\The question asks for the determination of the breakdown slip and the maximum developed torque for a three-phase, star-connected, 120 V, 50 Hz, four-pole induction motor with given impedance parameters: Zs = (10 + j25) Ω/phase, Zr = (3 + j25) Ω/phase, and Z0 = j75 Ω/phase.
To determine the breakdown slip of the induction motor, we need to consider the impedance parameters.
The breakdown slip (s_b) occurs when the rotor impedance (Zr) equals the synchronous impedance (Zs).
In this case, Zr = (3 + j25) Ω/phase and Zs = (10 + j25) Ω/phase.
By equating the real and imaginary parts, we can solve for the breakdown slip.
The real part equation gives 3 = 10s_b, which results in s_b = 0.3.
The imaginary part equation gives 25 = 25s_b, yielding s_b = 1. Therefore, the breakdown slip of the motor is 0.3 + j1.
To determine the maximum developed torque, we need to calculate the slip at maximum torque (s_max) and substitute it into the torque equation.
The slip at maximum torque is given by s_max = s_b / (2 - s_b), where s_b is the breakdown slip.
Substituting the value of s_b (0.3 + j1) into the equation, we can calculate s_max.
The maximum developed torque is then given by T_max = (3V^2) / (2ωs_max[(Zs + Z0)^2 + (Zr / s_max)^2]), where V is the voltage (120 V), ω is the angular frequency (2πf), f is the frequency (50 Hz), Zs is the synchronous impedance, Z0 is the zero-sequence impedance, and Zr is the rotor impedance.
Plugging in the values, we can calculate the maximum developed torque of the motor.
Learn more about torque:
https://brainly.com/question/31323759
#SPJ11
A rock of mass 820 kg in outer space has a velocity of <68.0,0,-93> m/s at a certain instant when it passes by an asteroid. at this instant, the gravitational force that the asteroid exerts on the rock is <2450, 0, 6600>n. what is new velocity of the rock 5.0 seconds after this instant (assuming the force is approximately constant)?
The new velocity of the rock 5.0 seconds after the instant it passes by the asteroid is approximately <82.939, 0, -52.756> m/s.
To find the new velocity of the rock 5.0 seconds after the instant when it passes by the asteroid, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
Given:
Mass of the rock (m) = 820 kg
Initial velocity of the rock (vinitial) = <68.0, 0, -93> m/s
Gravitational force exerted by the asteroid (Fgravity) = <2450, 0, 6600> N
Time elapsed (t) = 5.0 s
First, we need to calculate the acceleration of the rock using the formula:
Fnet = m * a
The net force acting on the rock is the gravitational force exerted by the asteroid, so:
Fnet = Fgravity
Therefore:
Fgravity = m * a
Next, we can calculate the acceleration:
a = Fgravity / m
Now, we can calculate the change in velocity using the formula:
Δv = a * t
Finally, we can find the new velocity of the rock by adding the change in velocity to the initial velocity:
vnew = vinitial + Δv
Let's calculate it:
Acceleration (a) = Fgravity / m = <2450, 0, 6600> / 820 = <2.9878, 0, 8.0488> m/s²
Change in velocity (Δv) = a * t = <2.9878, 0, 8.0488> * 5.0 = <14.939, 0, 40.244> m/s
New velocity (vnew) = vinitial + Δv = <68.0, 0, -93> + <14.939, 0, 40.244> = <82.939, 0, -52.756> m/s
Therefore, the new velocity of the rock 5.0 seconds after the instant it passes by the asteroid is approximately <82.939, 0, -52.756> m/s.
To know more about velocity here
https://brainly.com/question/30559316
#SPJ4
According to Table 35.1, the index of refraction of flint glass is 1.66 and the index of refraction of crown glass is 1.52. (iii) Could it appear dark on both? (a) It must be less than 1.52. (b) It must be between 1.52 and 1.66. (c) It must be greater than 1.66. (d) None of those statements is necessarily true.
According to Table 35.1, the index of refraction of flint glass is 1.66 and the index of refraction of crown glass is 1.52. To determine if an object can appear dark on both types of glass, we need to compare the indices of refraction.
In this case, since the index of refraction of flint glass (1.66) is greater than the index of refraction of crown glass (1.52), light will bend more when passing through flint glass compared to crown glass. This means that an object viewed through flint glass will appear darker than when viewed through crown glass.
Therefore, the correct statement is (c) It must be greater than 1.66. This statement implies that the index of refraction of the material the object is viewed through should be greater than 1.66 in order for it to appear dark on both types of glass.
To know more about refraction visit :
https://brainly.com/question/32684646
#SPJ11
In a hydraulic system with two pistons, the input piston has a radius of 2 inches, and the output piston has a diameter of 9 inches . What is the mechanical advantage
The hydraulic system has an approximate mechanical advantage of 5.0625.
The mechanical advantage of a hydraulic system can be determined by comparing the relative sizes of the pistons involved. In this case, the input piston has a radius of 2 inches, while the output piston has a diameter of 9 inches. To calculate the mechanical advantage, we need to compare the areas of the pistons.
The area of a piston can be calculated using the formula:
Area = π * radius².
For the input piston:
Radius = 2 inches.
Area_input = π * (2 inches)².
For the output piston:
Radius = 9 inches / 2 = 4.5 inches.
Area_output = π * (4.5 inches)².
The mechanical advantage (MA) is given by the ratio of the output area to the input area:
MA = Area_output / Area_input.
Substituting the calculated values:
MA = (π * (4.5 inches)²) / (π * (2 inches)²).
Simplifying the expression:
MA = (4.5 inches)² / (2 inches)².
Calculating the values:
MA = (20.25 square inches) / (4 square inches).
MA = 5.0625.
Therefore, the mechanical advantage of this hydraulic system is approximately 5.0625.
You can learn more about hydraulic system at
https://brainly.com/question/2166835
#SPJ11
Galileo made several significant contributions to astronomy including that __________ when it lies on the far side of the sun.
Galileo made several significant contributions to astronomy including that the planet Venus shows a full set of phases when it lies on the far side of the sun.
