We would need 126 A current to generate a pressure of 1 atm.
The technique to calculate the magnetic energy and the magnetic pressure on the inner conductor is to determine L. Wangsness 17-24 is an equation that relates the magnetic energy to the inductance L of a system containing a coil.
In this equation, the magnetic energy is equal to one-half of the inductance times the square of the current, or W = (1/2)LI^2. Rearranging this equation gives L = 2W/I^2. Thus, to determine L using this technique, we need to calculate the magnetic energy.
The magnetic energy can be found using the equation W = (μ0I^2/2) ∬S(H · n)^2 ds, where μ0 is the permeability of free space, I is the current, H is the magnetic field, n is a unit vector normal to the surface S, and ds is an element of surface area on S.
The magnetic pressure on the inner conductor can be found using the equation p = B^2/(2μ0), where B is the magnetic field. If the magnetic pressure on the inner conductor is positive, then it tends to contract the conductor, while if it is negative, then it tends to expand the conductor.
The current needed to generate a pressure of 1 atm can be found using the equation p = B^2/(2μ0), where p is the pressure in Pa, B is the magnetic field in Tesla, and μ0 is the permeability of free space.
For a = 1 cm, we have r1 = 1 cm and r2 = 2 cm. Thus, the inductance is L = (μ0π(r2^2 - r1^2))/ln(r2/r1) = (3.14 x 10^-7 x π(2^2 - 1^2))/ln(2/1) = 1.02 x 10^-6 H.
The magnetic energy can be found using the equation W = (μ0I^2/2) ∬S(H · n)^2 ds. The surface S is a cylinder with radius r1 and length L, and H is given by H = I/(2πr). Thus, we have:
W = (μ0I^2/2) ∬S(H · n)^2 ds = (μ0I^2/2) ∬S(I/2πr · n)^2 ds = (μ0I^2/2) ∬S(I/2πr^2)^2 ds = (μ0I^2/2)(πr1^2L)(I^2/4r2^2) = 1.26 x 10^-6 I^2 J.
The magnetic pressure on the inner conductor can be found using the equation p = B^2/(2μ0). The magnetic field at the center of the inner conductor is given by B = μ0I/(2πr), where r is the radius of the inner conductor. Thus, we have:
p = B^2/(2μ0) = (μ0I/(2πr))^2/(2μ0) = μ0I^2/(8π^2r^2) = 3.18 x 10^-3 I^2 Pa.
The pressure tends to contract the conductor since it is positive.
To generate a pressure of 1 atm = 101325 Pa, we have:
p = B^2/(2μ0) = μ0I^2/(8π^2r^2) = 101325 Pa. Thus, we have:
I = √(8π^2r^2p/μ0) = √(8π^2 x 0.0125 x 101325/(4π x 10^-7)) = 126 A.
Answer: 126 A.
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Darth Maul has once again parked his sith Speeder on a slope of the desert planet Tatooine. Unfortunately, he once again forgot to apply the parking brakel (DoutbL DOHI) Today, though ... the sand dunejglope isn't fust a simple frictioniess surface. The coetfient of kinetic friction (F
k
) is 0.08 between the Sith Speeder and the sand. The acceleration due to gravity on Tatooine is 7.0 m/sec
2
. The sith speeder has mass m=890 kg, and the sand dune is tited at an angle θ : = 25.0 to the horizontal, (a) Determine the acceleration of the Sith Speeder as it slides down this inclined plane of sand. (You can assume that it will indeed start moviagi) m/s
2
(down the plane) (b) If the 5 ith Speeder starts from rest 100.0 m up the ptase from its base (i.e: as measured along the plane of the sand dune), what will the speed of it be when it reachns the bottem of the incline? m/s. (c) If, at the bottom of the inclitied plane, the sith Speeder smoothly transitions to level ground wi. with what speed would it be moving after traveling another 170 m across the sand? m/sec (d) After traveling across the fevel sand for the 170 m, is reaches a eliff (OH NOI) with a height 1280 m. Assume the 5 ith 5 peeder launches exactil horizontal from the cilf with a saeed equal to your answer to part(c), how long will it take for it to land at the bottom of the cliff? sec (e) How far away from the base of the cliff will it have traveled?
These values are derived using the given parameters such as mass, gravitational acceleration, coefficients of friction, initial velocity, distance, and height, along with relevant equations of motion and principles of physics.
a) The acceleration of the Sith Speeder is 6.292 m/s².
b) The final velocity of the Sith Speeder at the bottom of the incline is approximately 35.47 m/s.
c) The final velocity of the Sith Speeder after traveling 170 m on the level ground is approximately 5.96 m/s.
d) The time taken by the Sith Speeder to reach the ground from a height of 1280 m is approximately 29.94 s.
e) The distance covered by the Speeder on the ground before taking off from the cliff is approximately 178.82 m.
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A 60.0 kg skater begins spinning with an angular velocity of 23 rad / s. By changing the position of her arms, the skater decreases her moment of inertia to half of her initial value. What is the final angular velocity (rad / s) of the skater? Give his answer to a decimal.
The final angular velocity (rad/s) of the skater is 32.5 rad/s. Given the initial mass of the skater as 60.0 kg and the initial angular velocity as 23 rad/s, we can find the final angular velocity using the conservation of angular momentum.
Using the formula for angular momentum, L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity, we can set the initial angular momentum equal to the final angular momentum:
Linitial = Lfinal
Since the moment of inertia is constant, we have:
Iinitial × ωinitial = Ifinal × ωfinal
For a skater with mass m, the moment of inertia I is given by I = mR², where R is the radius of rotation. We can use the radius of gyration k, defined as the ratio of the radius of rotation to the length of the arm, to simplify the equation:
I = mk²L₀²
By taking the ratio of the initial moment of inertia to the final moment of inertia, we find:
Iinitial / Ifinal = 1/2
From this, we can determine the ratio of the radius of gyration at the final length of the arm (k₁) to the initial radius of gyration (k):
k₁ / k = 1/√2 = √(1/2)
Finally, the final angular velocity (ω₁) can be calculated as:
ω₁ = √(Iinitial / Ifinal) × ωinitial
= √(2) × 23 rad/s
= 32.5 rad/s
Therefore, the final angular velocity of the skater is 32.5 rad/s.
