (353 - 283) = [tex]m_{i}[/tex](334 + (4190 x (283 - 2730))
1.8 x 4190 x 70 = [tex]m_{i}[/tex](334 + (4190 x 10))
527940 = 42234[tex]m_{i}[/tex]
[tex]m_{i}[/tex] = [tex]\frac{527940}{42234}[/tex]
= 12.5004
[tex]m_{i}[/tex] = 12.5 kg
The required mass of ice is 12.5 kg.
The required amount of ice to bring the mixture to 10°C is 12.5 kg.
Given data:
The mass of hot tea is, m' = 1.8 kg.
The initial temperature of hot tea is, T = 80°C = 353 K.
The initial temperature of ice is, T' = 0°C = 273 K.
The final temperature of mixture is, T'' = 10°C = 283 K.
The heat of fusion of ice is, h = 334 kJ/kg.
The specific heat of water is, c = 4190 J/kg·K.
Apply the condition of thermal equilibrium which says that the heat released by the hot tea will be gained by the ice.
Heat lost by tea = Heat gained by ice
[tex]m'c(T-T'') = mh +mc(T''- T')[/tex]
Here, m is the mass of ice.
Solving as,
[tex]1.8 \times 4190 \times (353-283) = (m \times 334) +(m \times 4190(283- 273))\\\\527940 = 42234m\\\\m = 12.5 \;\rm kg[/tex]
Thus, we can conclude that the required amount of ice to bring the mixture to 10°C is 12.5 kg.
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As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a constant speed of 35 m/s. How fast is the watermelon going when it passes Superman
Answer:
70 m/s
Explanation:
The watermelon will go pass superman at the instance when they are at the same distance from the top of the building.
Superman flies by with a constant velocity = 35 m/s
This distance where he will be overtaken by the watermelon will be = vt
where v is his velocity
t is the time the watermelon and superman are side by side
For the watermelon,
the initial velocity u = 0 m/s (since it starts from rest)
The distance where it is side by side with superman will be gotten from the equation
s = ut + [tex]\frac{1}{2}gt^2[/tex]
where is the distance down at which they meet
g is the acceleration due to gravity = 9.81 m/s^2
t is the time they meet
ut = 0, since u = 0 m/s
Equating this distance that they meet, we'll have
vt = [tex]\frac{1}{2}gt^2[/tex]
substituting values, we have
35t = [tex]\frac{1}{2}*9.81*t^2[/tex]
35 = 4.905t
t = 35/4.905 = 7.135 s
The watermelon's speed at this instant can be calculated from
v = u + gt
where v is the velocity at this instant
u = initial speed of the watermelon = 0 m/s
g is the acceleration due to gravity = 9.81 m/s^2
t is the time they meet side by side = 7.135 s
substituting values, we have
v = 0 + 9.81(7.135)
v = 69.99 ≈ 70 m/s
A car drove 200 km east on an interstate highway, then was finally able to make an
exit and drove for another 70 km to the north before reaching their destination.
What was the direction of car's resultant displacement?
Answer:
70.66°Explanation:
To find the direction of the displacement vector, we have to solve for the ratio of both displacements, and furthermore the inverse tangent of the ratio.
Given data
200km east represents the x axis
70 km north represents y axis
the direction of the resultant is given as
∅= tan-1x/y
∅=tan-1 200/70
∅= tan-120/7
∅= tan-12.85
∅= 70.66°
hence the direction of the resultant is 70.66°
Electrons are important to electric current because they are able to
Samus is exploring the planet Zebes in the star system Metroid Prime (where the laws of physics are the same as on Earth and in our universe) in a ship moving at constant velocity. She turns on her headlamps as she encounters some strange fog. Ridley, the villain lying in wait, is at rest with respect to Samus. The speed of the light from Samus's headlamps as measured by Ridley depends most importantly on
Answer:
c. the speed of light in a vaccum
Explanation:
The complete question is...
Samus is exploring the planet Zebes in the star system Metroid Prime (where the laws of physics are the same as on Earth and in our universe) in a ship moving at constant velocity. She turns on her headlamps as she encounters some strange fog. Ridley, the villain lying in wait, is at rest with respect to Samus. The speed of the light from Samus's headlamps as measured by Ridley depends most importantly on
a. the speed of light in the fog
b. the speed of light of Samus's ship
c. the speed of light in a vaccum
d. the speed of Samus with respect to the ether
e. the total addition of speeds of Samus's ship, the planet Zebes, and the system Metroid Prime.