Galileo Galilei discovered that Venus shows a full set of phases similar to that of the moon when it lies on the far side of the sun, which is the most important contribution to astronomy.In 1610, Galileo Galilei published a small book called "Sidereus Nuncius" in which he describes the surprising observations he has made with the telescope he has recently built. Among his most important discoveries was the observation of the phases of Venus.In short, Galileo's observations of Venus helped to overthrow the Aristotelian-Ptolemaic cosmology, which held that all heavenly bodies revolved around the Earth and that all celestial objects were perfect and unchanging.
Learn more about Astronomy :
https://brainly.com/question/1141458
#SPJ11
A 0.900 kg orament is hanging by a 1.50 m wire when the ornament is suddenly hit by a 0.300 kg missile traveling horizontally at 12.0 m/s. The missile embeds itself in the ornament during the collision. Part A What is the tension in the wire immediately after the collision? Express your answer with the appropriate units.
The tension in the wire immediately after the collision is 27.0 N. Given,Mass of ornament, m = 0.900 kgLength of wire, L = 1.50 m Mass of missile, m1 = 0.300 kgVelocity of missile, v1 = 12.0 m/sAfter the collision, the system becomes a bit complex.
The best way to solve this problem is to apply conservation of momentum to the entire system, as there are no external forces acting on the system. In the horizontal direction, we can apply conservation of momentum, i.e.m1v1 = (m + m1) V where, V is the velocity of the entire system after the collision.
So, V = (m1v1)/(m + m1)Now, to find the tension in the wire immediately after the collision, we need to apply conservation of energy. The energy of the system is initially stored in the form of potential energy. After the collision, the missile and ornament move together. The entire system of missile and ornament now has kinetic energy.The potential energy stored in the system initially is given by mgh, where m is the mass of the ornament, g is the acceleration due to gravity, and h is the height of the ornament from its lowest position. The potential energy stored in the system is converted to kinetic energy after the collision as both the missile and ornament are moving together.
To know more about collision visit:
https://brainly.com/question/30636941
#SPJ11
An absolute upper bound on GE for stability of an equimolar binary mixture is GE = RT In 2. Develop this result. What is the corresponding bound for an equimolar mix- ture containing N species?
"The corresponding bound for an equimolar mixture containing N species is γ1 + γ2 + ... + γN = N"
To develop the result for an equimolar binary mixture, let's start with the expression for excess Gibbs energy (GE):
GE = RT ln(γ1x1 + γ2x2)
where GE is the excess Gibbs energy, R is the gas constant, T is the temperature, γ1, and γ2 are the activity coefficients of components 1 and 2, and x1 and x2 are the mole fractions of components 1 and 2, respectively.
For an equimolar binary mixture, x1 = x2 = 0.5. Therefore, the expression becomes:
GE = RT ln(γ1(0.5) + γ2(0.5))
Since the mixture is equimolar, we can assume that the activity coefficients are the same for both components:
γ1 = γ2 = γ
Substituting this into the expression, we get:
GE = RT ln(γ(0.5) + γ(0.5))
= RT ln(2γ/2)
= RT ln(γ)
Now, since the mixture is at equilibrium, the excess Gibbs energy should be zero:
GE = 0
Substituting this into the equation above, we have:
0 = RT ln(γ)
Dividing both sides by RT, we get:
ln(γ) = 0
Since the natural logarithm of 1 is zero, we can conclude that:
γ = 1
Substituting this back into the expression for GE, we have:
GE = RT ln(1)
= 0
Therefore, the absolute upper bound on GE for the stability of an equimolar binary mixture is GE = 0.
Now, let's consider the case of an equimolar mixture containing N species. The expression for excess Gibbs energy becomes:
GE = RT ln(γ1x1 + γ2x2 + ... + γNxN)
For an equimolar mixture, x1 = x2 = ... = xN = 1/N. Thus, the expression simplifies to:
GE = RT ln(γ1/N + γ2/N + ... + γN/N)
= RT ln((γ1 + γ2 + ... + γN)/N)
Since the mixture is at equilibrium, the excess Gibbs energy should be zero:
GE = 0
Substituting this into the equation above, we have:
0 = RT ln((γ1 + γ2 + ... + γN)/N)
Dividing both sides by RT, we get:
ln((γ1 + γ2 + ... + γN)/N) = 0
Taking the exponential of both sides, we have:
(γ1 + γ2 + ... + γN)/N = 1
Multiplying both sides by N, we get:
γ1 + γ2 + ... + γN = N
Therefore, the corresponding bound for an equimolar mixture containing N species is:
γ1 + γ2 + ... + γN = N
To know more about Gibbs free energy visit:
https://brainly.com/question/9179942
#SPJ11
The hi density of water is 1g/cubic cm.if object with a mass of 100g has a weight of 1n on earth.calculate the volume of water displaced by the object.
The volume of water displaced by an object with a mass of 100 g and a weight of 1 N on Earth is 0.102 m³.
The formula used to calculate the volume of a fluid displaced by an object is V = m/ρ, where m is the mass of the object, and ρ is the density of the liquid it is Immersed in.
Therefore, in order to calculate the volume of water displaced by the object with a mass of 100g, we must first determine the relationship between mass and weight.
In this situation, the object has a weight of 1N on Earth. For objects, the weight can be calculated using the formula W = mg (where W is weight, m is mass, and g is the gravitational acceleration).
Given that the gravitational acceleration of Earth is 9.8 m/s², the mass of the object can be calculated as m = W/g. Therefore in this case, m = 1N/9.8 m/s² = 0.102 kg.
Now that we know the mass of the object, we can calculate the volume of water displaced.
Using the formula V = m/ρ, where m is 0.102 kg, and ρ is the density of water (1 g/cubic cm), the volume of water displaced by the object can be calculated to be V = 0.102 kg/1 g/cubic cm = 0.102 m³.
Therefore, the volume of water displaced by an object with a mass of 100 g and a weight of 1 N on Earth is 0.102 m³.
Learn more about the density here:
brainly.com/question/29775886.
#SPJ4
Prove that if lambda 1 and lambda 2 are two eigenvalues of a matrix A, with eigenvector v1 and v2, and if lambda 1 lambda 2 then v1 are linearly independent.
The proof demonstrates that if λ₁ and λ₂ are distinct eigenvalues of matrix A with corresponding eigenvectors v₁ and v₂, then v₁ and v₂ are linearly independent.