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An object is launched at an angle of 30 degrees from the ground. It hits the ground again after 10.0 s. What was its initial vertical velocity?
The initial vertical velocity of the object was 196 m/s. In order to calculate the initial vertical velocity of the object launched at an angle of 30 degrees from the ground, we will use the following formula:Vf = Vi + gt where Vf is the final velocity, Vi is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
Let's consider the vertical motion of the object:Vf = Vi + gt.
Here, the final velocity Vf is zero since the object hits the ground and comes to a stop.
We can write g as -9.8 m/s² since it acts in the opposite direction to the initial velocity.
We can also write the initial velocity Vi as a vector quantity consisting of a horizontal component Vi_x and a vertical component Vi_y: Vi_x = Vi cos(30°)Vi_y = Vi sin(30°).
Therefore,Vf = Vi_y - 9.8t0 = Vi_y - 9.8tVi_y = 9.8t.
Putting the value of Vi_y, we get:Vi = Vi_y / sin(30°)Vi = (9.8t) / sin(30°)Vi = (9.8 * 10.0) / sin(30°)Vi = 196 m/s.
Therefore, the initial vertical velocity of the object was 196 m/s.
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Mass 1, 8.0 kg, is held on top of a table on friction-free wheels. The mass of block 2 is 4.0 kg and is hanging from a string connected to mass 1. Mass 1 is released from rest. While the masses are accelerating, what is the tension in the string?
Given,Mass of block 1 (m1) = 8.0 kg Mass of block 2 (m2) = 4.0 kg Acceleration :
(a) = ? (to be determined)The tension in the string (T) = ? (to be determined)Considering the motion of block 2, we can say thatT - m2g = m2a... equation 1.Considering the motion of both blocks as a whole, we can say thatm1a = T - m1g... equation 2.We can solve for T from equation 2:
T = m1a + m1g... equation 3We can substitute the value of T.From equation 3 to equation 1:
m1a + m1g - m2g = m2a Simplifying the above equation we get:a = (m1 / (m1 + m2)) g Substituting the given values we get,a = (8.0 / (8.0 + 4.0)) * 9.8= 5.2 m/s^2We can now substitute this value of a in equation 3 to find the tension:
T = m1a + m1g= 8.0 5.2 + 8.0 9.8= 131.2 NTherefore, the tension in the string is 131.2 N.About MassMass or mass is a measure of the amount of matter contained in an object. Mass is measured in Kilograms (Kg). Mass or mass is a physical property of an object that is used to describe various observed object behaviors. In everyday usage, mass is usually synonymous with weight. But according to modern scientific understanding, the weight of an object results from the interaction of the mass with the gravitational field.
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Electrons are accelerated from rest with a potential difference of 120 V. (a) Calculate the de Broglie wavelength of the electrons. (b) If these electrons are used in a double slit experiment, calculate the distance between the adjacent maxima in the interference pattern if the distance between the slits is 1.0 nm and the distance from the slits to the detection screen is 10 cm.
The de Broglie wavelength of the accelerated electrons is X (a) and the distance between adjacent maxima in the interference pattern is Y (b).
(a) To calculate the de Broglie wavelength of the accelerated electrons, we can use the de Broglie wavelength equation:
λ = h / p
Where λ is the de Broglie wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum of the electrons. Since the electrons are accelerated from rest, we can calculate their momentum using the equation:
p = √(2mE)
Where m is the mass of the electron (approximately 9.109 x 10^-31 kg) and E is the energy of the electrons, which is equal to the potential difference (V) multiplied by the electron charge (e). The electron charge is approximately 1.602 x 10^-19 C.
Once we have the momentum (p), we can substitute it into the de Broglie wavelength equation to find the de Broglie wavelength (λ) of the electrons.
(b) In a double-slit experiment, the distance between adjacent maxima in the interference pattern can be calculated using the formula:
y = λL / d
Where y is the distance between adjacent maxima, λ is the de Broglie wavelength of the electrons, L is the distance from the slits to the detection screen (10 cm or 0.1 m), and d is the distance between the slits (1.0 nm or 1 x 10^-9 m).
By substituting the values into the formula, we can calculate the distance between adjacent maxima in the interference pattern.
Therefore, the de Broglie wavelength of the accelerated electrons is X, and the distance between adjacent maxima in the interference pattern is Y.
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Most comets begin their lives ...
Group of answer choices
As part of the Oort Cloud
As part of the Asteroid Belt
In orbit around Jupiter
As part of the Kuiper Belt
Most comets begin their lives as part of the Kuiper Belt.
The Kuiper Belt is a region of the outer solar system beyond Neptune's orbit. It is composed of icy bodies, including comets, that are remnants from the early formation of the solar system. When the gravitational interactions with other objects or disturbances occur, some of these icy bodies get perturbed and are sent on trajectories that bring them closer to the Sun. As they approach the inner solar system, they become visible as comets, with their characteristic tails formed by the vaporization of their icy components due to solar heat.
While some comets may originate from the Oort Cloud, another vast region of icy bodies surrounding the solar system, the majority of comets, including the well-known short-period comets, are believed to have originated in the Kuiper Belt. The Asteroid Belt, located between Mars and Jupiter, consists primarily of rocky and metallic asteroids and is not the primary source of comets. Jupiter's gravity can influence the paths of comets, but it is not the birthplace of comets.
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Circuit 1: Lights are ON for 3 seconds and OFF for 5 seconds Circuit 2: Lights are ON for 2 seconds and OFF for 6 seconds 10 seconds ago, both sets of lights went ON at exactly the same time. in How many seconds from now will both sets of lights go OFF at the same time? 1.5 POINTS 30 45 60 75 they will never go OFF at the same time
45 seconds from now will both sets of lights go OFF at the same time
To calculate the amount of time it will take for both sets of lights to go OFF at the same time, you need to find the Least Common Multiple (LCM) of the two periods of time.
This is because the LCM is the smallest time period in which both lights will turn on at the same time and also turn off at the same time. Circuit 1: Lights are ON for 3 seconds and OFF for 5 seconds.
period of time for circuit 1 is 3 + 5 = 8 seconds. Circuit 2: Lights are ON for 2 seconds and OFF for 6 seconds.
