Astronomers can study how clusters of stars and gas move around the galactic center in nearby galaxies and use those movements to calculate the mass of the central black hole.
How can we calculate the black hole's mass at the galactic center?By monitoring the star motions in the galaxy's center, Webb will calculate the black hole's mass. Astronomers will calculate the mass of that black hole using NASA's James Webb Space Telescope. The outcome may appear to be unimportant, but a black hole's mass controls how it feeds and interacts with its surroundings.
Black holes are discovered when nearby material, such as gas, is pulled by gravity into a disk around the black hole. The gas molecules in the disk of the black hole are spinning so quickly that they heat up and release X-rays. From Earth, one can observe these X-rays.
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at what frequency should a 200-turn, flat coil of cross sectional area of 300.0 cm2 be rotated in a uniform 30.0-mt magnetic field to have a maximum value of the induced emf equal to 8.0 v?
At 7.1 Hz a 200-turn, flat coil of cross sectional area of 300.0 cm2 be rotated in a uniform 30.0-mt magnetic field to have a maximum value of the induced emf equal to 8.0 v
What is magnetic field?An electric charge, an electric current, and magnetic materials are all affected magnetically by a magnetic field, which is a vector field. A force perpendicular to the magnetic field and its own velocity acts on a moving charge in a magnetic field.
Given,
number of turns is N = 200 turns
cross-sectional area is A = 300 cm² = 300 x 10⁻⁴ m²
the magnitude of magnetic field strength is B = 30 x 10⁻³ T
the maximum value of the induced emf is E = 8 V
Now,
Maximum induced emf is, E = NBAω
where,
ω is the angular velocity (ω = 2πf)
Now,
E = NBA2πf
where,
f is minimum frequency
So, f = E / (NBA2π)
f = 8 / (200 x 30 x 10⁻³ x 300 x 10⁻⁴ x 2 x 3.142)
f = 7.073 Hz
f = 7.1 Hz
∴ the minimum frequency of the coil is 7.1 Hz.
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a large 1.9 m wide and 0.5 m high plate is carried above a truck perpendicular to the vehicle motion (like a flat plate normal to the free stream). calculate the additional power required to carry the plate at a speed of 72 km/hr. use air density as 1.22 and estimate the drag coefficient from tables in the book.
The additional power required to carry the plate at speed of 72 km/hr is 4867.8 m/s.
Given data,
[tex]l[/tex] (wide of plate) = 1.9m
[tex]h[/tex] (high of plate) = 0.5m
ρ (air density) = 1.22
[tex]V[/tex] (speed) = 72km/hr
assume [tex]C_{D}[/tex] (Drag coefficient) = 1.05
To determine the additional power can be calculated as follows:
First, we have to determine the area of plate
Area of plate = [tex]l[/tex]×[tex]h[/tex]
= 1.9×0.5
Then, we have to convert the unit of speed from km/hr to m/s
72km/hr = [tex]\frac{72000}{3600}[/tex]
= 20 m/s
Next, we can determine the power by using the formula
=[tex]\frac{1}{2}[/tex]×[tex]C_{D}[/tex]×ρ×[tex]V^{2}[/tex]×[tex]A[/tex]×[tex]V[/tex]
=[tex]\frac{1}{2}[/tex]×[tex]1.05[/tex]×[tex]1.22[/tex]×[tex]20^{2}[/tex]×[tex]0.95[/tex]×[tex]20[/tex]
=4867.8 watt
Thus, The additional power required to carry the plate at speed of 72 km/hr is 4867.8 m/s.
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a 14,000-kg boxcar is coasting at 1.50 m/s along a horizontal track when it hits and couples with a stationary 10,000-kg boxcar. what is the speed of the cars after the collision?
The speed of the cars just after the collision is 0.875 m/s.the formula to be used m1u1 + m2u2 = m1v1 + m2v2.V=14000*1.5÷14000+1000=0.875m/s
How is speed used? What is speed?Teenagers, young adults, and the others take the stimulant drug "speed" to feel more focused and alert, as well as, in some circumstances, to get high. Several types of speed are also used by some people to suppress their appetite.
Why do people drive fast?Simply because they are not paying attention on their driving pace, drivers frequently go above the speed limit. Traffic flow, operating a powerful car, and listening to music were all mentioned as contributing factors. Some drivers claimed that passengers' distraction caused them to accelerate.
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a child pulls a friend in a little wagon with constant speed. if the child pulls with the force of 16 n for 10.0 m and the handle of the wagon is inclined 25 degrees with respect to the horizontal, how much work does the child do on the wagon?
The work done by the child on the wagon is 158.4 J
Work done is defined as the product of the force applied on the object and the component of distance traveled by the object in the direction of the force. Mathematically,
W = FdCosθ
where,
W = work done = ?
F = force applied = 16 N
d = displacement = 10 m
θ = angle of inclination = 25°
Therefore,
W = (16 N) (10 m)Cos(25°)
W = 158.4 J
Hence, work done by the child on the wagon is 158.4 J
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The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true?.
The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object if and only if the object is partially or completely submerged in a liquid.
What exactly is Buoyant Force?When a rigid object is immersed in a fluid (completely or partially), it experiences an upward force equal to the weight of the fluid displaced by the object.
This is referred to as Archimedes' principle.
