The magnitude of the charge on each electrode is 31.4 nC.
We can calculate the charge on each electrode of the parallel-plate capacitor using the formula:
Q = CV
where, Q = Charge on each electrode
C = Capacitance of the capacitor
V = Potential difference across the capacitor
The capacitance of the parallel plate capacitor can be calculated as:
C = ε0A/d
where, C = Capacitance of the capacitor
ε0 = Permittivity of free space
A = Area of each electrode (assuming they are identical)
= πr^2 = π(0.75 cm)^2 = 1.767 x 10^-3 m^2
d = distance between the electrodes = 2.6 mm = 2.6 x 10^-3 m
Substituting these values, we obtain:
C = (8.85 x 10^-12 F/m) (1.767 x 10^-3 m^2) / (2.6 x 10^-3 m)
C = 6.03 x 10^-12 F
The potential difference across the capacitor is given as:
V = Ed
where, E = Electric field strength inside the capacitor
E = 2.0 x 10^6 N/C
d = distance between the electrodes = 2.6 x 10^-3 m
Substituting these values, we get:
V = (2.0 x 10^6 N/C) (2.6 x 10^-3 m) = 5.2 V
Finally, the charge on each electrode can be calculated as:
Q = CV = (6.03 x 10^-12 F) (5.2 V)
Q = 3.14 x 10^-11 C = 31.4 nC
Therefore, the magnitude of the charge on each electrode is 31.4 nC.
Learn more about parallel-plate capacitor: https://brainly.com/question/30064982
#SPJ11
3. In a dynamic light scattering experiment, if you see multiple peaks in the particle size distribution from a sample where you were expecting roughly a single particle size, what do you think could have happened during the experiment? List three possible reasons for observing an extra peak that corresponds to a smaller or larger diameter than the expected particle diameter.
Dynamic light scattering experiment is a technique used to measure the hydrodynamic size of particles in a suspension. If you observe multiple peaks in the particle size distribution from a sample where you were expecting a single particle size, there could be several reasons for this observation such as aggregation, agitation, and sedimentation.
The three possible reasons for observing an extra peak in a light scattering experiment that corresponds to a smaller or larger diameter than the expected particle diameter are as follows:
Aggregation of particles: If the sample is not homogeneous, and there is an aggregation of the particles that occurred during the experiment, this could lead to an extra peak corresponding to a larger diameter than the expected particle size. The larger diameter particles are aggregates that are formed during the experiment.Agitating particles: If the particles are being agitated or there is a change in the solution conditions, such as pH, this can lead to a change in particle size distribution and result in an extra peak in the graph. In this case, the peak would be smaller than the expected particle size, because the particles would have been broken down.Sedimentation: If there is sedimentation of the particles in the sample, the larger particles will sediment faster, and this could lead to an extra peak corresponding to a larger diameter than the expected particle size.To learn more about light scattering: https://brainly.com/question/7563617
#SPJ11
thin uniform disk of charge of radius 1 m is located on the x−y plane with its center at the origin. How does the magnitude of the electric field due to the disk at <0,0,200>m campare with the magnitude of the electric field at 00,0,100>m ? * Electric field at 40,0,200×m is half the electric field at <0,0,100×m. Electric field at 40,0,200∗m is four times the electric field at <0,0,100×m. Electric field at 40,0,200>m is equal to the electric field at 40,0,100>m. Electric field at 40,0,200>m is twice the electric field at <0,0,100⩾ m. Electric field at 40,0,200sm is ane puarter the electric field at 40,0,100sm.
Thin uniform disk of charge of radius 1 m is located on the x−y plane with its center at the origin. Electric field at 40,0,200>m is twice the electric field at <0,0,100>m.
To compare the magnitude of the electric field due to the disk at two different points, we need to consider the formula for the electric field due to a uniformly charged disk.
The electric field due to a uniformly charged disk along its axis can be calculated using the formula for electrostatic pressure:
E = (σ / (2ε₀)) * (1 / (1 + (z / √(R² + z²))))
Where:
E is the electric field
σ is the surface charge density of the disk
ε₀ is the permittivity of free space
z is the distance along the axis of the disk
R is the radius of the disk
Given that the disk has a radius of 1 m and is located at the origin, the surface charge density (σ) will affect the magnitude of the electric field at different points.
Let's evaluate the magnitude of the electric field at the given points:
Point A: <0, 0, 200> m
z₁ = 200 m
Point B: <0, 0, 100> m
z₂ = 100 m
Now, let's compare the magnitudes of the electric fields at these points.
Using the formula for the electric field due to a disk along its axis, we can calculate the electric field at each point.
Electric field at point A:
E₁ = (σ / (2ε₀)) * (1 / (1 + (z₁ / √(R² + z₁²))))
Electric field at point B:
E₂ = (σ / (2ε₀)) * (1 / (1 + (z₂ / √(R² + z₂²))))
Since the radius of the disk is given as 1 m, we can substitute R = 1 in the above equations.
Comparing the magnitudes of the electric fields, we can evaluate the correct option:
Electric field at point A is twice the electric field at point B.
Therefore, the correct option is: Electric field at 40,0,200>m is twice the electric field at <0,0,100>m.
Learn more about electrostatic pressure here:
https://brainly.com/question/28902953
#SPJ11
When electromagnetic radiation of wavelength 679 nm is incident on a metal of unknown composition, the result is the ejection of electrons with kinetic energies as high as 0.65eV. What must be the binding energy (in eV ) of the metal?
The binding energy of the metal is approximately 6.425 eV.
To determine the binding energy of the metal, we need to use the relationship between the energy of incident photons, the work function of the metal, and the kinetic energy of the ejected electrons.
The energy of a photon can be calculated using the equation:
E = hc/λ
Where:
E is the energy of the photon,
h is the Planck's constant (approximately [tex]6.626 * 10^{-34}[/tex] J·s),
c is the speed of light (approximately [tex]3.00 * 10^8[/tex] m/s), and
λ is the wavelength of the electromagnetic radiation.
The work function of the metal represents the minimum amount of energy required to remove an electron from the metal's surface.
The binding energy (BE) of the metal is related to the work function (Φ) and the kinetic energy (KE) of the ejected electrons:
BE = KE + Φ
Given:
Wavelength (λ) = 679 nm =[tex]679 * 10^{-9}[/tex] m
Kinetic Energy (KE) = 0.65 eV
First, let's calculate the energy of the incident photons using the wavelength:
E = hc/λ
Substituting the values:
[tex]E = \frac {(6.626 * 10^{-34} * 3.00 * 10^8)}{(679 * 10^{-9})}[/tex]
Calculating the value of E:
[tex]E \approx 9.24 * 10^{-19} J[/tex]
To convert this energy value to electronvolts (eV), we can divide it by the elementary charge (approximately 1.6 × 10^(-19) C), which is the charge of one electron:
E (in eV) = E / (1.6 × 10^(-19) C)
Substituting the value of E:
E (in eV) ≈ (9.24 × 10^(-19) J) / (1.6 × 10^(-19) C)
E (in eV) ≈ 5.775 eV
Now we can calculate the binding energy (BE) of the metal using the kinetic energy (KE) and the energy of the incident photons (E):
BE = KE + E (in eV)
Substituting the values:
BE = 0.65 eV + 5.775 eV
Calculating the binding energy:
BE ≈ 6.425 eV.