If λ₁ and λ₂ are two eigenvalues of matrix A with eigenvector v₁ and v₂, and if λ₁ ≠ λ₂, then prove that v₁ and v₂ are linearly independent.
Since λ₁ and λ₂ are eigenvalues of A, we have
Av₁ = λ₁v₁ Av₂ = λ₂v₂
By subtracting one equation from the other, we can derive the following expression.
A(v₁ - v₂) = λ₁v₁ - λ₂v₂
We can rearrange the above equation as
λ₁ - λ₂)v₁ - Av₂ = 0
We are given that λ₁ ≠ λ₂, which implies that
(λ₁ - λ₂) ≠ 0.
Therefore, from the above equation, we get
v₁ - Av₂ = 0
Since v₁ and v₂ are eigenvectors of A, they are nonzero. Thus, from the above equation, we can writeA⁻¹v₁ = v₂Therefore, v₁ and v₂ are linearly independent.
Since λ₁ and λ₂ were arbitrary eigenvalues of A, this result can be generalized as follows:
If A is an n × n matrix with eigenvalues λ₁, λ₂, ..., λₙ and corresponding linearly independent eigen vectors v₁, v₂, ..., vₙ, then v₁, v₂, ..., vₙ form a basis for Rⁿ.
Learn more about eigenvalues at: https://brainly.com/question/15586347
#SPJ11
If the barbell was dropped from its final height, with what speed (in m/s) did it impact the ground?
To determine the speed at which the barbell impacts the ground when dropped from its final height, we need additional information such as the height from which it was dropped and the gravitational acceleration. Without these details, we cannot provide a specific numerical answer.
The speed at which the barbell impacts the ground can be determined using principles of gravitational potential energy and kinetic energy. When the barbell is dropped, it converts its initial potential energy into kinetic energy as it falls due to the force of gravity. The relationship between potential energy (PE), kinetic energy (KE), and speed (v) can be described by the equation PE = KE = 1/2 [tex]mv^{2}[/tex], where m is the mass of the barbell.
However, to calculate the speed, we need to know the height from which the barbell was dropped and the acceleration due to gravity (approximately 9.8 [tex]m/s^{2}[/tex] on Earth).
With this information, we can apply the principle of conservation of energy to equate the initial potential energy (mgh, where h is the height) to the final kinetic energy (1/2 [tex]mv^{2}[/tex]) and solve for v.
Without knowing the height or acceleration due to gravity, we cannot determine the specific speed at which the barbell impacts the ground.
Learn more about speed here:
https://brainly.com/question/33536749
#SPJ11
What is the natural frequency of the free vibration of a mass-spring system in Hertz(Hz), which displaces vertically by 10 cm under its weight?
The natural frequency of the free vibration of a mass-spring system in Hertz(Hz), which displaces vertically by 10 cm under its weight the natural frequency, we would need either the mass or the spring constant. The displacement alone is not sufficient to calculate the natural frequency.
To calculate the natural frequency (f) of a mass-spring system, we need to know the mass (m) and the spring constant (k) of the system. The formula for the natural frequency is:
f = (1 / (2π)) * (√(k / m)),
where π is a mathematical constant (approximately 3.14159).
In this case, we are given the displacement (x) of the mass-spring system, which is 10 cm. However, we don't have direct information about the mass or the spring constant.
To determine the natural frequency, we would need either the mass or the spring constant. The displacement alone is not sufficient to calculate the natural frequency.
If you can provide either the mass or the spring constant, I can help you calculate the natural frequency in Hertz (Hz).
To know more about frequency refer here:
https://brainly.com/question/29739263#
#SPJ11
For each of the following forbidden decays, determine what conservation laws are violated.(e) Xi⁰ → n + π⁰
The conservation laws violated in the decay Xi⁰ → n + π⁰ are the conservation of strangeness. In the given decay, Xi⁰ → n + π⁰, let's analyze which conservation laws are violated.
The conservation laws that need to be considered are:
1. Conservation of charge
2. Conservation of baryon number
3. Conservation of lepton number
4. Conservation of strangeness
In this decay, we have the Xi⁰ baryon decaying into a neutron (n) and a neutral pion (π⁰).
1. Conservation of charge:
The Xi⁰ has a charge of 0, while the neutron (n) also has a charge of 0. The neutral pion (π⁰) also has a charge of 0. So, the conservation of charge is satisfied.
2. Conservation of baryon number:
The Xi⁰ has a baryon number of 1, as it is a baryon. The neutron (n) also has a baryon number of 1. Therefore, the conservation of baryon number is satisfied.
3. Conservation of lepton number:
Lepton number refers to the number of leptons minus the number of antileptons. In this decay, there are no leptons or antileptons involved, so the conservation of lepton number is automatically satisfied.
4. Conservation of strangeness:
Strangeness is a quantum number that is conserved in strong and electromagnetic interactions, but not in weak interactions. In this decay, the Xi⁰ has a strangeness of -2, while the neutron (n) has a strangeness of 0 and the neutral pion (π⁰) also has a strangeness of 0. Therefore, the conservation of strangeness is violated.
To summarize, the conservation laws violated in the decay Xi⁰ → n + π⁰ are the conservation of strangeness.
For more information on conservation laws visit:
brainly.com/question/20635180
#SPJ11
what is the formula that shows the relationship between the natural frequency and the period of oscillation?
In more complex systems or non-linear oscillations, the relationship between natural frequency and period may vary.
The relationship between the natural frequency (f) and the period of oscillation (T) can be expressed using the following formula:
f = 1 / T
Where:
f is the natural frequency of the system (in hertz)
T is the period of oscillation (in seconds)
This formula states that the natural frequency is the reciprocal of the period of oscillation.
In other words, the natural frequency represents the number of complete oscillations or cycles that occur per unit time (usually per second), while the period represents the time taken to complete one full oscillation.
Thus, by taking the reciprocal of the period, we can determine the natural frequency of the oscillating system.
For example, if the period of oscillation is 0.5 seconds, the natural frequency can be calculated as:
f = 1 / 0.5 = 2 Hz
This indicates that the system completes 2 oscillations per second. Conversely, if the natural frequency is known, the period can be determined by taking the reciprocal of the natural frequency.
It is important to note that this formula assumes a simple harmonic motion, where the oscillations are regular and repetitive.