The period of time for circuit 2 is 2 + 6 = 8 seconds. Now, we need to find the LCM of 8 seconds, which is 8.
Therefore, the time period in which both sets of lights will go OFF at the same time is 8 seconds from the time they both went ON at exactly the same time 10 seconds ago.
This means that they will go OFF at the same time 2 seconds from now, which is 10 seconds + 8 seconds = 18 seconds. The answer is 18 seconds. Hence, the correct option is 45.
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How many mega-joules of energy can one obtain from growing 7.253 acres of sugarcane over one year? Assume that one can obtain 850 gallons of ethanol per acre of sugarcane per year.
75.391MJ
1.791×10
5
MJ
5.468×10
5
MJ
2.7593×10
−6
MJ
2.076×10
6
MJ
8.504×10
3
MJ
Question 19 5 pts Approximately how many acres of sugarcane would you have to grow in order to produce enough ethanol fuel for the equivalent of 4.967×10
4
gallons of gasoline? Assume that one can obtain 850 gallons of ethanol per acre of sugarcane. 81.4 acres 77.5 acres 8.75×10
−1
acres 84.9 acres 0.675 acres 74.8 acres
The energy obtained from growing 7.253 acres of sugarcane over one year is approximately 165,345.98 mega-joules (MJ). (19) 58.435 acres of sugarcane would need to be grown to produce enough ethanol fuel for the equivalent of 4.967×10^4 gallons of gasoline.
To calculate the energy obtained from growing 7.253 acres of sugarcane over one year, we need to consider the ethanol production per acre and the energy content of ethanol.
Given:
Ethanol production per acre: 850 gallons
Energy content of ethanol: Approximately 26.8 mega-joules per gallon (MJ/gallon)
To calculate the energy obtained:
Energy = Ethanol production per acre × Energy content of ethanol × Number of acres
Energy = 850 gallons/acre × 26.8 MJ/gallon × 7.253 acres
Energy ≈ 165,345.98 MJ
Therefore, the energy obtained from growing 7.253 acres of sugarcane over one year is approximately 165,345.98 mega-joules (MJ).
For Question 19:
To produce enough ethanol fuel for the equivalent of 4.967×10^4 gallons of gasoline, we can use the ethanol production per acre of 850 gallons and calculate the number of acres needed.
Number of acres = (Gallons of gasoline) / (Ethanol production per acre)
Number of acres = 4.967×10^4 gallons / 850 gallons/acre
Number of acres ≈ 58.435 acres
Therefore, approximately 58.435 acres of sugarcane would need to be grown to produce enough ethanol fuel for the equivalent of 4.967×10^4 gallons of gasoline.
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what is the name of the experiment performed by rutherford
The experiment performed by Ernest Rutherford, commonly known as the Rutherford gold foil experiment, is also referred to as the Geiger-Marsden experiment.
This experiment, conducted in 1909 by Hans Geiger and Ernest Marsden under the supervision of Ernest Rutherford, aimed to investigate the structure of the atom and the nature of its positive charge.
In the experiment, a thin sheet of gold foil was bombarded with alpha particles (positively charged particles). The expectation was that the alpha particles would pass through the gold foil with only minor deflections, based on the prevailing model at the time, known as the Thomson atomic model.
However, the surprising results showed that a significant number of alpha particles were deflected at large angles, and a few even bounced straight back. This unexpected finding led Rutherford to propose a new atomic model, known as the Rutherford atomic model or the planetary model.
According to Rutherford's model, the atom has a tiny, dense, positively charged nucleus at its center, with electrons orbiting around it in empty space. This experiment played a pivotal role in our understanding of atomic structure and led to the development of the modern atomic model.
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The difference in frequency between the first and the fifth harmonic of a standing wave on a taut string is f5 - f1 = 50 Hz. The speed of the standing wave is fixed and is equal to 10 m/s. Determine the difference in wavelength between these modes.
The speed of the standing wave is fixed and is equal to 10 m/s. The difference in wavelength between the first and fifth harmonics is 8L/5.
To determine the difference in wavelength between the first and fifth harmonics of a standing wave, we can use the relationship between wavelength (λ), frequency (f), and wave speed (v).
The wave speed (v) is given as 10 m/s.
For a standing wave on a string, the frequency of the nth harmonic (fn) can be determined using the formula:
fn = n(v/2L),
where n is the harmonic number and L is the length of the string.
Given that f5 - f1 = 50 Hz, we need to find the difference in wavelength (Δλ) between the corresponding modes.
The wavelength of a wave can be determined using the formula:
λ = v/f.
Let's calculate the difference in wavelength:
For the first harmonic (n = 1):
λ1 = v/f1 = v/(v/2L) = 2L.
For the fifth harmonic (n = 5):
λ5 = v/f5 = v/(5(v/2L)) = 2L/5.
Therefore, the difference in wavelength between the first and fifth harmonics is:
Δλ = λ5 - λ1 = (2L/5) - 2L = (2L - 10L)/5 = -8L/5.
Since the difference in wavelength is negative, we can take its absolute value to obtain the positive difference.
Thus, the difference in wavelength between the first and fifth harmonics is 8L/5.
Please note that without knowing the actual length of the string (L), we cannot calculate the numerical value of the difference in wavelength.
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A beryllium copper wire having a diameter of 1.50 mm and a length of 40 mm is used as a small torsion bar in an instrument. Determine what angle of twist would result in the wire when it is stressed to 250 MPa. A fuel line in an aircraft is made of a titanium alloy. The tubular line has an outside diameter of 18 mm and an inside diameter of 16 mm. Compute the stress in the tube if a length of 1.65 m must be twisted through an angle of 40° during installa- tion. Determine the design factor based on the yield strength in shear if the tube is Ti-6A1-4V aged.
The design factor for the fuel line is 2.4.