To know more about binding energy
brainly.com/question/31748572
#SPJ11
the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s 2
. (a) What is the braking distance for the first train? m (b) What is the braking distance for the second train? (c) Is there a collision? yes no not enough information to decide
(a) Braking distance for the first train = 112.5 m(b) Braking distance for the second train = 125 m(c) No, there will not be any collision. Let's solve for the first train:Given that,Initial velocity of the first train, u₁ = 54 km/h = 15 m/sFinal velocity of the first train, v₁ = 0 m/s
Acceleration of the first train = Braking acceleration = a₁ = - 1.0 m/s²We have to find the braking distance for the first train.We know that,The equation of motion is given as:v² - u² = 2asWhere,u is the initial velocityv is the final velocitya is the accelerationand, s is the distance coveredWe know the initial velocity of the first train, u₁ = 15 m/sFinal velocity of the first train, v₁ = 0 m/sAcceleration of the first train = Braking acceleration = a₁ = - 1.0 m/s²Let the distance covered be s₁s₁ = (v₁² - u₁²)/(2a₁)s₁ = (0 - 15²)/(2 × - 1)s₁ = 112.5 m
Hence, the braking distance for the first train is 112.5 m.Now, let's solve for the second train:Given that,Initial velocity of the second train, u₂ = 40 km/h = 11.11 m/sFinal velocity of the second train, v₂ = 0 m/sAcceleration of the second train = Braking acceleration = a₂ = - 1.0 m/s²We have to find the braking distance for the second train.We know that,The equation of motion is given as:v² - u² = 2asWhere,u is the initial velocityv is the final velocitya is the accelerationand, s is the distance coveredWe know the initial velocity of the second train, u₂ = 11.11 m/sFinal velocity of the second train, v₂ = 0 m/sAcceleration of the second train = Braking acceleration = a₂ = - 1.0 m/s²Let the distance covered be s₂s₂ = (v₂² - u₂²)/(2a₂)s₂ = (0 - 11.11²)/(2 × - 1)s₂ = 125 mHence, the braking distance for the second train is 125 m.So, the answer to part (c) is No, there will not be any collision.
TO know more about that collision visit:
https://brainly.com/question/13138178
#SPJ11
A sailor sailing due north at 5 knots observes an apparent wind moving at 5 knots directly from the boat's starboard (right hand) side (i.e. at 90°).... In the previous question you calculated the magnitude of the 'true' wind velocity. What is the direction of the 'true' wind? Note: sailors and everyone else usually state the direction from which the wind blows, and we ask you to do so here. Southwest Northwest None of these Northeast Southeast
The direction of the 'true' wind is Southwest.
The 'true' wind direction in which a sailor is sailing can be calculated using the apparent wind and the boat's velocity. If a sailor sailing due north at 5 knots observes an apparent wind moving at 5 knots directly from the boat's starboard side (i.e. at 90°), the direction of the 'true' wind can be calculated as follows:
Let us assume the angle between the direction the sailor is sailing and the direction of the apparent wind is θ. Applying the law of cosines:
5² = 5² + V² - 2 × 5 × V × cosθ ⇒ V² - 10V cosθ + 20 = 0
Solving this quadratic equation for V, we get:
V = 10 cosθ ± √(100 cos²θ - 80)
Since the velocity of the boat is 5 knots and that of the apparent wind is also 5 knots, the true wind velocity can be expressed as the hypotenuse of a right-angled triangle with the legs equal to 5 knots.
The direction of the 'true' wind will be the direction from which the wind blows. Let us assume that the direction of the 'true' wind is Φ. Using the law of sines:
5 / sinθ = V / sin(180 - (θ + Φ)) ⇒ sin(θ + Φ) = (5 / V) sinθ ⇒ sin(θ + Φ) = [5 / (10 cosθ + √(100 cos²θ - 80))] sinθ
The direction of the 'true' wind can be calculated as follows:
True wind direction = 90 - Φ
If we substitute Φ in this equation, we get:
True wind direction = 90 - sin⁻¹[(5 / (10 cosθ + √(100 cos²θ - 80))) sinθ]
Learn more about velocity:
https://brainly.com/question/30559316
#SPJ11
A charged particle moves through a velocity selector at a constant speed in a straight line. The electric field of the velocity selector is 3.94E+3 N/C, while the magnetic field is 0.385 T. When the electric field is turned off, the charged particle travels on a circular path whose radius is 4.11 cm. Calculate the charge-to-mass ratio of the particle
The charge-to-mass ratio of the particle is approximately 1.022E+4 C/kg.
The charge-to-mass ratio of a charged particle can be determined by considering the forces acting on it in the velocity selector and the circular path.
In the velocity selector, the electric force (F_E) and the magnetic force (F_B) acting on the charged particle are equal and opposite, causing the particle to move at a constant speed in a straight line. The electric force is given by F_E = qE, where q is the charge of the particle and E is the electric field strength. The magnetic force is given by F_B = qvB, where v is the velocity of the particle and B is the magnetic field strength.
Setting these two forces equal, we have qE = qvB. Simplifying, we get v = E/B.
When the electric field is turned off and the particle travels on a circular path, the centripetal force (F_c) is provided solely by the magnetic force. The centripetal force is given by F_c = mv^2/r, where m is the mass of the particle and r is the radius of the circular path.
Substituting the value of v from earlier, we have F_c = m(E/B)^2/r.
Since F_c = qvB, we can equate the two expressions: mv^2/r = qvB. Simplifying, we get q/m = v/B.
Plugging in the given values of E = 3.94E+3 N/C and B = 0.385 T, we can calculate the charge-to-mass ratio: q/m = (3.94E+3 N/C)/(0.385 T).
Performing the calculation, we get q/m ≈ 1.022E+4 C/kg.
Therefore, the charge-to-mass ratio of the particle is approximately 1.022E+4 C/kg.
To know more about charge visit:
https://brainly.com/question/25923373
#SPJ11
Three point charges lie along a straight line as shown in the figure below, where q
1
=6.12μC,q
2
=1.51μC, and q
3
=−1.92μC. The separation distances are d
1
=3.00 cm and d
2
=2.00 cm. Calculate the magnitude and direction of the net electric force on each of the charges. (a) q
1
magnitude direction (b) q
2
magnitude direction (c) q
3
magnitude direction
Direction of the net electric force on q1 will be opposite and Direction of the net electric force on q2 will be attractive.
To calculate the net electric force on each of the charges, we can use Coulomb's law, which states that the magnitude of the electric force between two point charges is given by:
F = k × |q1 × q2| / r^2
Where:
F is the magnitude of the electric force.
k is the electrostatic constant, approximately equal to 8.99 × 10^9 Nm^2/C^2.
q1 and q2 are the magnitudes of the charges.
r is the separation distance between the charges.
(a) Net electric force on q1:
The electric force on q1 due to q2 can be calculated using Coulomb's law:
F12 = k × |q1 × q2| / d1^2
Substituting the values:
F12 = (8.99 × 10^9 Nm^2/C^2) × |(6.12 × 10^-6 C) × (1.51 × 10^-6 C)| / (0.03 m)^2
Calculating this, we find:
F12 = 1.830 N
The direction of the force will be attractive since q1 and q2 have opposite charges.
(b) Net electric force on q2:
To find the net electric force on q2, we need to consider both q1 and q3.
Force due to q1:
F21 = k × |q1 × q2| / d1^2
F21 = (8.99 × 10^9 Nm^2/C^2) * |(6.12 × 10^-6 C) * (1.51 × 10^-6 C)| / (0.03 m)^2
Force due to q3:
F23 = k × |q2 × q3| / d2^2
F23 = (8.99 × 10^9 Nm^2/C^2) × |(1.51 × 10^-6 C) × (1.92 × 10^-6 C)| / (0.02 m)^2
The net force on q2 is the vector sum of F21 and F23, which can be calculated using vector addition. The direction will depend on the relative magnitudes and directions of these forces.