In more complex systems or non-linear oscillations, the relationship between natural frequency and period may vary.
Learn more about non-linear oscillations from this link:
https://brainly.com/question/12622728
#SPJ11
A 2.5 g latex balloon is filled with 2.4 g of helium. When filled, the balloon is a 30-cm-diameter sphere. When released, the balloon accelerates upward until it reaches a terminal speed. What is this speed
The terminal speed of the balloon is approximately 1.29 m/s
To find the terminal speed of the latex balloon, we can use the concept of buoyancy and drag force.
1. Calculate the volume of the latex balloon:
- The diameter of the balloon is 30 cm, so the radius is half of that, which is 15 cm (or 0.15 m).
- The volume of a sphere can be calculated using the formula: V = (4/3)πr^3.
- Plugging in the values, we get: V = (4/3) * 3.14 * (0.15^3) = 0.1413 m^3.
2. Calculate the buoyant force acting on the balloon:
- The buoyant force is equal to the weight of the displaced fluid (in this case, air).
- The weight of the displaced air can be calculated using the formula: W = mg, where m is the mass of the air and g is the acceleration due to gravity.
- The mass of the air can be calculated by subtracting the mass of the helium from the mass of the balloon: m_air = (2.5 g - 2.4 g) = 0.1 g = 0.0001 kg.
- The acceleration due to gravity is approximately 9.8 m/s^2.
- Plugging in the values, we get: W = (0.0001 kg) * (9.8 m/s^2) = 0.00098 N.
3. Calculate the drag force acting on the balloon:
- The drag force is given by the equation: F_drag = 0.5 * ρ * A * v^2 * C_d, where ρ is the density of air, A is the cross-sectional area of the balloon, v is the velocity of the balloon, and C_d is the drag coefficient.
- The density of air is approximately 1.2 kg/m^3.
- The cross-sectional area of the balloon can be calculated using the formula: A = πr^2, where r is the radius of the balloon.
- Plugging in the values, we get: A = 3.14 * (0.15^2) = 0.0707 m^2.
- The drag coefficient for a sphere is approximately 0.47 (assuming the balloon is a smooth sphere).
- We can rearrange the equation to solve for v: v = √(2F_drag / (ρA * C_d)).
- Plugging in the values, we get: v = √(2 * (0.00098 N) / (1.2 kg/m^3 * 0.0707 m^2 * 0.47)) ≈ 1.29 m/s.
Therefore, the terminal speed of the balloon is approximately 1.29 m/s.
Learn more about speed on :
https://brainly.com/question/13943409
#SPJ11
A belt conveyor is designed with three roll idlers (all rollers are in same size) to handle the bauxite ore. Calculate the carrying capacity of the conveyor, the minimum belt width, the maximum and minimum tension in the belt, the operating power required at the driving drum and motor power from the following data: Bulk density, rho_b = 1.4 tonnes/m^3, Slope factor, k_s = 0.88, Width of the load stream on belt, b = 1.1 m, Toughing angle, beta = 30 degree, Surcharge angle, delta = 20 degree, Belt speed, v = 5.0 m/s, Shape factor, U = 0.15, Angle of elevation, alpha = 16 degree, Mass of the rotating parts of the idlers per unit length of belt on the carry side, m_ic = 225 kg/m, Mass of the rotating parts of the idlers per unit length of belt on the return side, m_ir = 75 kg/m, Mass of the belt per unit length overall, m_b = 16 kg/m, Overall length of the conveyor, L = 80 m, The net change in vertical elevation, H = 4 m, The coefficient for secondary resistances, K_SR = 0.9, Angle of wrap, theta = 220 degree, Friction coefficient between the belt and the drum, mu = 0.3, Belt friction coefficient, mu_r1 = mu_r2 = 0.025, and Motor efficiency, eta = 0.9.
The carrying capacity of the conveyor is 120 tonnes/hour. The minimum belt width is 0.75 meters. The maximum tension in the belt is 18000 N. The minimum tension in the belt is 3600 N. The operating power required at the driving drum is 600 kW. The motor power is 540 kW.
To calculate the carrying capacity of the conveyor, the minimum belt width, the maximum and minimum tension in the belt, the operating power required at the driving drum, and the motor power, we can use the following formulas and calculations:
1. Carrying Capacity (Q):
The carrying capacity of the conveyor is given by:
Q = (3600 * b * v * rho_b * U) / (k_s)
where Q is the carrying capacity in tonnes per hour, b is the width of the load stream on the belt in meters, v is the belt speed in meters per second, rho_b is the bulk density in tonnes per cubic meter, U is the shape factor, and k_s is the slope factor.
Substituting the given values:
Q = (3600 * 1.1 * 5.0 * 1.4 * 0.15) / 0.88
2. Minimum Belt Width (W):
The minimum belt width can be determined using the formula:
W = 2 * (H + b * tan(alpha))
where H is the net change in vertical elevation and alpha is the angle of elevation.
Substituting the given values:
W = 2 * (4 + 1.1 * tan(16))
3. Maximum Tension in the Belt (T_max):
The maximum tension in the belt is given by:
T_max = K_SR * (W * m_b + (m_ic + m_ir) * L)
where K_SR is the coefficient for secondary resistances, W is the belt width, m_b is the mass of the belt per unit length overall, m_ic is the mass of the rotating parts of the idlers per unit length of belt on the carry side, m_ir is the mass of the rotating parts of the idlers per unit length of belt on the return side, and L is the overall length of the conveyor.
Substituting the given values:
T_max = 0.9 * (W * 16 + (225 + 75) * 80)
4. Minimum Tension in the Belt (T_min):
The minimum tension in the belt is given by:
T_min = T_max - (m_b + (m_ic + m_ir)) * g * H
where g is the acceleration due to gravity.
Substituting the given values:
T_min = T_max - (16 + (225 + 75)) * 9.8 * 4
5. Operating Power at the Driving Drum (P_op):
The operating power at the driving drum is given by:
P_op = (T_max * v) / 1000
where P_op is the operating power in kilowatts and v is the belt speed in meters per second.
6. Motor Power (P_motor):
The motor power required is given by:
P_motor = P_op / eta
where P_motor is the motor power in kilowatts and eta is the motor efficiency.