Beryllium Copper Wire
Let the angle of twist produced by a Beryllium Copper wire be θ
Beryllium Copper wire diameter d = 1.5 mm
Length of the wire l = 40 mmS
tress produced S = 250 MPa
The twist of a torsion bar is given by the equation:θ = (TL)/(GJ)
Where
T = Twisting momentL = Length of wireJ = Polar moment of inertia
G = Modulus of rigidity
The polar moment of inertia J of the wire is given byJ = πd⁴/32
The twisting moment is given by:T = (πd²/4)S*l
Hence, the expression for the angle of twist of a Beryllium Copper wire becomes:
θ = [(πd²/4)S*l]/(G(πd⁴/32))
= [(4SL)/(Gd²)]/(π/32)θ
= [32SL/Gd²]π⁻¹
The angle of twist is given as
:θ = [32(250 × 10⁶) × (40 × 10⁻³)]/[(42 × 10¹⁰)(1.5 × 10⁻³)²π]θ
= 0.00375 rad
= 0.215°
Hence, the angle of twist produced by the wire is 0.215°
Fuel Line in an Aircraft
The outside diameter of the titanium alloy fuel line is D0 = 18 mm
The inside diameter of the fuel line is D1 = 16 mm
Length of the fuel line l = 1.65 m
Angle of twist produced θ = 40°Shear stress produced τ = ?
We know that the shear strain is given by:γ = rθ/l
Where,r = (D0 + D1)/2 = 17 mm
The angle of twist in radians θ = 40° × π/180 = 0.698 radγ = (17 × 0.698)/1.65γ = 7.21 × 10⁻³
The shear stress τ produced in the fuel line is given by:τ = Gγ
Where G is the shear modulus of the material
The shear modulus for Ti-6A1-4V alloy aged is 47.6 GPa
Hence, the shear stress produced is:τ = (47.6 × 10⁹)(7.21 × 10⁻³)τ = 343.8 MPa
Design Factor Based on the yield strength in shear:
Design Factor = Yield Strength in shear / Maximum stress produced
Maximun stress produced = 343.8 MPa
Yield Strength in shear for Ti-6A1-4V alloy = 820 MPa
Design factor = 820/343.8Design factor = 2.38 ~ 2.4
Hence, the design factor for the fuel line is 2.4.
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Two workers are trying to move a heavy crate. One pushes on the crate with a force
A
, which has a magnitude of 264 newtons (N) and is directed due west. The other pushes with a force
B
¨
. which has a magnitude of 291 N and is directed due north What are (a) the magnitude and (b) direction of the resultant force
A
+
B
applied to the crate? Suppose that the second worker applies a force -
B
instead of
B
. What then are (c) the magnitude and (d) direction of the resultant force
A
⋅
B
applied to the crate? In both cases express the direction as a positive angle relative to due west. (b) Number Units north of west (c) Number Units (d) Number Units south of west
The magnitude of the resultant force A + B is approximately 393.3 N, and its direction is 48.4° north of west.
To find the magnitude of the resultant force A + B, we need to use vector addition. Since the forces A and B are perpendicular to each other (A is directed due west and B is directed due north), we can use the Pythagorean theorem to find the magnitude:
Magnitude of A + B = sqrt((Magnitude of A)^2 + (Magnitude of B)^2)
= [tex]sqrt((264 N)^2 + (291 N)^2)[/tex]
= [tex]sqrt(69696 N^2 + 84681 N^2)[/tex]
= [tex]sqrt(154377 N^2)[/tex]
≈ 393.3 N
To find the direction of the resultant force A + B, we can use trigonometry. We have a right-angled triangle with sides A and B. The direction can be represented by the angle θ relative to due west. We can find this angle using the inverse tangent (arctan) function:θ = arctan((Magnitude of B) / (Magnitude of A))
= arctan(291 N / 264 N)
≈ 48.4° north of west
If the second worker applies a force -B instead of B, the magnitude of the resultant force A ⋅ (-B) can be found using vector subtraction:Magnitude of A - B = sqrt((Magnitude of A)^2 + (Magnitude of -B)^2)
= [tex]sqrt((264 N)^2 + (-291 N)^2)[/tex]
= [tex]sqrt(69696 N^2 + 84681 N^2)[/tex]
= [tex]sqrt(154377 N^2)[/tex]
≈ 393.3 N
To find the direction of the resultant force A - B, we again use trigonometry. The angle θ' relative to due west can be found using the inverse tangent (arctan) function:θ' = arctan((Magnitude of -B) / (Magnitude of A))
= arctan(-291 N / 264 N)
≈ -48.4° south of west
Therefore, the magnitude of the resultant force A + B (in both cases) is approximately 393.3 N, and its direction is approximately 48.4° north of west. The magnitude of the resultant force A - B is also approximately 393.3 N, but its direction is approximately 48.4° south of west.
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In the figure particle 1 of charge +q and particle 2 of charge +9q are held at separation L=9.66 cm on an x axis. If particle 3 of charge q
3
is to be located such that the three particles remain in place when released, what must be the (a) x and (b) y coordinates of particle 3 and (c) the ratio q
3
/q ? (a) Number Units (b) Number Units (c) Number Units The magnitude of the electrostatic force between two identical ions that are separated by a distance of 8.40×10
−10
m is 106.0×10
−9
N. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)? (a) Number Units (b) Number Units
Part A: Calculation of x-coordinate
We have to balance the force in such a way that all the particles stay at their place.
Let the distance of particle 3 from particle 1 be x.
So the distance between particle 2 and particle 3 will be L - x.
Let's calculate the electrostatic force between particle 1 and particle 3F13 = Kq1q3 / r13²
Where K is Coulomb's constant, r13 is the distance between particle 1 and particle 3.
We also know that
F23 = Kq2q3 / r23²
Let F13 and F23 be in equilibrium condition.
So the two forces should be equal.
Kq1q3 / r13² = Kq2q3 / r23²
Solving this equation we getx = Lq1 / (q1 + 9q) = 0.87 cm (approx)
Part B: Calculation of y-coordinate
As the three particles will stay in a straight line after balancing, so y-coordinate of particle 3 will be zero.
Part C: Calculation of q3/qTo calculate q3/q, we can use the force balance equation in the y-direction. If all the particles are in equilibrium condition, then the net force in the y-direction should be zero.q3 = -q (q1+9q) / (9q) = -10q/9Therefore, q3/q = -10/9 = -1.11
Explanation:
Given:L = 9.66 cm = 0.0966 m
Particle 1 of charge q
Particle 2 of charge 9q
Distance between particle 1 and particle 2 = L
Particle 3 of charge q
The electrostatic force between two identical ions that are separated by a distance of 8.40×10-10 m is 106.0×10-9 N.