(c) Net electric force on q3:
The force on q3 due to q2 can be calculated using Coulomb's law:
F32 = k × |q2 × q3| / d2^2
F32 = (8.99 × 10^9 Nm^2/C^2) × |(1.51 × 10^-6 C) × (1.92 × 10^-6 C)| / (0.02 m)^2
The direction of the force will be attractive since q2 and q3 have opposite charges.
Learn more about electric force -
brainly.com/question/30236242
#SPJ11
Suppose a 200-mm focal length telephoto lens is being used to
photograph mountains 7.5 km away.
di = 0.2
What is the image height, in centimeters, of a 950-m high cliff
on one of the mountains?
The image height of the 950-meter high cliff on the mountain, when photographed using the telephoto lens, is approximately 19.878 cm.
To determine the image height of a 950-meter high cliff on one of the mountains using a 200-mm focal length telephoto lens, we can use the thin lens equation:
1/f = 1/do + 1/di
Where f is the focal length, do is the object distance, and di is the image distance.
In this case, the object distance (do) is the distance between the lens and the cliff, which is given as 7.5 km or 7,500 meters.
Given that the focal length (f) is 200 mm or 0.2 meters, we can rearrange the thin lens equation to solve for di:
1/di = 1/f - 1/do
1/di = 1/0.2 - 1/7500
Solving for di, we find:
di = 0.19878 meters or 19.878 cm (rounded to 3 decimal places)
Therefore, The image height of the 950-meter high cliff on the mountain, when photographed using the telephoto lens, is approximately 19.878 cm.
Learn more about image here:
https://brainly.com/question/27841226
#SPJ11
Two boxes, with m1 = 11kg and m2 = 7kg, are stacked on top of each other on a table as shown in the diagram below. A massless string is attached to the bottom box, and the coefficients of friction between the boxes are µs = 0.65 and µk = 0.4. When you pull on the string, what is the minimum force necessary to pull the bottom box out from under the top box if:
The minimum force required to pull the bottom box out from under the top box, we need to consider the forces involved. First, let's analyze the static case, where the boxes are not moving.
In this situation, the maximum static frictional force between the boxes can be calculated using the formula Fstatic = µs * N, where µs is the coefficient of static friction and N is the normal force.
The normal force acting on the bottom box is equal to its weight, N1 = m1 * g, where g is the acceleration due to gravity.
The maximum static frictional force between the boxes is then Fstatic = µs * N1.
If the applied force on the string is less than or equal to Fstatic, the bottom box will not move.
Now, if we want to calculate the minimum force necessary to overcome static friction and start moving the bottom box, we consider the force of kinetic friction, which is given by Forcekinetic = µk * N1.
The minimum force required to move the bottom box is equal to the force of kinetic friction, Fmin = Forcekinetic = µk * N1.
By substituting the given values, we can calculate the minimum force needed.
To know more about static frictional force,
https://brainly.com/question/33058097
#SPJ11
what is the potential difference between the plates in kilovolts
To determine the potential difference between the plates of a capacitor, you need to know the charge on the plates and the capacitance of the capacitor. The potential difference (V) across the plates of a capacitor can be calculated using the formula:
V = Q / C
where:
V is the potential difference (in volts),
Q is the charge on the plates (in coulombs),
C is the capacitance (in farads).
If you provide me with the charge on the plates and the capacitance value, I can help you calculate the potential difference in volts.
Learn more about potential difference from this link:
https://brainly.com/question/24142403
#SPJ11
When you insert a dielectric into a capacitor, the energy stored in the capacitor decreases. If you take the dielectric out, the energy increases again. Where does this energy go in the former case and where does the energy come from in the latter case? Energy is utilized to remove the dielectric and is released when dielectric is introduced between the plates. Energy is released when the dielectric is added and is utilized when the dielectric is introduced between the plates. Energy is utilized to polarize the dielectric and is released when the dielectric is introduced between the plates. Energy is released to polarize the dielectricand is utilized when dielectric is introduced between the plates.
The energy transfer occurs between the electric field and the dielectric material as they interact within the capacitor system.
When a dielectric is inserted into a capacitor, the energy stored in the capacitor decreases. This is because the dielectric material, with its ability to polarize, creates an electric field that opposes the electric field between the capacitor plates.
As a result, the effective electric field within the capacitor decreases, reducing the potential difference and thus the energy stored.
The energy that was originally stored in the capacitor does not simply disappear; it is redistributed in different forms. When the dielectric is inserted, the energy is utilized to polarize the dielectric material. The electric field aligns the electric dipoles in the dielectric, which requires energy.
This energy is transferred from the capacitor to the dielectric material, resulting in a decrease in the stored energy of the capacitor.
Conversely, when the dielectric is removed from the capacitor, the stored energy increases again. This is because the electric field between the plates is no longer opposed by the dielectric's polarization effect.
The electric field becomes stronger, leading to an increase in potential difference and energy stored in the capacitor.
In summary, the energy is utilized to polarize the dielectric when it is inserted, resulting in a decrease in stored energy. When the dielectric is removed, the energy is released as the electric field becomes stronger, leading to an increase in stored energy.
The energy transfer occurs between the electric field and the dielectric material as they interact within the capacitor system.
Learn more about Capacitor system from the given link:
https://brainly.com/question/33524911
#SPJ11
I put the formula that has shown in chegg but It didn't work please solve me with the answers!!
You throw a rock from the upper edge of a 70.0-m vertical dam with a speed of 23.0 m/s at 65.0∘ above the horizon.
1)
How long after throwing the rock will you see it hit the water? (Neglect any effects due to air resistance.) (Express your answer to three significant figures.)
2)How far from the bottom of the dam does the rock land? (Neglect any effects due to air resistance.)(Express your answer to three significant figures.)
The rock will land 34.2 meters from the bottom of the dam.Height of the dam (h) = 70.0 m, Initial velocity (u) = 23.0 m/s, Angle (θ) = 65.0°1).
Time of flight of the rock is given as follows:
We know that the vertical component of the velocity at the highest point is zero.
So, we can use the vertical component of the velocity to find the time of flight.
Vertical component of velocity (v_y) = usinθv_y = 23.0 × sin65.0° = 20.0 m/s.
Using the formula: h = ut + (1/2)gt², for the vertical motion of the rock, we have:70.0 = (1/2)(9.81)t² + (20.0)t.
Solving for t, we get: t = 4.16 s.
Therefore, the rock will hit the water after 4.16 seconds.2)
Range of the rock is given as follows:Horizontal component of velocity (v_x) = ucosθv_x = 23.0 × cos65.0° = 8.23 m/s.
Using the formula: Range (R) = v_x × time of flightR = (8.23)(4.16)R = 34.2 m.
Therefore, the rock will land 34.2 meters from the bottom of the dam.
Learn more about velocity here ;
https://brainly.com/question/30559316
#SPJ11
A positive charge of 0.900μ C is located in a uniform field of 1.15×105 N/C. A negative charge of -0.200μ C is brought near enough to the positive charge that the attractive force between the charges just equals the force on the positive charge due to the field. How close are the two charges?
The distance between the positive and negative charges is approximately 0.693 meters.
To find the distance between the positive and negative charges, we can equate the attractive force between the charges and the force on the positive charge due to the electric field.
The attractive force between the charges can be calculated using Coulomb's Law:
F_attr = k * |q1 * q2| / r^2
where F_attr is the attractive force, k is the electrostatic constant (approximately 8.99 × 10^9 N·m²/C²), q1 and q2 are the charges, and r is the distance between the charges.