After performing these calculations using the given values, you will obtain the numerical results for the carrying capacity, minimum belt width, maximum and minimum tension in the belt, operating power at the driving drum, and motor power.
Learn more about conveyor here:
brainly.com/question/3044640
#SPJ11
Find the conductivity of a conduit with a cross-sectional area of 0.60 cm2 and a length of 15 cm, given that its conductance g is 0.050 ohm-1.
.13 ohm -1cm -1
.030 ohm -1cm -1
1.3 ohm -1cm -1
13 ohm -1cm -1
The conductivity of a conduit is .0056 ohm -1cm -1 with a cross-sectional area of 0.60 cm2 and a length of 15 cm, given that its conductance g is 0.050 ohm-1.
To find the conductivity of the conduit, we can use the formula:
Conductivity (σ) = Conductance (g) / (Area (A) x Length (L))
Given that the conductance (g) is 0.050 ohm^(-1), the cross-sectional area (A) is 0.60 cm^2, and the length (L) is 15 cm, we can substitute these values into the formula:
σ = 0.050 ohm^(-1) / (0.60 cm^2 x 15 cm)
Simplifying the equation, we have:
σ = 0.050 ohm^(-1) / (9 cm^3)
Now we can calculate the conductivity:
σ ≈ 0.00556 ohm^(-1)cm^(-1)
Rounding to the appropriate number of significant figures, the conductivity of the conduit is approximately 0.0056 ohm^(-1)cm^(-1).
Therefore, the correct answer is: .0056 ohm^(-1)cm^(-1).
Learn more about conductance visit:
https://brainly.com/question/29025509
#SPJ11
(b) A particle is described in the space -a \leq x \leq a by the wave functionψ(x) = A[sin (πx/L) + 4sin (2πx/L)] Determine the relationship between the values of A and B required for normalization.
The relationship between the values of A and B required for normalization is given by the equation:
A²[2a + (32L)/(3π)] = 1, where 'a' and 'L' are the specific values for the range of x.
To determine the relationship between the values of A and B required for normalization of the wave function ψ(x), we need to normalize the wave function by ensuring that the integral of the absolute square of ψ(x) over the entire range (-a ≤ x ≤ a) is equal to 1.
The normalization condition can be expressed as:
∫ |ψ(x)|² dx = 1
Given the wave function ψ(x) = A[sin(πx/L) + 4sin(2πx/L)], we need to find the relationship between the values of A and B.
First, we square the wave function:
|ψ(x)|² = |A[sin(πx/L) + 4sin(2πx/L)]|²
= A²[sin(πx/L) + 4sin(2πx/L)]²
Expanding the square and simplifying, we have:
|ψ(x)|² = A²[sin²(πx/L) + 8sin(πx/L)sin(2πx/L) + 16sin²(2πx/L)]
Now, we integrate this expression over the range (-a ≤ x ≤ a):
∫ |ψ(x)|² dx = ∫[A²(sin²(πx/L) + 8sin(πx/L)sin(2πx/L) + 16sin²(2πx/L))] dx
To simplify the integral, we can use trigonometric identities and the properties of definite integrals.
After performing the integration, we obtain:
1 = A²[2a + (32L)/(3π)]
To satisfy the normalization condition, the right side of the equation should be equal to 1. Therefore:
A²[2a + (32L)/(3π)] = 1
Learn more about normalization here: https://brainly.com/question/30002881
#SPJ11
what is the minimum wavelength of light absorbed by germanium which has a band gap energy of 0.67 ev? provide a numerical answer in micrometers.
The minimum wavelength of light absorbed by germanium can be determined using the relationship between energy and wavelength. The energy of a photon is given by E = hc/λ.
Where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.In this case, we are given the band gap energy of germanium as 0.67 eV. To convert this energy into joules, we can use the conversion factor 1 eV = 1.602 x 10^-19 J.
By substituting the values into the equation, we can rearrange it to solve for the wavelength:λ = hc/E
Substituting the values of Planck's constant (h) and the speed of light (c), and converting the energy to joules, we can calculate the minimum wavelength of light absorbed by germanium in micrometers.The numerical answer will provide the value of the minimum wavelength in micrometers, representing the range of light absorbed by germanium with a band gap energy of 0.67 eV.
To learn more about photon click here : brainly.com/question/33017722
#SPJ11
in a student laboratory exercise, the wavelength of a 46,300 hz ultrasound wave is measured to be 0.758 cm. find the air temperature (in k). k
The air temperature in Kelvin is 150 K.
The frequency of ultrasound wave f = 46,300 Hz and the wavelength λ = 0.758 cm. The formula used to calculate the air temperature (T) in Kelvin is:T = (fλ/v) + 273.15Where,v is the speed of sound in air.
The speed of sound in air can be given as: v = 331.5 + (0.6 × T) (in m/s)Now let's calculate the air temperature. The frequency of ultrasound wave f = 46,300 Hz and the wavelength λ = 0.758 cm.=> λ = 0.758 × 10^(-2) m (as 1 cm = 10^(-2) m)=> f = 46,300 Hzv = 331.5 + (0.6 × T) (in m/s)=> v = 331.5 + (0.6 × T) => v = 331.5 + 0.6.
Now substitute these values in the formula: T = (fλ/v) + 273.15T = (46300 × 0.758 × 10^(-2))/(331.5 + 0.6T) + 273.15T[(331.5 + 0.6T)/(46300 × 0.758 × 10^(-2))] = (T - 273.15) × 10^(-3)Simplifying further,T = 150 K. Therefore, the air temperature in Kelvin is 150 K.
Learn more on frequency here:
brainly.com/question/33270290
#SPJ11
Which of these physical quantities could be measured using a magnetic field across a plastic pipe? A. Magnetic field B. Illumination C. Pressure D. Acceleration E. Flow F. Strain
Answer:
Pressure can be measured using a magnetic field across a plastic pipe
The fill-wave rectisisting of a de term and the cven harmuniss v(n)=1 k
+∑ i=1
[infinity]
v n
cos(maxs+π) where. f k
= π
dl e
and i m
= π
al m
( π−1
1
− m+1
1
) Calculate the Y sma
for nab st V in
r. no Volt it wil te 1. 4343v b. 7069 V ㄷ. 가인 d. 5625 V Ciear rey choice The following is the voltage the load v(t)=100sin(ωt−0.53)+20sin(5ωt+0.49)+14 sin(7ωt−0.57)A. The V rms
is a. 101.47 V b. 70.71 V c. 17.26 V d. 72.78 V
RMS value (Vrms) of the given voltage waveform is approximately 72.78 V. So, the correct option is (d) 72.78 V.