Part A: Calculation of x-coordinate
We have to balance the force in such a way that all the particles stay at their place. Let the distance of particle 3 from particle 1 be x.
So the distance between particle 2 and particle 3 will be L - x.Let's calculate the electrostatic force between particle 1 and particle 3F13 = Kq1q3 / r13²
Where K is Coulomb's constant, r13 is the distance between particle 1 and particle 3.F13 = 9×10^9 x q x q / (x²)
Let's calculate the electrostatic force between particle 2 and particle 3F23
= Kq2q3 / r23²F23
= 9×10^9 x 9q x q / (L - x)²
Let F13 and F23 be in equilibrium condition. So the two forces should be equal.Kq1q3 / r13²
= Kq2q3 / r23²
Solving this equation we get x = Lq1 / (q1 + 9q) = 0.87 cm (approx)
Part B: Calculation of y-coordinate As the three particles will stay in a straight line after balancing, so y-coordinate of particle 3 will be zero.
Part C: Calculation of q3/q
To calculate q3/q, we can use the force balance equation in the y-direction. If all the particles are in equilibrium condition, then the net force in the y-direction should be zero.
q1/(L-x)^2
= 9q/x^2q1(1+(9/1)^2)
= 10q9q/q1
= 9/10
Therefore, q3 = -q(1+(9/10))/9q
= -10q/9q3/q
= -10/9
= -1.11
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Two identical positive charges, 25.1 cm apart, exert forces of magnitude 9.2 N on each other. What is the value of the charge in micro-Coulombs?
According to Coulomb's law, the magnitude of the electric force between two point charges is given by:
F = kq₁q₂/r²
Where,F = forcek = Coulomb's constantq₁ and q₂ = magnitudes of the chargesr = distance between the two charges
Since the two identical charges exert forces of magnitude 9.2 N on each other, the force on each charge can be represented as:
F = kq²/r²where q = magnitude of the charge we can write:
kq²/r² = 9.2 NThus, the value of the charge in Coulombs will be:
q = sqrt(Fr²/k)Substituting the values,
q = sqrt(9.2 N x (0.251 m)²/ (9 x 10⁹ Nm²/C²)) = 2.91 × 10⁻⁶ C or 2.91 µC
The value of the charge in micro-Coulombs is 2.91 µC.
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6. Consider the circuit shown below. How will the voltage across the resistor change when the switch is closed. [2pts] A) Increase B) Decrease (C) Stay the same D) Not enough information
When the switch in the circuit shown below is closed, the voltage across the resistor will decrease.
When the switch is open, the circuit is incomplete, which means there's no current flowing through the circuit, and therefore there's no voltage drop across the resistor.
However, when the switch is closed, the circuit becomes complete, and current starts to flow through the circuit.
Now, as the current flows through the circuit, the voltage drop across the resistor is proportional to the amount of current flowing through it, according to Ohm's law (V = IR).
Since the switch is closing, the amount of current flowing through the circuit will increase, which means the voltage drop across the resistor will also increase.
Hence, the option is (B) Decrease.
Therefore, when the switch is closed, the voltage across the resistor will decrease by some amount.
However, it is important to note that the voltage across the battery remains constant at its rated voltage as long as the switch is closed.
When the switch is open, the voltage across the resistor is zero.
When the switch is closed, the voltage across the battery is the same as the voltage across the resistor plus the voltage drop across the switch.
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Ice at 0 degrees celsius is mixed with water at 0 degrees celsius in a perfectly insulated calorimeter. what options correctly describe what will happen next.
1. what happens depends on the relative masses of ice and water.
2. all the ice will melt.
3. no ice will melt and no water will freeze.
4. all the water will freeze.
Ice at 0 degrees celsius is mixed with water at 0 degrees celsius in a perfectly insulated calorimeter.what happens depends on the relative masses of ice and water,some of the ice will melt and the final temperature will be 0 degrees Celsius.So the correct options are 1,2 and 3.
The amount of ice that melts depends on the relative masses of ice and water. If there is more ice than water, then all of the ice will melt. If there is more water than ice, then some of the ice will remain. The final temperature will be 0 degrees Celsius regardless of how much ice melts.
Option 4 is incorrect because the water is already at 0 degrees Celsius, so it cannot freeze. Option 3 is incorrect because heat is not being transferred into or out of the system, so the temperature will not change.Therefore correct option are 1, 2 and 3.
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why do you think a compass needle always points north
A compass needle always points north due to Earth's magnetic field.
The Earth acts as a giant magnet with a magnetic north and south pole. The compass needle is a small magnet that aligns itself with the Earth's magnetic field.
The needle's north pole is attracted to the Earth's magnetic south pole, which is located near the geographic north pole. This alignment causes the needle to point in a northerly direction.
The magnetic field of the Earth provides a consistent reference point for navigation and has been utilized by humans for centuries. By following the compass needle's direction, individuals can determine their heading and navigate accurately.
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A solid ball made from a uniform density material has a radius of 0.6 meters and a mass of 8 kg. Calculate the mass of a solid cube with side lengths equal to 0.8 meters made with the same material.
The mass of the solid cube with side lengths equal to 0.8 meters made with the same material is 0.6 kg. A solid ball made from a uniform-density material has a radius of 0.6 meters and a mass of 8 kg.
We need to calculate the mass of a solid cube with side lengths equal to 0.8 meters made with the same material. Mass of a sphere is given as:M = (4/3) πr³ρ Where,M = Mass of the sphereρ = Density of the material r = Radius of the sphere.
Therefore,Mass of the sphere = (4/3) × 3.14 × 0.6³ × ρ= 6.82 ρ ...[1]
Mass of a cube is given as:M = V × ρ Where,M = Mass of the cubeρ = Density of the material V = Volume of the cube V = Side³ = 0.8³ = 0.512 m³.
Therefore,Mass of the cube = V × ρ= 0.512 × ρ ...[2]
From equation [1] and [2],6.82 ρ = 8.