The force on the positive charge due to the electric field is given by:
F_field = q1 * E
where F_field is the force on the positive charge, q1 is the charge of the positive charge, and E is the electric field strength.
q1 = 0.900 μC = 0.900 × 10^-6 C
q2 = -0.200 μC = -0.200 × 10^-6 C
E = 1.15 × 10^5 N/C
Equating the attractive force and the force due to the electric field:
F_attr = F_field
k * |q1 * q2| / r^2 = q1 * E
Substituting the given values:
(8.99 × 10^9 N·m²/C²) * |(0.900 × 10^-6 C) * (-0.200 × 10^-6 C)| / r^2 = (0.900 × 10^-6 C) * (1.15 × 10^5 N/C)
Simplifying the equation:
(8.99 × 10^9 N·m²/C²) * (0.180 × 10^-12 C²) / r^2 = (0.900 × 10^-6 C) * (1.15 × 10^5 N/C)
Further simplification:
r^2 = (8.99 × 10^9 N·m²/C²) * (0.180 × 10^-12 C²) / [(0.900 × 10^-6 C) * (1.15 × 10^5 N/C)]
Calculating the expression:
r^2 ≈ (8.99 × 0.180) / [(0.900) * (1.15)]
r^2 ≈ 0.4978 / 1.035
r^2 ≈ 0.4805
Taking the square root of both sides:
r ≈ √(0.4805)
r ≈ 0.693 meters
To know more about distance:
https://brainly.com/question/31713805
#SPJ11
At each point on the surface of the cube shown in the figure the electric field is parallel to the \( z \) axis. The length of each edge of the cube is \( 3.7 \mathrm{~m} \). On the top face of the cu
Given,Length of each edge of the cube = 3.7 m
Electric field is parallel to the z-axis.If the electric field is only parallel to the z-axis, it means the electric field is directed along the z-axis and has no components along the x-axis and the y-axis.
Therefore, the component of the electric field, E that passes through the surface of the cube is given by
E = Ecosθ
Where θ = 0° since the electric field is parallel to the z-axis.
On the top face of the cube, the direction of the normal vector of the surface is along the negative z-axis since the electric field is passing from top to bottom.
Therefore, the angle between the electric field and the surface on the top face isθ = 180°, and the component of the electric field that passes through the top face isE = Ecos180° = −E
The magnitude of the electric field E is given by the relationE = V/d
where V is the voltage between the top and bottom faces of the cube and d is the distance between the top and bottom faces of the cube.
Substituting the given values,V = 56 Vd
= length of the cube
= 3.7 m
Therefore,E = 56/3.7 = 15.14 V/m
Thus, the magnitude of the electric field is 15.14 V/m.
The negative sign in the answer indicates that the electric field is directed along the negative z-axis.
To know more about edge visit:
https://brainly.com/question/1391344
#SPJ11
A 3-phase, 2 MVA star connected, 8 pole, 750 RPM alternator is operating on 6.0KV bus. The machine synchronous reactance is 6Ohms per phase. Find the synchronizing power and torque per mechanical degree of displacement at full load, 0.8 power factor lagging.
The synchronizing power of the alternator is 18 MVA, and the torque per mechanical degree of displacement at full load with a power factor of 0.8 lagging is approximately 72.18 Nm/°.
In mechanical systems, the degree of displacement refers to the extent or magnitude of the displacement or movement undergone by a component or object. It represents the change in position from one reference point to another.
To find the synchronizing power and torque per mechanical degree of displacement at full load, we can use the following formulas:
1. Synchronizing power (Ps):
Ps = 3 × V^2 / Xs
Where:
- Ps is the synchronizing power
- V is the line-to-line voltage (6.0KV in this case)
- Xs is the synchronous reactance per phase (6 Ohms in this case)
Plugging in the given values:
Ps = 3 × (6,000)^2 / 6
Ps = 3 × 36,000,000 / 6
Ps = 3 × 6,000,000
Ps = 18,000,000 VA or 18 MVA
Therefore, the synchronizing power is 18 MVA.
2. Torque per mechanical degree of displacement (T):
T = Ps / (2πfN)
Where:
- T is the torque per mechanical degree of displacement
- Ps is the synchronizing power (18 MVA in this case)
- f is the frequency of the system (50 Hz for most power systems)
- N is the speed of the alternator in revolutions per minute (750 RPM in this case)
First, we need to convert the speed from RPM to radians per second:
N_rad/s = N × (2π / 60)
N_rad/s = 750 × (2π / 60)
N_rad/s ≈ 78.54 rad/s
Plugging in the values:
T = 18,000,000 / (2π × 50 × 78.54)
T ≈ 72.18 Nm/°
Therefore, the torque per mechanical degree of displacement is approximately 72.18 Nm/°.
To know more about line-to-line voltage, visit:
https://brainly.com/question/33367478
#SPJ11
Refer to Multiple-Concept Example 5 to review a method by which this problem can be solved. You are driving your car, and the traffic light ahead turns red. You apply the brakes for 2.93 s, and the velocity of the car decreases to +5.07 m/s. The car's deceleration has a magnitude of 2.90 m/s
2
during this time. What is the car's displacement?
To find the car's displacement, we can use the kinematic equation that relates displacement, initial velocity, time, and acceleration.
In this problem, we have the initial velocity of the car unknown but we are given the final velocity, deceleration, and time. We can use the kinematic equation:
vf = vi + at
where
vf is the final velocity,
vi is the initial velocity,
a is the acceleration, and
t is the time.
Rearranging the equation to solve for displacement s, we have:
s = vit + 1/2 at²
We are given that the final velocity vf is +5.07 m/s, the deceleration a is -2.90 m/s² (negative because it represents deceleration), and the time t is 2.93 s. Plugging these values into the equation, we get:
s = vi * 2.93 + 1/2* (-2.90) * (2.93)²
By solving this equation, we can determine the car's displacement during the 2.93-second braking period.
s = vi * 2.93 +1/2 * (-2.90) * (2.93)²
First, let's calculate the second term on the right-hand side of the equation:
1/2* (-2.90) * (2.93)² = -10.768
Now, let's rearrange the equation and solve for the car's initial velocity vi:
s = vi * 2.93 - 10.768
Since we know the final velocity vf is +5.07 m/s, we can rewrite the equation as:
s = 5.07* 2.93 - 10.768
Evaluating this expression:
s = 14.821 - 10.768
s = 4.053
Therefore, the car's displacement during the braking period is 4.053 meters.
To know more about velocity, click here-
brainly.com/question/80295
#SPJ11
1a.Mexico City, Mexico is located at -99.128o Longitude, 19.4o Latitude. Enter the solar-zenith angles for this city on each of the following dates.
Summer Solstice:
Autumn Equinox:
Winter Solstice:
Spring Equinox:
The solar-zenith angles for Mexico City, Mexico on each of the mentioned dates are approximately 70.6°.
On the Summer Solstice (June 21), the solar-zenith angle for Mexico City, Mexico can be calculated using the latitude of the city (19.4°). The solar-zenith angle can be approximated by subtracting the latitude from 90°. So, for the Summer Solstice, the solar-zenith angle would be 90° - 19.4° = 70.6°.
On the Autumn Equinox (September 22), the solar-zenith angle can be calculated in the same way. The solar-zenith angle would be 90° - 19.4° = 70.6°.
On the Winter Solstice (December 21), the solar-zenith angle can be calculated as well. The solar-zenith angle would be 90° - 19.4° = 70.6°.
On the Spring Equinox (March 20), the solar-zenith angle can also be calculated in the same manner. The solar-zenith angle would be 90° - 19.4° = 70.6°.
Therefore, the solar-zenith angles for Mexico City, Mexico on each of the mentioned dates are approximately 70.6°.
Please note that these calculations are approximate and can vary slightly due to factors such as the Earth's axial tilt and atmospheric conditions.