According to relativity,
1. The laws of physics are the same for all observers in any inertial frame of reference relative to one another.
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source.
This means that The speed of the light from Samus's headlamps as measured by Ridley depends most importantly on the speed of light in a vacuum.
A liquid thermometer can be used to test for fevers. When body temperature increases, the liquid inside the thermometer expands and
rises to show a higher
temperature reading. Which of the following explanations best describes the changes in thermal energy of the
particles during this specific example of heat transfer?
A. The tip of the thermometer is heated by radiation from the person's body. The particles of the thermometer tip then transfer heat
by convection through the liquid inside of it. The particles inside the liquid then convect heat causing the warmer particles to slow
down, rise, and expand.
B. The tip of the thermometer is heated by conduction from the person's body. The particles of the thermometer tip then transfer heat
by convection through the liquid inside of it. The particles inside the liquid then convect heat causing the warmer particles to slow
down, rise, and expand.
© C. The tip of the thermometer is heated by convection with the person's body. The particles of the thermometer tip then transfer heat
by conduction with the liquid inside of it. The particles inside the liquid then conduct heat causing the warmer particles to speed up,
rise, and expand
© D The tip of the thermometer is heated by conduction with the person's body. The particles of the thermometer tip then transfer heat
by conduction with the liquid inside of it. The particles inside the liquid then convect heat causing the warmer particles to speed up,
rise, and expand
Answer:
A
Explanation:
dafdfsfsf
The tip of the thermometer is heated through radiation from the person's body. The particles of the thermometer tip then transfer heat by the convection of heat through the liquid inside of it. The particles inside the liquid then convert heat which causes the warmer particles to slow down, rise, and expand. Thus, the correct option is A.
What is Convection?The process of heat transfer from one part of a fluid to another part of the system or fluid through the actual movement of the particles of the fluid substance is called convection. Liquid and gas particles are heated through the process of convection.
The tip of the thermometer is heated by radiation from the person's body. The particles of the thermometer tip then transfer heat energy through convection of heat through the liquid inside of the thermometer. The particles inside the liquid then convert heat causing the warmer particles to slow down, rise, and expand in the thermometer.
Therefore, the correct option is A.
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Question 1 (1 point)
Meliodas gets up in the morning and then follows his per pig Hawk a distance of 12 km away from his home. They stop, have a picnic, look as
some butterflies, and talk about their epic adventures, They make it halfway back before the food they are (Meliodas made it) makes them feel
sick so they stop to camp for the night,
How far did they travel (their distance)?
How far are they from home (their displacement)?
Answer:
Travelled 18 km, they are 6 km from home.
Explanation:
12/2 (halfway) is 6km. So, 6 + 12 would be 18 km, total amount travelled. The total distance of the trip would be 24 km (12 km out, 12km back) if they travelled 12+6 (18km) then they only have 6 km more to go.
Given a 45 45 90 prism with index of 1.5, immersed in air. The hypotenuse acts as the reflecting face by TIR. A ray of light enters horizontal (perpendicular to one of the non- hypotenuse faces) hitting the hypotenuse at 45º and is reflected. If the original ray is now the center of a converging bundle of rays, converging toward the original intersection point on the hypotenuse, what full convergence angle (in air) is allowed, if TIR at the hypotenuse is to be preserved for the whole bundle of rays?
Answer:
83.6°
Explanation:
For the ray to be totally internally reflected, at the boundary, the angle of refraction is 90. Using the law of refraction where
n₁sinθ₁ = n₂sinθ₂ where n₁ = refractive index of prism = 1.5, θ₁ = critical angle in prism, n₂ = refractive index of air = 1 and θ₂ = refractive angle = 90°.
So, substituting these values into the equation,
n₁sinθ₁ = n₂sinθ₂
1.5 × sinθ₁ = 1 × sin90
1.5 × sinθ₁ = 1
sinθ₁ = 1/1.5
sinθ₁ = 0.6667
θ₁ = sin*(0.6667)
θ₁ = 41.8°
So, for total internal reflection, an incidence angle of 41.8° is required. So, a full convergence angle of 2 × 41.8° = 83.6° is required for the whole bundle of rays.