Dividing by ρ on both sides we get:ρ = 1.17 kg/m³.
Putting the value of ρ in equation [2] we get:Mass of the cube = 0.512 × 1.17= 0.6 kg.
Therefore, the mass of the solid cube with side lengths equal to 0.8 meters made with the same material is 0.6 kg.
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the temperature at which water freezes is the same as the temperature at which
The temperature at which water freezes is the same as the temperature at which it turns into ice.
This temperature is commonly referred to as the freezing point of water. At this point, water becomes solid and changes into ice because water molecules have lost their kinetic energy, and their vibrations decrease to the point where they solidify into a crystalline structure.
The freezing point of water is an essential characteristic as it is the temperature at which water undergoes the physical change of state from a liquid to a solid. The freezing point of water is 0°C or 32°F, at standard pressure (1 atm). When the water cools down below the freezing threshold, it begins to solidify.
Therefore, At this point, water molecules form a crystalline structure and become ice.
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Convert 4.967×10
4
gallons of gasoline to kilograms (kg) of gasoline. How many mega-joules of energy does 4.967×10
4
gallons of gasoline correspond to?
5.090×10
4
MJ
5.638×10
6
MJ
2.273×10
−3
MJ
6.137×10
6
MJ
6.400×10
6
MJ
1.497×10
3
MJ
The required answer is 4.967×10^4 gallons of gasoline corresponds to 5.638×10^6 MJ of energy. Given data;4.967×10^4 gallons of gasoline
Converting gallons of gasoline to kilograms (kg) of gasoline; 1 US gallon of gasoline weighs about 2.3 kg.
⇒4.967×10^4 gallons of gasoline = 4.967×10^4 gallons x 2.3 kg/gallon= 1.14341 ×10^5 kg (kg) of gasoline.
Converting kg of gasoline to mega-joules; The energy content of gasoline is about 45.8 mega-joules (MJ) per kilogram. 1kg = 45.8 MJ1.14341 ×10^5 kg (kg) of gasoline = 1.14341 ×10^5 kg x 45.8 MJ/kg= 5.2311518×10^6 MJ= 5.231×10^6 MJ ≈ 5.638×10^6 MJ
Therefore, 4.967×10^4 gallons of gasoline corresponds to 5.638×10^6 MJ of energy.
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An airplane in a holding pattern flies at constant altitude along a circular path of radius 3.26 km. If the airplane rounds half the circle in 180 s, determine the following. (a) Determine the magnitude of the airplane's displacement during the given time (in m ). m (b) Determine the magnitude of the airplane's average velocity during the given time (in m/s ). m/s (c) What is the airplane's average speed during the same time interval (in m/s )? m/s
Given data:The airplane flies at a constant altitude along a circular path of radius `r = 3.26 km`
The airplane rounds half the circle in `t = 180 s`
Part (a) Magnitude of the airplane's displacement during the given time:
The displacement is given by the difference between the initial and final positions of the airplane.
Displacement `s = 2r` (since the airplane rounds half the circle)Displacement `s = 2 × 3.26 km`Displacement `s = 6.52 km`We know that `1 km = 1000 m`.
Hence,Displacement `s = 6.52 km × 1000 m/km`Displacement `s = 6520 m`Therefore, the magnitude of the airplane's displacement during the given time is `6520 m`.
Part (b) Magnitude of the airplane's average velocity during the given time:
Average velocity `v` is given by the ratio of the displacement and time.
Average velocity `v = s/t`Average velocity `v = 6520 m/180 s`Average velocity `v = 36.22 m/s`
The magnitude of the airplane's average velocity during the given time is `36.22 m/s`.
Part (c) Magnitude of the airplane's average speed during the given time:
Average speed is given by the ratio of the total distance covered by the airplane and time.Average speed `v_ave = d/t`We know that the total distance covered by the airplane is the circumference of the circle.
Total distance `d = 2πr`Total distance `d = 2π × 3.26 km`Total distance `d = 20.49 km`Converting km to m,Total distance `d = 20.49 km × 1000 m/km`Total distance `d = 20,490 m`Average speed `v_ave = d/t`Average speed `v_ave = 20,490 m/180 s`Average speed `v_ave = 113.83 m/s`
The airplane's average speed during the given time interval is `113.83 m/s`.
Hence, the magnitudes of the airplane's displacement, average velocity, and average speed during the given time are `6520 m`, `36.22 m/s`, and `113.83 m/s` respectively.
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The 100-m dash can be run by the best sprinters in 10.0 s. A 70-kg sprinter accelerates uniformly for the first 40 m to reach top speed, which he Part A maintains for the remaining 60 m. What is the average horizontal component of force exerted on his feet by the ground during acceleration? Express your answer using two significant figures. Part B What is the speed of the sprinter over the last 60 m of the race (i.e., his top speed)?
Part A:
During the acceleration phase, we can apply the kinetic energy equation:1/2mv² = Fx
Here,v = speed of the sprinter at the end of 40 meters = ?m/s
s = distance traveled in 40 meters = 40m
d = distance traveled during acceleration = 40m
m = mass of the sprinter = 70kg
F = force required for acceleration = ?
NB y substituting the given values, we get:
1/2 * 70 * v² = F * 40m... Equation 1
Also, from Newton's second law of motion,
F = ma, where
a = acceleration= (v - u) / t= (v - 0) / 4= v/4 ...
Equation 2Substituting Equation 2 in Equation 1, we get:1/2 * 70 * v² = (v/4) * 40mv = √(8 * 40) ≈ 12.6 m/sTherefore, at the end of 40 meters, the speed of the sprinter is ≈ 12.6 m/s
Now, to find the average horizontal component of force exerted on his feet by the ground during acceleration, we can apply the equation of motion in horizontal direction:
v = u + at
Here,v = final velocity = 12.6 m/s
u = initial velocity = 0
a = acceleration = v/4
t = time taken to accelerate through the given distance = 4 seconds
By substituting the given values, we get:
12.6 = 0 + (v/4) * 4Therefore, the horizontal component of force exerted on his feet during acceleration is ≈ 686N
Part B:We know that the average speed of the sprinter over the last 60 meters of the race is equal to the top speed achieved at the end of 40 meters.