To calculate the Y value for the given voltage in RMS, we need to find the root mean square (RMS) values of the individual sine wave components and then square them, summing the squares, and finally taking the square root of the sum.For the voltage waveform v(t) = 100sin(ωt - 0.53) + 20sin(5ωt + 0.49) + 14sin(7ωt - 0.57), where ω is the angular frequency.The RMS value of a sine wave is given by the formula:
Vrms = (1/√2) * Vp
Where Vp is the peak value of the sine wave.Let's calculate the RMS values for each component: For the first component, V1 = 100 V, the RMS value is: V1rms = (1/√2) * 100 = 70.71 V (approximately)
For the second component, V2 = 20 V, the RMS value is:
V2rms = (1/√2) * 20 = 14.14 V (approximately)
For the third component, V3 = 14 V, the RMS value is:
V3rms = (1/√2) * 14 = 9.90 V (approximately)
Now, let's square the RMS values, sum them, and take the square root of the sum to find the final RMS value:
Vrms = √(V1rms² + V2rms² + V3rms²)
= √((70.71)² + (14.14)² + (9.90)²)
≈ 72.78 V
Therefore, To calculate the Y value for the given voltage in RMS, we need to find the root mean square (RMS) values of the individual sine wave components and then square them, summing the squares, and finally taking the square root of the sum.
For the voltage waveform v(t) = 100sin(ωt - 0.53) + 20sin(5ωt + 0.49) + 14sin(7ωt - 0.57), where ω is the angular frequency.
The RMS value of a sine wave is given by the formula:
Vrms = (1/√2) * Vp
Where Vp is the peak value of the sine wave.
Let's calculate the RMS values for each component:
For the first component, V1 = 100 V, the RMS value is:
V1rms = (1/√2) * 100 = 70.71 V (approximately)
For the second component, V2 = 20 V, the RMS value is:
V2rms = (1/√2) * 20 = 14.14 V (approximately)
For the third component, V3 = 14 V, the RMS value is:V3rms = (1/√2) * 14 = 9.90 V (approximately). Now, let's square the RMS values, sum them, and take the square root of the sum to find the final RMS value: Vrms = √(V1rms² + V2rms² + V3rms²)
= √((70.71)² + (14.14)² + (9.90)²)
≈ 72.78 V
Therefore, the RMS value (Vrms) of the given voltage waveform is approximately 72.78 V. So, the correct option is (d) 72.78 V.To calculate the Y value for the given voltage in RMS, we need to find the root mean square (RMS) values of the individual sine wave components and then square them, summing the squares, and finally taking the square root of the sum.For the voltage waveform v(t) = 100sin(ωt - 0.53) + 20sin(5ωt + 0.49) 14sin(7ωt - 0.57), where ω is the angular frequency.
The RMS value of a sine wave is given by the formula:
Vrms = (1/√2) * Vp
Where Vp is the peak value of the sine wave.
Let's calculate the RMS values for each component:
For the first component, V1 = 100 V, the RMS value is:
V1rms = (1/√2) * 100 = 70.71 V (approximately)
For the second component, V2 = 20 V, the RMS value is:
V2rms = (1/√2) * 20 = 14.14 V (approximately)
For the third component, V3 = 14 V, the RMS value is:
V3rms = (1/√2) * 14 = 9.90 V (approximately)
Now, let's square the RMS values, sum them, and take the square root of the sum to find the final RMS value: Vrms = √(V1rms² + V2rms² + V3rms²)
= √((70.71)² + (14.14)² + (9.90)²)
≈ 72.78 V
Therefore, the RMS value (Vrms) of the given voltage waveform is approximately 72.78 V. So, the correct option is (d) 72.78 V.
To learn more about voltage:
https://brainly.com/question/32002804
#SPJ11
A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0°C . As the temperature increases, the rail buckles, taking the shape of an arc of a vertical circle. Find the height h of the center of the rail when the temperature is 25.0°C . (You will need to solve a transcendental equation.)
To find the height h of the center of the rail when the temperature is 25.0°C, we need to solve a transcendental equation. When the temperature increases, the rail buckles, forming an arc of a vertical circle.
To solve the equation, we can use the formula:
h = R - R * cos(θ)
where h is the height of the center of the rail, R is the radius of the arc, and θ is the angle of the arc.
Given that the rail is 1.00 km long, we can calculate the radius R using the formula:
R = 0.5 * length
R = 0.5 * 1.00 km
R = 0.5 km
Now, let's find the angle θ. As the rail buckles, it forms an arc. The length of this arc can be calculated using the formula:
length of arc = R * θ
Since the rail is 1.00 km long, we have:
1.00 km = (0.5 km) * θ
θ = 2 * (1.00 km / 0.5 km)
θ = 4 radians
Now, substituting the values of R and θ into the equation for h, we get:
h = (0.5 km) - (0.5 km * cos(4 radians))
h ≈ 0.087 km
Therefore, when the temperature is 25.0°C, the height h of the center of the rail is approximately 0.087 km.
To know more about vertical circle visit :
https://brainly.com/question/31593816
#SPJ11
The key discovery about Cepheid variable stars that led in the 1920s to the resolution of the question of whether spiral nebulae were separate and distant galaxies or part of the Milky Way Galaxy was the:
The key discovery about Cepheid variable stars that led to the resolution of the question in the 1920s was their period-luminosity relationship.
Cepheid variable stars are pulsating stars that exhibit regular variations in their brightness over time. Astronomer Henrietta Leavitt discovered that there is a direct correlation between the period (the time it takes for a Cepheid variable star to complete one cycle of brightness variation) and its intrinsic luminosity (the true brightness of the star). This relationship allows astronomers to determine the distance to Cepheid variable stars by measuring their periods and comparing them to their observed brightness.