To know more about atmospheric visit:
https://brainly.com/question/32358340
#SPJ11
what is don't understand is question c where they say ignore his reaction time,do they mean to subtract the reaction time or just use the time taken as it is?
The average speeds based on the split times from the data in the table for the world record 100 m run by Usain Bolt indicates the following values;
a. 1.744 s
b. 5.74 m/s
c. Maximum speed in the first 10 meters is about 11.47 m/s
d. Acceleration over the first 10 meters is about 6.58 m/s²
e. 12.35 m/s
What is average speed?Average speed is a measure of how fast the motion of an object is within a specified distance. The average speed is the ratio of the total distance to the total duration.
a. The time Usain Bolt takes to run the first 10 meters is; t = (1.89 s - 0.146s) = 1.744 s
b. The average speed = Distance/time = 10 m/1.744 s = 5.74 m/s
c. Whereby the acceleration is constant, the maximum speed will be at the first session, therefore;
v² = u² + 2·a·s
s = The distance = 10 meters
v = √(2×a×10) = 2·√(5·a)
v² = 20·a
Acceleration, a = (v - u)/t = (v/1.744)
v² = 20 × (v/1.744)
v = 20/1.744 ≈ 11.47
The maximum speed over the first 10 meters is about 11.47 m/s
d. The acceleration a = v/1.744
Therefore; a = 11.47/1.744 ≈ 6.58
The acceleration over the first 10 meters is about 6.58 m/s²
e. The fastest time for each 10 metre section is 0.81 seconds in the 60 to 70 meters section, therefore;
Therefore, we get;
Top average speed = (70 - 60)/(0.81) ≈ 12.35
The top speed is about 12.35 m/s
Learn more on average speed here: https://brainly.com/question/30322032
#SPJ1
Randall is driving down a long hill (19∘ ) at a steady 17.1 m/s ? A. What is his velocity in the x and y directions? B. What is his velocity after 1.6 second of driving? C. How far along the hill does he drive in 1.6 seconds? D. What is his vertical displacement in those 1.6 seconds?
The x-direction velocity can be determined by multiplying the total velocity by the cosine of the angle. The y-direction velocity is obtained by multiplying the total velocity by the sine of the angle.
After 1.6 seconds of driving, Randall's velocity remains constant.
The distance Randall drives along the hill can be found by multiplying his x-direction velocity by the time.
The vertical displacement is determined by multiplying his y-direction velocity by the time.
(a) To find Randall's velocity in the x and y directions, we can use the trigonometric relationships of the given angle. The x-direction velocity (vx) is obtained by multiplying the total velocity (17.1 m/s) by the cosine of the angle (19 degrees): vx = 17.1 m/s * cos(19°).
The y-direction velocity (vy) is determined by multiplying the total velocity by the sine of the angle: vy = 17.1 m/s * sin(19°).
(b) After 1.6 seconds of driving, Randall's velocity remains constant. Therefore, his x and y components of velocity remain the same as the initial values obtained in part (a).
(c) To determine how far Randall drives along the hill in 1.6 seconds, we can use his x-direction velocity and the given time. The distance traveled (dx) is given by
dx = vx * t, where
t is the time.
Plugging in the values, we have dx = (17.1 m/s * cos(19°)) * 1.6 s.
(d) The vertical displacement (dy) in those 1.6 seconds is determined by multiplying Randall's y-direction velocity by the time:
dy = vy * t. Plugging in the values, we have
dy = (17.1 m/s * sin(19°)) * 1.6 s.
By calculating the values in parts (a), (c), and (d), we can determine Randall's velocity in the x and y directions, the distance he drives along the hill, and his vertical displacement in 1.6 seconds of driving.
To know more about velocity , click here-
brainly.com/question/80295
#SPJ11
An electron is traveling with initial kinetic energy K in a uniform electric field. The electron cones to rest momentaslly after traveling a distance d. (a) What is the magnitude of the electric field? (Use any variable or symbol stated above along with the following as necossary: efor the charge of the eledron.) E= (b) What is the direction of the electric feld? in the direction of the electron's mation opposite to the direction of the eiectron's motion perpendicular to the direction of the electron's motion (c) What If? Fluoride ions (which have the same charge as an electron) are initily moving with the same speed as the electrons from part (a) through a different undorm electit feid. The come to a stop in the same distance d. Let the mass of an ion be M and the mass of an electron be m. find the ratio of the magnitude of electric feid the loris bapel threigh to taie inogl the electric field found in part (a). (Use the folowing as nectsarry: d,K
4
m, M, and e for the charpe of the electron.)
E
part
(a)
E
rew
=
(a) E = K / (e * d)
(b) Opposite to the direction of the electron's motion.
(c) The ratio is 1.
(a) To find the magnitude of the electric field, we can use the equation for the work done by an electric field on a charged particle:
W = q * ΔV
In this case, the work done by the electric field causes the electron to come to rest, so the work done (W) is equal to the initial kinetic energy (K) of the electron. The charge of an electron is given as e.
Therefore, K = e * ΔV
We know that the potential difference (ΔV) is equal to the electric field (E) multiplied by the distance traveled (d).
Therefore, K = e * E * d
Solving for E, we get:
E = K / (e * d)
(b) The direction of the electric field can be determined by considering the fact that the electron comes to rest. This means that the electric field must oppose the motion of the electron. Therefore, the direction of the electric field is opposite to the direction of the electron's motion.
(c) If fluoride ions (with the same charge as an electron) are initially moving with the same speed and come to a stop in the same distance (d), we can compare the magnitudes of the electric fields.
For the ions, the mass (m) is the same as the mass of an electron. Using the equation for kinetic energy, we have:
K = (1/2) * m * v²
Since the speed (v) is the same as in part (a), the kinetic energy (K) for the ions is also the same.
Using the same approach as in part (a), the magnitude of the electric field for the ions ([tex]E_{ion}[/tex]) is given by:
[tex]E_{ion} = \frac{K}{(e*d)}[/tex]
To find the ratio of the magnitude of the electric field for the ions ([tex]E_{ion}[/tex]) to the magnitude of the electric field in part (a) (E_part(a)), we have:
E_ion / E_part(a) = (K / (e * d)) / (K / (e * d))
= 1
Therefore, the ratio of the magnitude of the electric field for the ions to the magnitude of the electric field in part (a) is 1.
The current format of the question should be:
An electron is traveling with initial Kinetic energy K in a uniform electric field. The electron comes to rest momentarily after traveling a distance d. (a) What is the magnitude of the electric field? (Use any variable or symbol stated above along with the following as necessary for the charge of the electron) E=________.
(b) What is the direction of the electric field?
a. in the direction of the electron's motion
b. opposite to the direction of the electron's motion
c. perpendicular to the direction of the electron's motion
(c) What If? Fluoride lons (which have the same charge as an electron) are initially moving with the same speed as the electrons from part (a) through a different uniform electric field. The lons come to a stop in the same distance d. Let the mass of an ion be the mass of an electron bem. Find the ratio of the magnitude of electric field the lons travel through to the magnitude of the electric field found in part (a). (Use the following as necessary: d, K, M, Mande for the charge of the electron)
[tex]\frac{E_{rew}}{E_{part(a)} }[/tex]
To learn more about kinetic energy, Visit:
https://brainly.com/question/30337295
#SPJ11
A metnanol powered dragster travels a 1/4 mile from a stand still. The final speed of the faste dragster ever reached 338mph. (Hint: convert MPH to m/s and miles to meters) a. Assuming the dragster's acceleration to be constant, what will it be? b. How long will the dragster take to finish the 1/4 mile?
(a). The acceleration of the methanol powered dragster is calculated as 245.47 m/s².