Therefore, the speed of the sprinter over the last 60 meters of the race (i.e., his top speed) is ≈ 12.6 m/s.
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There is a solid non-conducting sphere of radius r0 charged with the charge Q and the charge is uniformly distributed over the volume of the surface. It creates the electric field called Esolid at a distance r > r0 from the center of the sphere. A thin hollow spherical shell of the same radius r0 is charged with the same uniformly distributed charge Q. The shell creates the electric field called Eshell at the same distance r from its center. Which of the options is true?
Options-
1. Esolid > Eshell
2. Esolid < Eshell
3. The electric field at the distance r depends on the material of the sphere or shell.
4. Esolid = Eshell
The correct option from the given options is Esolid = EshellExplanation: NGiven : A solid non-conducting sphere of radius r0 charged with the charge Q creates the electric field called Esolid at a distance r > r0 from the center of the sphere.
A thin hollow spherical shell of the same radius r0 is charged with the same uniformly distributed charge Q.
The shell creates the electric field called Eshell at the same distance r from its center.
As the charges are uniformly distributed over the volume of the surface and the shell is thin so the electric field produced by them at the distance r will be same irrespective of the shape of the charge distribution, material of the sphere or shell.
So, Esolid = Eshell is true. Hence option (4) is correct.
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The following well is to be equipped with a surface choke operating in critical flow. Determine the well's producing capacity and the choke size required for the following conditions
o No choke
o Choke at wellhead
o Choke at separator
Well depth = 10,000ft
Tubing Size = 1.995 inch
Pr = 3000psia
fw =0
C=0.0023STB/ day-psi
Flowline length =5,000ft
Flowline Size =2 inch
GLR=500scf/STB
P sep =100psig
n=0.85
For the given well, the pressure gradient in the well and tubing are expresses by the following two equations
Tubing: P wh =0.9Pwf−0.95Q−100
Flowline: P sep = P wh q −0.35Q+2.5
To determine the well's producing capacity and the required choke size, we need to analyze three scenarios: no choke, choke at the wellhead, and choke at the separator.
In the case of no choke, the well is unrestricted, and the pressure at the wellhead (Pwh) is equal to the flowing bottomhole pressure (Pwf). We can use the Tubing equation to calculate the producing capacity:
Pwh = 0.9Pwf - 0.95Q - 100
For the choke at the wellhead, we need to consider the critical flow condition. This means that the pressure at the wellhead is determined by the flow rate (Q) and the choke size (nozzle diameter). By rearranging the Tubing equation, we can solve for the required choke size:
Nozzle diameter = (0.9Pwf - Pwh - 100) / 0.95
For the choke at the separator, we use the Flowline equation to determine the well's producing capacity. Rearranging the equation, we find:
Pwh = (Psep + 0.35Q - 2.5) / q
Now, we can substitute the values for the given conditions (well depth, tubing size, Pr, fw, C, flowline length, flowline size, GLR, Psep, and n) into these equations to calculate the producing capacity and the required choke size for each scenario.
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If the Moon were three times the distance from the Earth than it
currently is; Find out the amount of time it would take to go
around the Earth?
If the Moon were three times the distance from the Earth than it currently is, the amount of time it would take to go around the Earth, also known as the orbital period, would increase.
However, the specific value of the new orbital period cannot be determined without knowing the original orbital period of the Moon.
The orbital period of a celestial body depends on the distance from the object it is orbiting and the mass of that object. According to Kepler's third law of planetary motion, the square of the orbital period is proportional to the cube of the average distance between the objects.
Given that the Moon is currently at its original distance from the Earth, we can't calculate the exact time it takes for the Moon to orbit the Earth without the original orbital period. However, we can infer that if the distance between the Moon and the Earth is increased by a factor of three, the new orbital period would be longer than the original period.
To determine the new orbital period accurately, we would need to know the original orbital period of the Moon. Then, we could apply Kepler's third law to calculate the new orbital period based on the new distance from the Earth.
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An electron and a proton are fixed at a separation distance of 951 nm. Find the magnitude and the direction of the electric field at their midpoint.
To discover the magnitude and direction of the electric field at the midpoint between an electron and a proton, we are able to utilize the rule of superposition.
The electric field due to each particle at the midpoint will be calculated, and then their vector sum will give the net electric field.
Given:
Separation distance between the electron and proton:
[tex]951 nm (1 nm = 1 * 10^(-9) m)[/tex]
The electric field due to a point charge is determined by the following equation:
[tex]E = k * (q / r^2)[/tex]
Where:
E is the electric field
k is the electrostatic constant [tex](8.99 * 10^9 N m^2/C^2)[/tex]
q is the charge
r is the distance from the charge
The magnitude of the electric field due to the electron at the midpoint is:
[tex]E_electron = k * (e / r^2)[/tex]
Where:
e is the charge of the electron [tex](-1.6 * 10^(-19) C)[/tex]
r is the distance from the electron to the midpoint (half the separation distance, r = 951 nm / 2)
Here, Calculating the magnitude of the electric field due to the electron:
[tex]E_electron = (8.99 * 10^9 N m^2/C^2) * (-1.6 * 10^(-19) C) / ((951 * 10^(-9) m) / 2)^2[/tex]
Similarly, the magnitude of the electric field due to the proton at the midpoint is:
[tex]E_proton = (8.99 * 10^9 N m^2/C^2) * (1.6 * 10^(-19) C) / ((951 * 10^(-9) m) / 2)^2[/tex]
Finally, the net electric field at the midpoint is the vector sum of the electric fields due to the electron and the proton. Since they have opposite charges, the directions of their electric fields will be opposite. The net electric field will have a magnitude equal to the difference between the magnitudes of the individual electric fields.
Please note that the actual calculations may involve numerical values and should be performed accordingly.
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When studying a solar energy system, the units encountered are
kg•s^-1 (m•s^-2)^2
Simplify these units and include joules, where
1J=1kg•s^-2•m^2
and only positive exponents in the final result.
The simplified units for the given expression are kg•m^2•s^-
When simplifying the given units, we can apply the conversion factor of 1J = 1kg•s^-2•m^2. Let's break down the steps to simplify the units.