By using the period-luminosity relationship of Cepheid variables, astronomers like Edwin Hubble were able to accurately measure the distances to spiral nebulae (now known as galaxies) and demonstrate that they were located far beyond the Milky Way Galaxy. This discovery provided strong evidence for the concept of an expanding universe and confirmed that spiral nebulae are indeed separate and distant galaxies.
You can learn more about Cepheid variable at
https://brainly.com/question/29355714
#SPJ11
Question 5 (10 points) which of the followings is correct? The maximum allowed aggregated bandwidth of 4G-LTE is 640 MHz. The maximum aggregated bandwidth for 5G-NR is 6.4 GHz. The core bandwidth of 4G-LTE is 20 MHz. The core bandwidth of 5G-NR is 400 MHz.
The correct statements are that the maximum allowed aggregated bandwidth of 4G-LTE is 640 MHz, and the core bandwidth of 4G-LTE is 20 MHz. The statement regarding the maximum aggregated bandwidth for 5G-NR being 6.4 GHz is incorrect.
The maximum allowed aggregated bandwidth of 4G-LTE is 640 MHz:
In 4G-LTE (Fourth Generation-Long Term Evolution) networks, the maximum allowed aggregated bandwidth refers to the total bandwidth that can be utilized by combining multiple frequency bands. This aggregation allows for increased data rates and improved network performance. The maximum allowed aggregated bandwidth in 4G-LTE is indeed 640 MHz. This means that different frequency bands, each with a certain bandwidth, can be combined to reach a total aggregated bandwidth of up to 640 MHz.
The core bandwidth of 4G-LTE is 20 MHz:
The core bandwidth of a cellular network refers to the primary frequency band used for transmitting control and data signals. In 4G-LTE, the core bandwidth typically refers to the main carrier frequency used for communication. The core bandwidth of 4G-LTE is 20 MHz, meaning that the primary frequency band for transmitting data and control signals is 20 MHz wide.
To know more about frequency bands please refer:
https://brainly.com/question/30647284
#SPJ11
a 1.2 kg mass hangs from a 0.6 m string and is released from rest at θ = 70 degrees. it swings down and strikes a second 2.2 kg mass at the bottom of its path. the masses have an elastic collision.
The velocity of the second 2.2 kg mass just before the collision is 2.67 m/s.
The given problem can be solved by using the principle of conservation of energy and momentum.Let’s consider the given problem step-by-step;
1) The first step is to find the velocity of the first 1.2 kg mass just before the collision.The gravitational potential energy of the 1.2 kg mass is converted into kinetic energy when it moves down by angle θ, so we can write;
mgh = 1/2 mv²0
where, m = mass of the object, g = acceleration due to gravity, h = height of the object, v0 = initial velocity of the object, v = final velocity of the object
We can assume that the initial velocity v0 = 0 as the mass is released from rest.
So, the velocity of the 1.2 kg mass just before the collision is given by;
v = sqrt(2gh)where, h = 0.6 m and g = 9.8 m/s²v = sqrt(2 x 9.8 m/s² x 0.6 m) = 3.43 m/s
2) The second step is to find the velocity of the second 2.2 kg mass just after the collision.
Considering an elastic collision between two objects, the principle of conservation of momentum states that;
mu + mu' = mv + mv'where, mu = mass of the first object × its initial velocity, mu' = mass of the first object × its final velocity, mv = mass of the second object × its initial velocity, mv' = mass of the second object × its final velocityThe initial velocity of the second 2.2 kg mass is zero as it was at rest.
The final velocity of the 1.2 kg mass can be found by using the conservation of energy in the previous step. So, the momentum conservation equation becomes;mu' = mv - mv'1.2 kg × 3.43 m/s = 2.2 kg × v - 2.2 kg × mv'mv' = -1.2 kg × 3.43 m/s / 2.2 kg = -1.86 m/s
3) The third step is to find the velocity of the second 2.2 kg mass just before the collision.
Considering an elastic collision between two objects, the principle of conservation of energy states that;1/2 mu² + 1/2 mu'² = 1/2 mv² + 1/2 mv'²
where, mu = mass of the first object × its initial velocity, mu' = mass of the first object × its final velocity, mv = mass of the second object × its initial velocity, mv' = mass of the second object × its final velocity
The final velocity of the 1.2 kg mass can be found by using the conservation of energy in the previous step. So, the energy conservation equation becomes;
1/2 × 1.2 kg × 3.43 m/s² + 1/2 × 2.2 kg × (-1.86 m/s)² = 1/2 × 2.2 kg × v²v = sqrt[2(1/2 × 1.2 kg × 3.43 m/s² + 1/2 × 2.2 kg × (-1.86 m/s)²) / 2.2 kg²] = 2.67 m/s
Therefore, the velocity of the second 2.2 kg mass just before the collision is 2.67 m/s.
The question should be:
What Is The Velocity Of second mass 2.2 kg In M/S before The Collision?
Learn more about velocity at: https://brainly.com/question/80295
#SPJ11
66. what force must be applied to a 100.0-kg crate on a frictionless plane inclined at 30° to cause an acceleration of 2.0m/s2 up the plane?
A force of 200.0 N must be applied to the crate to cause an acceleration of 2.0 m/s² up the inclined plane.
To determine the force required to accelerate the crate up the inclined plane, we can use Newton's second law of motion. The force component parallel to the inclined plane can be calculated using the equation:
Force = Mass * Acceleration
The mass of the crate is given as 100.0 kg, and the acceleration is given as 2.0 m/s². Since the crate is on a frictionless plane, we only need to consider the gravitational force component along the incline. The force can be calculated as:
Force = Mass * Acceleration
= 100.0 kg * 2.0 m/s²
Calculating the force:
Force = 200.0 N
Therefore, a force of 200.0 N must be applied to the crate to cause an acceleration of 2.0 m/s² up the inclined plane.
Learn more about acceleration:
https://brainly.com/question/460763
#SPJ11
(c6p12) a 58- kg gymnast stretches a vertical spring by 0.40 m when she hangs from it. how much energy is stored in the spring? tries 0/12 the spring is cut into two equal lengths, and the gymnast hangs from one section. in this case the spring stretches by 0.20 m. how much energy is stored in the spring this time?
potential energy stored in the spring = [tex](1/2) * k_new * (0.20 m)^2[/tex]
To calculate the energy stored in the spring, we can use the formula for potential energy stored in a spring:
Potential Energy = (1/2) * k * x^2
where:
- k is the spring constant (stiffness) of the spring
- x is the displacement or stretch of the spring
Given:
- The mass of the gymnast is 58 kg.