Need Help with this physics question, just a written response
Answer:
Explanation:
According to Newton's third law, every action has an equal and opposite reaction
so it tells us that the force exerted by the earth on the spacecraft is equal to the force exerted by the spacecraft on the earth. But we do not see the earth moving towards the spacecraft because the inertia of the spacecraft is very less than the inertia of the earth.
A car speeds up from 12.0 M/S to 16.0 M/S in 8.00 S what is the acceleration of the car
We have,
Initial velocity,u = 12 m/s
Final velocity,v = 16 m/s
Time taken,t = 8 s
Now,
[tex] \sf \: a = \frac{v - u}{t} [/tex]
[tex] \bf \implies \: a = \frac{16 - 12}{8} [/tex]
[tex] \bf \implies a = \frac{4}{8} [/tex]
[tex] \bf \implies \: a = 0.5 \: m {s}^{ - 2} [/tex]
Point charges of 16.7 nC and 47.3 nC are placed 0.500 m apart. What is the electric field halfway between them? Indicate direction by a positive or a negative value. Keep in mind that a positive vector is one directed to the right and a negative vector is one directed to the left. Your answer should be a positive or a negative number with two decimal places, do not include the unit. Hint: 1 nC = 10-9 C
Answer:
-4320
Explanation:
Using the formula for electric field between two points
E = kq/r²
The electric field at a midpoint, say x, is
E(x) = [(k * 16.7*10^-9)/0.5²] - [(k * 47.3*10^-9)/0.25²]
E(x) = [k * (16.7*10^-9 - 47.3*10^-9)/0.25²]
E(x) = [(k * -30.6*10^-9)/0.0625]
E(x) = [(9*10^-9 * -30.6*10^-9)/0.0625]
E(x) = -270/0.0625
E(x) = -4320
Therefore, we can conclude that the electric field, halfway in between them is -4320
Which of these is an example of acceleration? A a bicyclist turning around a corner B a car traveling south with its cruise control set C a bus traveling north at 25m/s D a helicopter waiting to take off
The answer is A.
Acceleration means when you go faster in speed. Since the bicyclist is turning, he has to slow down but when he finishes turning, he is going to pedal harder and gain more speed. This is called Acceleration.
Best of Luck!
Answer:
a
Explanation:
A bicyclist, traveling with a constant speed, covers 61.Om in 7.80s.
Determine all unknowns.
S =
7.82
m/s
d =
61
m
t =
Answer:
The velocity is 7.82 m/sExplanation:
In this problem, we are going to solve for the velocity since what we are given as parameters are:
1. Distance covered s= 61m
2. time taken to cover the distance t= 7.8 secs
we know that the expression for velocity is given as
velocity= distance/time
We then substitute the given data into the formula to solve for velocity.
velocity= 61/7.8
velocity= 7.82 m/s
The velocity is 7.82 m/sTwo aluminum soda cans are charged and repel each other, hanging motionless at an angle. Which of the forces on the left can has the greatest magnitude? T FE they are all the same impossible to tell mg Changed: Your submitted answer was incorrect. Your current answer has not been submitted.
Answer:
the tension is the greatest force the system
Explanation:
For this exercise we use Newton's second law, in the equilibrium condition, this means that the acceleration is zero a = 0
X-axis (horizontal)
FE - Tₓ = 0
Fe = Tₓ
Y axis (vertical)
[tex]T_{y}[/tex] - W = 0
T_{y} = W
let's use trigonometry for the stress components
sin θ = Tₓ / T
Tₓ = T sin θ
cos θ = T_{y} / T
T_{y} = T cos θ
we substitute
FE = T sin θ
W = T cos θ
Since the sine and cosine function have values between 0 and 1, the voltage must be greater than the electrical force and greater than the weight of the body.
Therefore the tension is the greatest force the system
1. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its
speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its
average acceleration?
Answer:
6 m/s²
Explanation:
Average acceleration = change in velocity / change in time
a = Δv / Δt
a = (22 m/s − 4 m/s) / 3 s
a = 6 m/s²
Answer:tryna get points don't mind me
Explanation:
n engineer is given the task of comparing the fuel efficiency of four car models. She reports the following findings: Model 1, 14 kilometers per liter. Model 2, 9 miles per liter. Model 3, 56 kilometers per gallon. Model 4, 1600 meters per liter. The data for which two models consistently follow the use of SI units?
D because it uses meters
Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 941 V/m in the positive y-direction. What is the instantaneous magnitude of the Poynting vector at the same point and time? The speed of light is 2.99792 x 108 m/s, the permittivity of free space is 8.85419 x 10-12 C2/N/m2 and the permeability of free space is 47 x 10-7 T N/A.