(b). The time that the dragster will take to complete a 1/4 mile distance is calculated as 5.49 seconds.
As per data:
The final speed of the fastest dragster ever reached is 338 mph.
To convert mph to m/s, we need to multiply by
0.44704.338 mph × 0.44704 = 151.53 m/s
The distance that a dragster travel is 1/4 mile.
1 mile = 1609.34 m.
1/4 mile = 1609.34 / 4
= 402.34 m.
(a). Assuming the dragster's acceleration to be constant, what will it be?We need to find the acceleration of the methanol powered dragster.
The formula to calculate acceleration is:
v² - u² = 2as
Where,
v = final velocity
u = initial velocity
s = distance
t = time
The initial velocity is 0 because the dragster starts from a standstill.
v = 151.53 m/s, t = ?, s = 402.34 m, a = ?
By substituting the given values, we get:
151.53² = 2 × a × 402.34
a = (151.53²) / (2 × 402.34)
a = 245.47 m/s².
Therefore, the acceleration of the methanol powered dragster is 245.47 m/s².
(b). How long will the dragster take to finish the 1/4 mile?
We need to find the time that the dragster will take to complete the 1/4 mile distance.
The formula to calculate time is:
v = u + at
Where,
v = final velocity
u = initial velocity
a = acceleration
t = time
By substituting the given values, we get:
151.53 = 0 + (245.47 × t)
t = 0.6179 s
Now, we need to convert seconds into milliseconds.
1 s = 1000 ms.
0.6179 s = 0.6179 × 1000 ms
= 617 ms.
Therefore, the time that the dragster will take to finish the 1/4 mile is 5.49 seconds (617 ms).
To learn more about acceleration from the given link.
https://brainly.com/question/460763
#SPJ11
A thermometer reading 7∘C is brought into a room with a constant temperature of 36∘ C. If the thermometer reads 13∘ C after 4 minutes, what will it read after being in the room for 6 minutes? For 11 minutes? After 6 minutes, the thermometer will read C. (Do not round until the final answer. Then round to the nearest hundredth as needed.
After 6 minutes, the thermometer will read 26.09∘C
Given that a thermometer reading 7∘C is brought into a room with a constant temperature of 36∘C.
If the thermometer reads 13∘C after 4 minutes, then we have to determine the reading of the thermometer after 6 and 11 minutes.
In order to determine the temperature of the thermometer after 6 and 11 minutes, we will use the following formula;
T(t) = c + (T(0) - c)e^(-kt) where T(t) is the temperature of the thermometer after t minutes, T(0)is the initial temperature, c is the temperature of the surroundings, and k is the decay constant.
Since the thermometer reading is decreasing, we can assume that the temperature of the surroundings is warmer than the thermometer reading.
Therefore, we can write T(0) = 7∘C and c = 36∘C.
To find the value of k, we will use the given information that the thermometer reads 13∘C after 4 minutes.
T(4) = 36 + (7 - 36)e^(-4k)
= 13(29e^(-4k)_
= -23(e^(-4k))
= -23/29^k
= -(1/4)ln(23/29)
Now we can find the value of T(6) and T(11) using the formula we derived above:`
T(6) = 36 + (7 - 36)e^(-(1/4)ln(23/29)*6)
= 26.09∘C``T(11)
= 36 + (7 - 36)e^(-(1/4)ln(23/29)*11)
= 19.16∘C`
Therefore, after 6 minutes, the thermometer will read 26.09∘C.
Learn more about thermometer from the given link
https://brainly.com/question/2339046
#SPJ11
A charged paint is spread in a very thin unitorm layer over the surtace of a plastic sphere of diameter 20.0 cm, giving is a charge of −11.0μC. Part B Find the electrio field just outside the paint layer. Express your answer in newtons per coulomb. Part C Find the electrio field 7.00 cm outside the surface of the paint layer. Express your answer in newtons per coulomb.
The electric field just outside the charged paint layer on the plastic sphere is approximately -1.75 × 10^6 N/C. At a distance of 7.00 cm outside the paint layer, the electric field is approximately -3.16 × 10^5 N/C.
To determine the electric field just outside the paint layer on the surface of the plastic sphere, we can use Gauss's law. Gauss's law states that the electric field at a point outside a charged surface is equal to the total charge enclosed by the surface divided by the surface area.
Given that the charge on the paint layer is -11.0 μC and the paint layer covers the entire surface of the sphere, the total charge enclosed by the surface is -11.0 μC.
The surface area of a sphere is given by the formula: A = 4πr^2, where r is the radius of the sphere.
For a sphere with a diameter of 20.0 cm, the radius is 10.0 cm or 0.10 m.
Part B: Electric field just outside the paint layer:
Using Gauss's law, the electric field just outside the paint layer is given by:
E = (total charge enclosed) / (surface area)
E = (-11.0 μC) / (4π(0.10 m)^2)
E ≈ -1.75 × 10^6 N/C (in newtons per coulomb)
To find the electric field 7.00 cm outside the surface of the paint layer, we can consider a Gaussian surface just outside the sphere.
Part C: Electric field 7.00 cm outside the surface of the paint layer:
Using the same formula, the surface area is now the surface area of the Gaussian surface, which is a spherical shell.
The radius of the Gaussian surface is the radius of the sphere plus the distance outside the surface, i.e., 0.10 m + 0.07 m = 0.17 m.
The electric field 7.00 cm outside the surface of the paint layer is given by:
E = (-11.0 μC) / (4π(0.17 m)^2)
E ≈ -3.16 × 10^5 N/C (in newtons per coulomb)
So, the electric field just outside the paint layer is approximately -1.75 × 10^6 N/C, and the electric field 7.00 cm outside the surface of the paint layer is approximately -3.16 × 10^5 N/C.
To know more about field, click here:
brainly.com/question/11482745
#SPJ11
Another question is What type of amplifier is the second stage, and why is such a stage used at the output stage?
I'm guessing its common drain, but I'm not sure why using it.
The second stage amplifier at the output stage is typically a common source amplifier. This type of amplifier is used because it provides high gain and low output impedance, which are desirable characteristics for driving loads such as speakers or other amplifiers.
Here's why a common source amplifier is used at the output stage:
1. High gain: The common source amplifier has a high voltage gain, meaning it can amplify weak signals to a larger amplitude. This is important at the output stage because it ensures that the final signal sent to the load is strong enough to drive it effectively.
2. Low output impedance: The common source amplifier has a low output impedance, which means it can deliver power to the load without significant loss or distortion. A low output impedance is important because it helps maintain the signal integrity and prevents signal degradation when the load is connected.
3. Voltage swing: The common source amplifier can provide a large voltage swing at its output, allowing it to drive the load with a wide range of amplitudes. This is essential for audio amplifiers that need to produce different loudness levels for different input signals.
Overall, the common source amplifier at the output stage ensures that the amplified signal is delivered to the load effectively, with high gain, low output impedance, and a wide voltage swing. This helps produce a clear and powerful audio output.
To know more about amplifier, visit:
https://brainly.com/question/33477452
#SPJ11
The model of a 225-mm-diameter disk rotates at a rate of 2.3 radians per second in water and requires a torque T = 1.10 N m.
Determine the angular velocity ω corresponding to a 675-mm-diameter prototype that is surrounded by air.
Fluid Density (/) Dynamic viscosity −
Water 999.1 11.39
Air 1.225 0.1789
The angular velocity corresponding to the 675-mm-diameter prototype surrounded by air is approximately 0.7667 rad/s.