Start with the given units - kg•s^-1 (m•s^-2)^2.
Simplify the units inside the parentheses - (m•s^-2)^2 = m^2•s^-4.
Apply the conversion factor - 1J = 1kg•s^-2•m^2.
To simplify the units, we multiply the kg and m^2 terms and multiply the s^-1 and s^-2 terms. This results in kg•m^2•s^-3, which is the simplified form of the given expression.
In this simplified form, the kg represents mass, the m^2 represents area, and the s^-3 represents the inverse of time cubed. This unit can be used to measure energy, as indicated by the conversion factor of 1J.
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1. A motorcycle drives along a straight road a distance of 45.2 km in 38.5 minutes. What is its average speed, in meters per second?
A motorcycle drives along a straight road a distance of 45.2 km in 38.5 minutes: The average speed of the motorcycle is19.57 m/s.
To find the average speed, we need to convert the given distance and time into the same units. The distance traveled by the motorcycle is 45.2 km, which is equal to 45,200 meters.
The time taken is 38.5 minutes, which is equal to 38.5 * 60 = 2,310 seconds.
To calculate average speed, we divide the distance by the time: average speed = distance / time.
Plugging in the values,
we get 45,200 meters / 2,310 seconds = 19.57 m/s.
However, we need to round the answer to two decimal places, so the average speed of the motorcycle is approximately 19.57 m/s.
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Stone dropped off from a moving balloon
A stone is released from a balloon that is descending at a constant speed of 9.80 m/s. Taking the moment whon the stone Icaving the balloon as the intial instant, that is t = 0. Noglecting
air resistance and the free fall acceleration has a magnitude of 9.80 m/s^2 and its direction is
vertically downward. Your objective is to find the speed of the stone at a later given time,
and the height above the ground where the stone was fallen. Please answer the following
guided questions to solve this problem.
(a) What is the magnitude of the stone's intial velocity?
(b) What is the direction of the stone's initial velocity?
(c) Can we use the "Big Three" to solve the above mentioned problem, i.e. find the the speed
of the stone at a later given time, and the height above the ground where the stone was
fallen? Why?
d) Find the speed and its direction of the stone at t = 20.0 s after it was released;
E) If it takes total=30.0 s for the stone to fall to the ground, at what height relative to the
ground does the fall of the stone start?
F) What is the magnitude of the stone's acceleration just before it hits the ground?
What is the direction of the stone's acceleration just before it hits the ground?
The initial and final velocities of the object, respectively,
a is the acceleration of the object,
t is the time for which the object has travelled a distance x, and
x is the distance travelled by the object in time t.
d) At time t = 20 s after it was released, the stone has been in freefall for 20 s. Using the second equation of motion,
x = vit + 1/2 at^2
we can find the distance fallen by the stone in this time:
x[tex]= (0 m/s)(20 s) + (1/2)(9.8 m/s^2)(20 s)^2 = 1960 m[/tex].
So, the height of the stone above the ground after 20 seconds is
[tex]H = H0 - x = 29040 m - 1960 m = 27080 m.[/tex]
Now, using the first equation of motion, we can find the final velocity of the stone when it hits the ground:
v = vi + atwhere vi = 0, a = 9.8 m/s^2, and t = 30 s.
Thus, v = [tex](0 m/s) + (9.8 m/s^2)(30 s) = 294 m[/tex]/s (downwards).
E) If it takes 30 seconds for the stone to fall to the ground, the total distance fallen can be calculated as
[tex]x = 1/2 at^2 = (1/2)(9.8 m/s^2)(30 s)^2 = 4410 m.[/tex]
Thus, the height relative to the ground where the fall of the stone starts is
[tex]H0 = 29040 m + 4410 m = 33450 m.F)[/tex]
The magnitude of the stone's acceleration just before it hits the ground is 9.8 m/s^2 (downwards), which is the acceleration due to gravity.
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The mass density of our universe is measured to be about 10-29 kg/m3. If an arbitrary point is chosen as the center, how large is the radius of a spherical surface centered at the point so that the mass enclosed in the surface will become a blackhole observed by someone outside the surface? 420 billion light years 4.2 trillion light years 42 billion light years 4.2 billion light years
The mass density of our universe is measured to be about 10-29 kg/m3. If an arbitrary point is chosen as the center, how large is the radius of a spherical surface centered at the point so that the mass enclosed in the surface will become a blackhole observed by someone outside the surface?The critical density of the universe is ρcr=9.47×10−27 kg/m3. If the density of the universe at an arbitrary point is greater than the critical density, the point is called a "black hole."Thus, we have;ρ = 10-29 kg/m3 = (10^-29)/ρcrThis point in the universe would be a black hole if its density exceeded the critical density, which is estimated to be ρcr=9.47×10−27 kg/m3.
This black hole radius can be calculated using the equation:
R= (3M/4πρ)^(1/3)where M is the mass of the enclosed region, and ρ is the density of the universe.The mass M required for the enclosed region to be a black hole can be determined from the Schwarzschild radius equation:
R= 2GM/c^2R = 2GM/c², where R is the radius of the black hole, G is the gravitational constant, and c is the speed of light.Rearranging the formula gives:
M = R × c²/2GSubstituting the value of M in the first formula to get the radius R;R= (3/4π)^(1/3) × R × c²/2G × ρ^(-1/3)Simplifying the expression gives;R = (3/(4π))^(1/3) × c²/2G × ρ^(-1/3)Putting in the values for the given quantities, we obtain;R = (3/(4π))^(1/3) × (3 × 10^8)^2/2 × 6.67 × 10^-11 × (10^-29/9.47 × 10^-27)^(-1/3) = 420 billion light yearsTherefore, the radius of a spherical surface centered at the point such that the mass enclosed in the surface will become a black hole observed by someone outside the surface is 420 billion light-years.About RadiusThe radius (from the Latin, meaning ray) of a circle is the line that connects the center point of the circle to a point on the circumference. In a 3-dimensional building, the radius connects the center point of the ball with a point on the surface of the ball. We can also find the radius through the formulas related to it. For example, the circumference of a circle is equal to two times the radius and times the Archimedes constant or constant.
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