What is the direction of the instantaneous magnetic field?
1. B = - 2.
2. B = +î.
3. B = +j.
4. B = - j.
5. B = +k.
6. B = -k.
7. The magnetic field vector does not have an instantaneous direction.
What is the direction of the instantaneous Poynting vector?
1. Ŝ= -î.
2. Ŝ= -k
3. The Poynting vector does not have an instantaneous direction.
4. Ŝ = tî.
5. Ŝ = +Î.
6. Ŝ= -Î.
7. Ŝ= +ê.
Answer:
a) S = 2.35 10³ J/m²2 ,
b)and the tape recorder must be in the positive Z-axis direction.
the answer is 5
c) the direction of the positive x axis
Explanation:
a) The Poynting vector or intensity of an electromagnetic wave is
S = 1 /μ₀ E x B
if we use that the fields are in phase
B = E / c
we substitute
S = E² /μ₀ c
let's calculate
s = 941 2 / (4π 10⁻⁷ 3 10⁸)
S = 2.35 10³ J/m²2
b) the two fields are perpendicular to each other and in the direction of propagation of the radiation
In this case, the electro field is in the y direction and the wave propagates in the ax direction, so the magnetic cap must be in the y-axis direction, and the tape recorder must be in the positive Z-axis direction.
the answer is 5
C) The poynting electrode has the direction of the electric field, by which or which should be in the direction of the positive x axis
In a house, a circuit often includes multiple electrical outlets which are parallelconnected to a single voltage source. Each of these circuits also contains a 15-A circuit breaker. Design a parallel-connected circuit which shows three electrical outlets connected to a voltage source with a circuit breaker. What is the advantage of having outlets parallel-connected, and why is a circuit breaker connected in series with the voltage source
Answer:
In parallel circuits, if one element has a problem, it can be eliminated and the rest of the elements continue to work.
Explanation:
There are two ways to connect electrical circuits, in series and in parallel.
Series circuits have the problem that when one element is damaged, the entire circuit is interrupted and runs out of power.
In parallel circuits, if one element has a problem, it can be eliminated and the rest of the elements continue to work.
In Breaker it is connected in series so that when some maintenance is needed, all the energy can be interrupted simultaneously and if some equipment tries to consume a lot of energy, the circuit prevents this action by interrupting the energy of the entire circuit
Copper wire is a good electrical
(
Answer:
yes also good for pennies
Explanation:
Draw two unique free body diagrams that each show a net force of 30 N to the left.
Answer:
just trace a picture of it.
How can you serve the community through NSTP subject
Answer:
The answer is below
Explanation:
NSPT is an acronym for the National Service Training Program. It deals with the individual's role in society building. Most specifically, the youths in areas such as physical, ethical, virtuous, intellectual, and social well-being.
One can serve the community through the NSTP subject, by involving in creating awareness in literacy and social welfare undertakings, mostly during emergencies and mishaps, or be part of the Citizen Armed Force.
Which chemical reaction shows photosynethesis?
Answer: Endothermic Reaction
Explanation: Photosynthesis requires energy right, making it an endothermic reaction. Light, generally sunlight, is the source of this energy. The process converts the sun's electromagnetic energy into chemical energy, which is then stored in chemical bonds in the plant. Which then leads to Photosynthesis occuring.
Unlike velocity, speed is scalar, which means it is described by
Answer:
Magnitude
Explanation:
Scalar quantitys have no direction only a size aka magnitude
7. Starting at rest, a car accelerates at 5.5m/s/s for 12s. What is its
velocity at the end of 12s? *
Answer:
66 m/s
Explanation:
v=u+at
= 0 + 5.5 * 12
= 66 m/s
Which method is the typical first step when scientists communicate their scientific results? placing the results on an Internet site to maximize readership distributing the results in press releases to make them well established submitting the results to a scientific journal for a peer review declaring the results in a TV interview for public feedback
Answer:
Option C (submitting the results to a scientific journal for a peer review) is the correct choice.
Explanation:
If a researcher or a scientist decides to transmit his conclusions depends on a variety of considerations. At either the conclusion of the day, the scientist should concentrate on the final use of an individual's findings before settling on how to transmit it, either through science papers, announcements at professional journals, or personally with the public.Scientists often prefer to submit their articles to professional conferences rather than just going via scientific publications.The other solutions offered are not relevant to the situation in question. But the latter is the best answer.