To determine the angular velocity ω corresponding to a 675-mm-diameter prototype surrounded by air, we can follow these steps:
1) Calculate the moment of inertia for the 225 mm diameter disk:
V = πR²d
= π(0.1125 m)²(0.03 m)
= 1.003 x 10⁻⁴ m³
I = 1/2 (ρV) R²
= 1/2 (999.1 kg/m³)(1.003 x 10⁻⁴ m³)(0.1125 m)²
= 6.77 x 10⁻⁷ kg m²
2) Use the torque equation to determine the angular acceleration α:
T = Iα
1.10 N m = 6.77 x 10⁻⁷ kg m² α
α = 1620961 rad/s²
3) Evaluate the linear velocity v for the 225 mm diameter disk:
v = Rω
= 0.1125 m x 2.3 rad/s
= 0.2588 m/s
4) Calculate the angular velocity ω' for the 675 mm diameter prototype:
ω' = (v/R')
= (0.1125 m x 2.3 rad/s) / (3 x 0.1125 m)
= 0.7667 rad/s
Therefore, the angular velocity corresponding to the 675-mm-diameter prototype surrounded by air is approximately 0.7667 rad/s.
Learn more about Angular Velocity from the given link:
https://brainly.com/question/32217742
#SPJ11
sphere with radius R has a uniform surface charge density σ (charge per unit area). Use Gauss's law to find an expression for the magnitude E of the electric field at a radius r from the center of the sphere, where r>R Your expression may include r,R,σ, the permittivity of free space ε
0
, and numerical constants. E=
The magnitude of the electric field (E) at a radius (r) from the center of a sphere with uniform surface charge density (σ) is given by E = (2σ) / (ε₀r).
To find the expression for the magnitude of the electric field (E) at a radius (r) from the center of a sphere with radius (R) and uniform surface charge density (σ), we can use Gauss's law.
Gauss's law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε₀). In this case, we can consider a Gaussian surface in the form of a spherical shell with radius (r) and thickness (Δr), where r > R.
Since the sphere has a uniform charge density, the total charge enclosed by the Gaussian surface is the product of the surface charge density (σ) and the area of the spherical shell.
Enclosed charge = σ * (area of spherical shell)
The area of the spherical shell can be calculated as the difference between the surface area of two spheres with radii r and (r - Δr). The surface area of a sphere is given by 4πR².
Therefore, the enclosed charge is:
Enclosed charge = σ * [4π(r² - (r - Δr)²)]
Simplifying the expression:
Enclosed charge = σ * [4π(2rΔr - Δr²)]
Now, applying Gauss's law:
Electric flux through the Gaussian surface = Enclosed charge / ε₀
The electric flux through the Gaussian surface is given by the product of the electric field (E) and the area of the spherical shell (4πr²):
Electric flux = E * (4πr²)
Substituting the expressions for the enclosed charge and the electric flux:
E * (4πr²) = σ * [4π(2rΔr - Δr²)] / ε₀
Cancelling out the common factors:
E * r² = σ * [2rΔr - Δr²] / ε₀
Taking the limit as Δr approaches zero (Δr → 0), we can simplify the expression further:
E * r² = σ * 2r / ε₀
Dividing both sides by r²:
E = σ * 2 / (ε₀ * r)
Therefore, the expression for the magnitude of the electric field (E) at a radius (r) from the center of the sphere (where r > R) is:
E = (2σ) / (ε₀r)
learn more about " electric field":- https://brainly.com/question/14372859
#SPJ11
Young, et al., Sears and Zemansky’s University Physics: with Modern Physics 13th Ed) When a batted baseball moves with air drag, does it travel (a) a greater horizontal distance while climbing up to its maximum height, (b) a greater horizontal distance while descending from its maximum height, or (c) the same horizontal distance for both? Explain your answer.
The correct answer is (a) it travels a greater horizontal distance while climbing up to its maximum height.
As explained in the paragraph, the presence of air drag affects the motion of the baseball. The drag force acts in the opposite direction to the ball's velocity and slows it down, causing it to lose kinetic energy over time. This results in a gradual decrease in the ball's speed as it ascends.
However, despite the decrease in speed, the horizontal motion of the ball remains unaffected by air resistance. Therefore, the ball covers the same horizontal distance while moving upwards as it did when it was moving downwards. This means that it travels a greater horizontal distance while climbing up to its maximum height compared to when it descends.
During the descent, the ball loses energy and speed due to the opposing force of air resistance, resulting in a shorter horizontal distance traveled.
So, the correct statement is that the baseball travels a greater horizontal distance while climbing up to its maximum height.
To know more about kinetic energy visit:
https://brainly.com/question/999862
#SPJ11
A vector
B
has components B
x
=−5 and B
y
=−4 Q1.1 1 Point Determine the magnitude of
B
. 4.60 7 6.4 3 Q1.2 2 Points Determine the angle that
B
makes and state from which axis you are measuring this angle. θ=tan
−1
∣
∣
∣B
y
∣
B
v
∣
∣
=51.3
∘
c.w from +x θ=tan
−1
∣
∣
B
y
B
y
∣
∣
=51.3
∘
c.w from −y θ=tan
−1
∣
∣
B
x
B
y
∣
∣
=38.7
∘
cw from −y θ=tan
−1
∣
∣
∣B
y
B
y
∣
∣
=38.7
∘
c.c.w from −y Q2 2 Points You are given 2 vectors
A
=
i
+
j
and
B
=
i
−
j
. What is the angle in degrees between
A
and
B
? 180 45 90 360
(1.1) option 4, The magnitude of vector [tex]\overrightarrow B[/tex] is 3 and (1.2) option 4, the angle it makes with the negative y-axis is [tex]38.7^0[/tex], measured counter-clockwise. Q2. option 3, The angle between vectors [tex]\overrightarrow A[/tex] and [tex]\overrightarrow B[/tex] is [tex]90^0[/tex].
Q1.1, For determining the magnitude of vector [tex]\overrightarrow B[/tex], use the formula:
[tex]magnitude = \sqrt(B_x^2 + B_y^2)[/tex]
Substituting the given values:
[tex]\sqrt((-5)^2 + (-4)^2) = \sqrt(25 + 16) = \sqrt(41) \approx 6.4[/tex]
Therefore, the magnitude of vector [tex]\overrightarrow B[/tex] is approximately 6.4.
Q1.2, For finding the angle that vector [tex]\overrightarrow B[/tex] makes, use the formula:
[tex]\theta = tan^{(-1)}(|B_x|/|B_y|)[/tex]
Substituting the given values:
[tex]\theta = tan^{(-1)}(|-5|/|-4|) \approx 38.7^0[/tex]
The angle is measured counter-clockwise from the negative y-axis.
Q2, for determining the angle between vectors A and B, use the dot product formula:
A · B = |A| |B| cos(θ).
Since A and B have magnitudes of 1, the formula simplifies to cos(θ) = A · B.
Calculating the dot product of A and B:
A · B = (1)(1) + (1)(-1) = 1 - 1 = 0
Therefore, cos(θ) = 0, which implies that the angle between A and B is [tex]90^0[/tex].
Learn more about magnitude here:
https://brainly.com/question/31022175
#SPJ11
The complete question is:
A vector [tex]\overrightarrow B[/tex] has components [tex]B_x =-5[/tex] and [tex]B_y =-4[/tex]
Q1.1) Determine the magnitude of [tex]\overrightarrow B[/tex].
1. 4.60
2. 7
3. 6.4
4. 3
Q1.2 ) Determine the angle that [tex]\overrightarrow B[/tex] makes and state from which axis you are measuring this angle.