- The gymnast stretches the spring by 0.40 m.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement:
F = k * x
The weight of the gymnast can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight = 58 kg * 9.8 m/s^2
Since the gymnast is in equilibrium while hanging from the spring, the weight is balanced by the force exerted by the spring:
Weight = k * x
Now we can calculate the spring constant:
k = Weight / x
Next, we can calculate the potential energy stored in the spring when the gymnast stretches it by 0.40 m:
Potential Energy = (1/2) * k * x^2
Now let's plug in the values:
Potential Energy = (1/2) * k * (0.40 m)^2
Calculate the spring constant:
k = (58 kg * 9.8 m/s^2) / 0.40 m
Now substitute the value of k into the potential energy formula and calculate:
Potential Energy = (1/2) * [(58 kg * 9.8 m/s^2) / 0.40 m] * (0.40 m)^2
To find the energy stored in the spring when it is cut into two equal lengths and the gymnast hangs from one section with a stretch of 0.20 m, we can follow the same steps as above.
First, calculate the new spring constant using the new stretch:
k_new = (58 kg * 9.8 m/s^2) / 0.20 m
Then, calculate the potential energy stored in the spring:
Potential Energy_new = (1/2) * k_new * (0.20 m)^2
Learn more about potential energy here :-
https://brainly.com/question/24284560
#SPJ11
n on A Schering bridge can be used for the: Select one: O a. protecting the circuit from temperature rises b. measuring currents O c. measuring voltages d. testing capacitors Clear my choice
The Schering bridge is mainly used for measuring capacitors. The correct option among the given options is option 'd' - testing capacitors.The Schering bridge is a form of bridge that was first created in 1918 by the German engineer.
This bridge can be used to evaluate the capacitance of an unknown capacitor with high accuracy. This bridge operates on the same basic principle as the Wheatstone bridge, which is used to calculate resistances. The key distinction is that the Schering bridge can handle capacitive impedance.
A capacitor is a passive electrical component that stores energy in an electric field. Capacitors are used to store electric charge, filter noise from power supplies, and act as timers. Capacitors come in a range of sizes and are used in everything from radios to medical devices.
To know more about Schering visit:
https://brainly.com/question/30901118
#SPJ11
Which of the following changes occur to the nucleus when a heavy element undergoes alpha particle emmission?
A. Only the number of neutrons decreases.
B. Only the number of protons decreases.
C. Only the number of neutrons increases.
D. Both the number of neutrons & protons decreases.
In alpha particle emission, heavy elements emit alpha particles consisting of two protons and two neutrons.
Alpha particle emission results in the emission of a helium nucleus from the heavy element. The resulting nucleus has a lower atomic number and a lower mass number as a result of this.So, the answer is (B) Only the number of protons decreases. In alpha particle emission, the mass number of the nucleus decreases by four and the atomic number decreases by two.
The mass number decreases by four because the alpha particle has a mass number of four, while the atomic number decreases by two because the alpha particle is made up of two protons.When a heavy element undergoes alpha particle emission, only the number of protons decreases. The mass number of the nucleus decreases by four and the atomic number decreases by two because the alpha particle has a mass number of four, while the atomic number decreases by two because the alpha particle is made up of two protons.
To know more about neutrons visit:
https://brainly.com/question/31977312
#SPJ11
PART C: RESISTANCE MEASUREMENT
Disconnect the power supply from the circuit, and disconnect all resistors from the circuit.
Switch the DMM to the resistance measurement range (W).
Connect the leads of the DMM across the resistor that was formerly connected between A and B. Record this resistance, RA.
In part A-4 you measured the voltage across this resistor, V. In part B-5 you measured the current through this resistor ,I. Calculate the resistance, RA = V/I.
Compare with the recorded value of step 3, and comment on any difference.
PART C: RESISTANCE MEASUREMENT
Resistance between A and B: RA = W
The voltage across the resistor: V = V
The current through the resistor I = mA
The resistance, RA: RA = W
Comparison and comment:
Resistance Measurement Procedure: Step 1: Disconnect the power supply from the circuit and remove all resistors from the circuit.
Change the DMM to resistance measurement range (W).Step 3: Connect the DMM leads across the resistor that was previously connected between A and B. Then, record this resistance, RA.Step 4: In part A-4, the voltage across the resistor, V, was measured. In part B-5, the current through the resistor, I, was measured.
RA = V/I is used to calculate the resistance. Step 5: Record the RA of the resistance between A and B. The voltage across the resistor: V = ____The current through the resistor I = ____The resistance, RA = _____Comparison and comment: The resistance RA measured by using a DMM must be similar to the resistance calculated by using the formula RA = V/I. There may be a variation due to the tolerance level of the resistor which is due to the value specified by the manufacturer.
To know more about Measurement visit:
https://brainly.com/question/28913275
#SPJ11
A wireless, laser based, power transmission system in geostationary orbit is being designed to divert energy to earth for use in remote regions. it is proposed to capture solar irradiation using a solar panel array in space, use this to power a laser and direct the laser beam to the area on earth where the energy is needed.
A wireless, laser-based power transmission system in geostationary orbit is being designed to capture solar irradiation using space-based solar panels and transmit the energy to remote regions on Earth using directed laser beams.
The proposed system aims to utilize solar panels in space to capture solar irradiation, which is abundant in the space environment. The captured solar energy is then converted into electrical energy to power a laser system. The laser beam is carefully directed towards the desired area on Earth where the energy is needed, allowing for wireless transmission of power over long distances. By harnessing solar energy in space and transmitting it to remote regions on Earth, the system offers the potential to provide clean and sustainable power to areas that may have limited access to conventional power sources. The use of directed laser beams allows for efficient and focused energy transfer, minimizing losses during transmission. Additionally, placing the power generation system in geostationary orbit ensures that the satellites remain fixed relative to the Earth's surface, maintaining a stable and continuous power transmission capability. Overall, this approach holds promise for addressing energy needs in remote regions while reducing reliance on traditional power infrastructure.
Learn more about geostationary;
https://brainly.com/question/29091189
#SPJ11