Answer:
it is letter c
Explanation:
Ryan places 0.150 kg of boiling water in a thermos bottle. How many kgs of ice at –12.0 °C must Ryan add to the thermos so that the equilibrium temperature of the water is 75?a. 0.0436 kgb. 0.0713 kgc. 0.0233 kgd. 0.0265 kge. 0.625 kg
Answer:
The value is [tex] m_i = 0.0234 \ kg [/tex]
Explanation:
Generally from the calorimetry principle we have that
[tex]Heat \ loss\ by\ ice = heat\ gained\ by\ water\[/tex]
So here heat gained water is mathematically represented as i.e
[tex]Q_w = m_w * c_w * (T_w - T )[/tex]
substituting 0.150 kg for [tex]m_w [/tex] , 4200 J/kg.°C for [tex]c_w [/tex] , 100°C for [tex]T_w [/tex] and 75°C for T
We have
[tex]Q_w = 0.150 * 4200 * (100 - 75 )[/tex]
[tex]Q_w =15750 \ J [/tex]
The Heat loss by the ice is mathematically represented as
[tex]Q_i = Q_1 + Q_2 + Q_3[/tex]
Here [tex]Q_1[/tex] is the energy to move the ice to its melting point which is evaluated as
[tex]Q_1 = m_i * c_i * ( T_o -T_i)[/tex]
Here [tex]m_i [/tex] is the mass of ice
[tex]c_i [/tex] is the specific heat of ice with value [tex]2.05 * 10^3 J/kg.°C[/tex]
[tex]T_o [/tex] temperature of ice at melting point with value 0°C
[tex]T_i [/tex] is the temperature of ice with value -12°C
[tex]Q_2[/tex] is the energy to move the ice from its its melting point to liquid which is evaluated as
[tex]Q_2 = m_i * L[/tex]
Here L is the Latent heat of melting of ice with value [tex]334 * 10^3 J/kg [/tex]
[tex]Q_3[/tex] is the energy to move the ice from liquid to the equilibrium temperature which is evaluated as
[tex]Q_1 = m_i * c_w * ( T -T_o)[/tex]
So
[tex]Q_i = m_i [ c_i * ( T_o -T_i) + L + c_w * ( T -T_o) ] [/tex]
=> [tex]Q_i = m_i [ 2.05 * 10^3 * ( 0 -(-12)) + 334 * 10^3 + 4200 * ( 75 - 0) ] [/tex]
From
[tex]Heat \ loss\ by\ ice = heat\ gained\ by\ water\[/tex]
We have that
[tex] m_i * 673600 =15750 [/tex]
=> [tex] m_i = \frac{15750}{673600} [/tex]
=> [tex] m_i = 0.0234 \ kg [/tex]
The amount of ice at –12.0 °C must Ryan add to the thermos so that the equilibrium temperature of the water is 75 - 0.0233 kg
The calorimetry principle we have thatheat is given by water = heat is received by ice
=>
Given:
mass of boiling water [tex]m_w = 0.150 kg[/tex]
temperature of ice [tex]T_i = - 12^0C[/tex]
Known:
specific heat of water [tex]c_w = 4.2 \times 10^3 J/kg-^0C[/tex] the Initial temperature of boiling water [tex]T_w = 100^0C[/tex]mass of ice = [tex]m_i[/tex]specific heat of ice [tex]c_i = 2.05 \times 10^3 J/kg-^0C[/tex] Latent heat of melting of ice [tex]L = 334 \times 10^3 J/kg[/tex] Melting point of ice [tex]T = 0^0C[/tex] Equilibrium temperature T = 75 CSolution:placing value in the formula:
=>
=>
= 0.0233 kg
Thus, the amount of ice at –12.0 °C must Ryan add to the thermos so that the equilibrium temperature of the water is 75 - 0.0233 kg
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Where do the local stall patterns occur for a Rectangular wing with no sweep?
a. Wing Tip
b. Wing Root
c. Leading Edge
a. Mean Aerodynamic Chord
Answer:
The answer is "Option b"
Explanation:
The root of the wing is also known as the wing portion of its airframe nearest to a chamfer or winged spaceship. It's typically helpful to identify either a basic monoplane layout.