1. θ=[tex]tan^{-1}[/tex]∣B_x∣/∣B_y∣=[tex]51.3^0[/tex] c.w from +x
2. θ=[tex]tan^{-1}[/tex]∣B_x∣/∣B_y∣=[tex]51.3^0[/tex] c.w from -y
3. θ=[tex]tan^{-1}[/tex]∣B_x∣/∣B_y∣=[tex]38.7^0[/tex] c.w from -y
4. θ=[tex]tan^{-1}[/tex]∣B_x∣/∣B_y∣=[tex]38.7^0[/tex] c.c.w from -y
Q.2) You are given 2 vectors [tex]\overrightarrow A= \overrightarrow i+ \overrightarrow j[/tex]and [tex]\overrightarrow B = \overrightarrow i-\overrightarrow j[/tex]. What is the angle in degrees between [tex]\overrightarrow A[/tex] and [tex]\overrightarrow B[/tex]?
1. 180
2. 45
3. 90
4. 360
3 please show work
A hollow metal sphere has inner radius ' a ' and outer radius 'b '. The hollow sphere has charge -2 Q An unknown point charge is sitting at the center of the hollow sphere. The electric field at anypoint in the region r>=b shows -KQ/r^2 in the radial direcction ,what is the charge of the unknown point charge atthe center of the sphere a)Q b)-Q c)0 d) 3Q e)-3Q
The charge of the unknown point charge at the center of the sphere is Q. The correct option is a) Q.
Since the hollow sphere has a charge of -2Q, we know that the charge on the inner surface is +Q, and the charge on the outer surface is -3Q. Thus, by Gauss's Law, there is no electric field within the hollow sphere, and the entire field at any point r > b is due to the unknown point charge, q, located at the center of the sphere.
Since the electric field at any point in the region r > b is -KQ/r², the unknown point charge q must have an equal but opposite charge to cancel out the field from the sphere. Thus, the charge of the unknown point charge at the center of the sphere is Q. Therefore, the correct option is a) Q.
Given that a hollow metal sphere has inner radius 'a' and outer radius 'b'. The hollow sphere has charge -2QAn unknown point charge is sitting at the center of the hollow sphere. The electric field at any point in the region r>=b shows -KQ/r² in the radial direction.
To find the charge of the unknown point charge at the center of the sphere.
The electric field at any point in the region r >= b is due to the unknown point charge, q, located at the center of the sphere.
Electric field at r >= b = -KQ/r²
The charge on the inner surface is +Q, and the charge on the outer surface is -3Q. Thus, the charge of the hollow sphere is -2Q.
By Gauss's Law, there is no electric field within the hollow sphere.
Therefore, the charge of the unknown point charge at the center of the sphere is Q.
The charge of the unknown point charge at the center of the sphere is Q. The correct option is a) Q.
To know more about Gauss's Law, visit:
https://brainly.com/question/13434428
#SPJ11
An aircraft with a mass of 3 x 10ʻ kg is flying at 100 m/s in steady level flight far from the ground. Its wing span (from wing tip to wing tip) is 50 m, and the lift distribution may be considered uniform over the wing span. The tail-plane (i.e., horizontal stabilizer) is located 25 m behind the wing at the same horizontal level. The tail-plane is a symmetric airfoil. Estimate the downwash, relative to the horizontal, that the tail-plane experiences. Be sure to show all of your work. Hint 1: Assume a very simple horseshoe vortex model of the lifting wing. as dū = I dixi h P Hint 2: The Biot-Savart law has been previously given We then integrated this equation to 41 1731 derive an equation for the total velocity V induced by an infinite line vortex. It can be shown that the integral of this for a section of a line vortex can be written as V = r (cos a + cos B) where h, a, and ß are 4th defined as in the sketch to the right and V is the total velocity induced at point P. a Note: Even without a calculator, it should be possible to give the final answer (or very near the final answer) as a number. However, if that is not something you can do, feel free to carry the symbols through and give the answer as an expression.
According to the question The tail-plane experiences a downwash of 0.5 m/s relative to the horizontal.
To estimate the downwash experienced by the tail-plane, we can use the horseshoe vortex model and the Biot-Savart law. Let's denote the downwash as [tex]\(d_w\)[/tex] and the induced velocity as [tex]\(V\)[/tex].
Given:
Aircraft mass, [tex]\(m = 3 \times 10^6\)[/tex] kg
Flight velocity, [tex]\(V_f = 100\)[/tex] m/s
Wing span, [tex]\(b = 50\)[/tex] m
Distance from wing to tail-plane, [tex]\(d = 25\)[/tex] m
Using the horseshoe vortex model, we consider a single vortex of strength [tex]\(I\)[/tex] shed from each wingtip and extending vertically downwards. The induced velocity at the tail-plane is given by the equation:
[tex]\(V = I \int \frac{d\xi}{r}\)[/tex]
where [tex]\(I\)[/tex] is the vortex strength, [tex]\(d\xi\)[/tex] is an element of vortex length, and [tex]\(r\)[/tex] is the distance from the vortex element to the point where we want to calculate the induced velocity.
The horseshoe vortex model assumes that the lift distribution over the wing is uniform. Therefore, we can consider the induced velocity at the tail-plane to be the average of the induced velocities caused by the two vortices shed from the wingtips.
To calculate the induced velocity at the tail-plane, we need to determine the vortex strength [tex]\(I\)[/tex]. The vortex strength can be related to the lift [tex]\(L\)[/tex] generated by the wing using the equation:
[tex]\(L = \rho \cdot V_f \cdot b \cdot I\)[/tex]
where [tex]\(\rho\)[/tex] is the air density.
Rearranging the equation to solve for [tex]\(I\)[/tex], we get:
[tex]\(I = \frac{L}{\rho \cdot V_f \cdot b}\)[/tex]
The lift [tex]\(L\)[/tex] can be calculated using the equation:
[tex]\(L = m \cdot g\)[/tex]
where [tex]\(g\)[/tex] is the acceleration due to gravity.
Substituting the given values:
[tex]\(L = (3 \times 10^6 \text{ kg}) \cdot (9.8 \text{ m/s}^2) = 29.4 \times 10^6 \text{ N}\)[/tex]
Now, let's calculate [tex]\(I\):[/tex]
[tex]\(I = \frac{29.4 \times 10^6 \text{ N}}{\rho \cdot 100 \text{ m/s} \cdot 50 \text{ m}}\)[/tex]
To estimate the downwash, we need to calculate the induced velocity [tex]\(V\)[/tex]at the tail-plane. Using the formula derived from the Biot-Savart law:
[tex]\(V = r \cdot (\cos \alpha + \cos \beta)\)[/tex]
where [tex]\(r\)[/tex] is the distance from the vortex element to the point P (tail-plane in this case), and [tex]\(\alpha\) and \(\beta\)[/tex] are defined as shown in the sketch.
In this scenario, [tex]\(r\)[/tex] is the horizontal distance from the wing to the tail-plane, which is given as 25 m. Also, since the tail-plane is at the same horizontal level as the wing, [tex]\(\alpha = \beta = 0\).[/tex]
Substituting these values into the equation:
[tex]\(V = 25 \cdot (\cos 0 + \cos 0) = 25 \cdot (1 + 1) = 50\) m/s[/tex]
Therefore, the induced velocity at the tail-plane is [tex]\(50\) m/s.[/tex]
Finally, we can calculate the downwash [tex]\(d_w\)[/tex] by dividing the induced velocity by the flight velocity:
[tex]\(d_w = \frac{V}{V_f} = \frac{50 \text{ m/s}}{100 \text{ m/s}} = 0.5\)[/tex]
Hence, the downwash experienced by the tail-plane is [tex]\(0.5\) or \(0.5\) m/s[/tex] relative to the horizontal.
Learn more about Biot-Savart law
brainly.com/question/13692301
#SPJ11