The use of floats often known as "wing fillets", that was popularised within the first half of the 20th Century, in such a bid to reduce interference here between wings and fuel tank. It used in fasteners achieved more desirable flying property at both higher and lower speeds.Which of these will have the same units if acceleration is multiplied by time? Force Time velocity Pressure
Answer:
Velocity
Explanation:
Velocity equals the original velocity... Plus
the acceleration is multiplied by time.
If the acceleration is multiplied by time then we get velocity as a result, therefore velocity has the same unit.
What is pressure?Pressure is measured as the amount of force applied in the one-meter of area. Pascal is used as the SI unit of it. The amount of pressure can be calculated by dividing the amount of force by the area of force applied. In relation to atmospheric pressure, the pressure is measured. Pressure does not represent any direction, so it comes under a scalar quantity. Many scientific and day-to-day life equipment use pressure principles like gauge meter thermometers in designing cars, ships, and every mechanical part.
We know that acceleration has an SI unit of m /[tex]s^{2}[/tex] So if we multiply the time with an acceleration whose unit is second we will get m / s which is the unit of velocity.
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bond formed when atoms share one or more pairs of electrons, but atoms do not always share electrons equally
Answer:
Polar covalent bond or just covalent bond
Explanation:
Problem: You and your friend are discussing last week’s recitation problem, in which an electron falling down a tunnel through a uniformly charged earth exhibits simple harmonic motion. Instead of being uniformly charged, imagine that the Earth is given a spherically symmetric charge density ⍴(r)=b/r, where b is a constant. If an electron is released from rest inside this tunnel at some initial distance from the center, find an expression for the acceleration of the electron inside the tunnel (ignore gravity). If the electron is released from rest at the surface, what value of b will ensure that the electron reaches the center of the Earth in 12 seconds? ………………………………………………………………………………………
Answer:
a. a = eb/2ε₀m b. b = 8.91 × 10⁻¹⁸ kg/V
Explanation:
a. Using Gauss' law
ε₀∫E.dA = q where E = electric field and q = charge enclosed.
Now , the charge has a spherical symmetric charge density ⍴(r) = b/r, the total charge enclosed at distance r is given by
q = ∫∫∫ρ(r)r²sinθdrdθdΦ
q = ∫∫∫(b/r)r²sinθdrdθdΦ
q = ∫∫∫brsinθdrdθdΦ
we integrate r from 0 to r, θ from 0 to π and Φ from 0 to 2π
q = ∫∫br[∫sinθdθ]drdθdΦ
q = ∫∫br[-cosθ]drdΦ
q = ∫∫br-[cosπ - cos0]drdΦ
q = ∫∫br-[-1 - 1]drdΦ
q = ∫2brdr∫dΦ
q = ∫2brdr[Φ]
q = ∫2brdr[2π - 0]
q = 4πb∫rdr
q = 4πb[r²/2]
q = 4πb[r²/2 - 0]
q = 2πbr²
The let side of the equation is
ε₀∫E.dA = ε₀E∫dA = ε₀E4πr² since there is spherical symmetry
Equating both sides of the equation
ε₀E4πr² = 2πbr²
E = 2πbr²/ε₀4πr²
E = b/2ε₀
Now, the force acting on the electron , F = ma where m = mass of electron and a = acceleration of electron.
F also equal F = eE where e = electron charge and E = electric filed acting on electron
So, eE = ma
a = eE/m
a = eb/2ε₀m
b. I(f the electron is released from rest and is to reach the center of the earth, it covers a distance of the radius of the earth. Using s = ut + 1/2at² where s = radius of earth = R = 6400 km = 6.4 × 10⁶ m , u = initial velocity = 0 m/s. and a = eb/2ε₀m. Substituting these values into s we have
R = 0t + 1/2(eb/2ε₀m)t²
R = ebt²/4ε₀m
making b subject of the formula, we have
b = 4ε₀mR/et²
when t = 12 s and e = 1.609 × 10⁻¹⁹ C, ε₀ = 8.854 × 10⁻¹² F/m and m = 9.109 × 10⁻³¹ kg.
Substituting these values into b we have
b = (4 × 8.854 × 10⁻¹² F/m × 9.109 × 10⁻³¹ kg × 6.4 × 10⁶ m)/(1.609 × 10⁻¹⁹ C × 12²)
b = 2064.67/ 231.696 × 10⁻¹⁸
b = 8.91 × 10⁻¹⁸ Fkg/C
b = 8.91 × 10⁻¹⁸ kg/V