[tex]F_{b}[/tex]= -ρgV
[tex]F_{b}[/tex] = force of buoyancy
ρ = density of fluid
g = gravitational acceleration
V = volume of fluid
If an object is partially or completely submerged in fluid, the fluid displacement is equal to the magnitude of the buoyant force.
Thus, The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object if - For every object partially or completely submerged in a liquid.
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suppose a ship flies toward you at nearly lightspeed. in the ship's reference frame, it is 10 m long (front to back). when you measure its length, what is the result?
Its length is 6.6m.
How is length contracted defined?Length contraction is a phenomena where a moving object's length is measured to be less than it actually is.
When an object is travelling faster than the viewer, but not at the speed of light, length contraction is seen. The relativity of space and time is the cause of this. The two extremes of a moving object will send out signals like light at somewhat different intervals to an observer watching the thing.
Using the relationship between length contraction,
l = l₀[tex]\sqrt{1-\beta^{2} }[/tex]
β = v/c
l₀ = 10m
v = 0.75c
v/c = 0.75
In place of, we have
l = 10×[tex]\sqrt{1-0.75^{2} }[/tex]
l = 10× 0.66
l = 6.6m.
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Earth's equator receives more direct sunlight than the regions to its north and south. this distribution of sunlight accounts directly for which phenomenon
This happens because of the movement of rising air currents away from the equator.
Equator is an imaginary circle, which divides the Earth in half; while the Poles are the two points (the North Pole and the South Pole) that are crossed by the axis of rotation of the Earth. In Equator the temperature is hot, while in the Poles it is cold.
So when there is rising in the air currents movements away from the equator then whatever sunlight reflections or absorptions made by airs are reduced so in that area air density is less an sue to that sunlight is more present.
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A 1 kg water balloon falls downward and experiences a 4.9 N air resistance as it approaches the ground. What is the acceleration of the water balloon when it experiences this air resistance?
answer each problem with only one note
A meteor is observed to explode in the sky.
A third of a minute later a "boom" is heard.
Knowing sound travels at 300 m/sec,
how far away did it break up?(in meters)
Answer:
Explanation:
Given:
t = (1/3) min = (60/3) s = 20 s
V = 300 m
_______________________
D - ?
Distance:
D = V·t
D = 300·20 = 6 000 m
Which is an example of an anomaly that led to a theory being overturned?
O The recognition that people use up energy, get tired, and need to rest
O The discovery that oil will cause a rolling ball to move farther
O The belief that as Earth rotates, it drags surrounding ether with it
The discovery that materials, when burned, release phlogiston
An example of an anomaly that led to a theory being overturned is: The discovery that materials, when burned, release phlogiston.
What is a theory?A theory can be defined as an integrated set of principles and rules that can be used by a scientist to explain and predict observed events.
According to Thomas Kuhn, the process of any scientific discovery usually starts with the awareness of an anomaly and ends with making an adjustment to scientific theory in order to make a previously anomalous to become expected.
What is the phlogiston theory?The phlogiston theory can be defined as a superseded scientific theory which stated that a fire-like materials (elements) referred to as phlogiston, are found within combustible bodies and they are released when burned or during combustion.
However, the phlogiston theory is an anomaly that was later overturned by a scientists known as Antoine Lavoisier in 1772, who proved that combustion and burning of any chemical substance or materials (elements) requires a gas that has mass.
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A toy cart at the end of a string 0.70 m long moves in a circle on a table. The cart has a mass of 2.0 kg and the string gives a centripetal force of 40. N. Calculate the speed of the cart.
3.74 m/s is the speed of the cart of mass 2.0 kg and the string gives a centripetal force of 40. N.
What does a circle's centripetal force look like?The force that creates centripetal acceleration is known as centripetal force. All objects in uniform circular motion accelerate toward the center of the circle, and as a result, they must likewise experience a force from the center. The centripetal force is that force.
Briefing :
Given ,The mass of the cart, m = 2 kg,
The standard equation would be F = ma , where a is acceleration, f is force, and m is mass. However, the breaking strength of the string is 40 N.
a = [tex]\frac{v^{2} }{r}[/tex]
F = ma
F = [tex]\frac{mv^{2} }{r}[/tex]
40 = [tex]\frac{2v^{2} }{0.70}[/tex]
[tex]v^{2}[/tex] = 14
v = [tex]\sqrt{14}[/tex]
v = 3.74 m/s
Therefore , the speed of the cart is 3.74 m/s .
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a proton moves in the direction shown in a uni- form magnetic field. at this instant, which arrow points in the direc- tion of the force on the proton by the magnetic field?
When the proton starts to move upward the direction of the magnetic force changes and when the proton moves straight up the magnetic force turns to the left.
The direction of the force is perpendicular to the direction of the magnetic field and current, as given by Fleming's left-hand rule. Here the magnetic field is to the right and the direction of the current is upward. Protons feel a force on themselves due to the magnetic field. The force on the proton is proportional to the proton's magnetic flux density and velocity.
The velocity and momentum of a proton are affected by the force acting on it. If the velocity of a charged particle is perfectly parallel to the magnetic field, the magnetic field exerts no force on the particle, so the velocity remains constant. The momentum of a proton moving freely in a magnetic field is the product of the proton's mass and the proton's velocity. As the speed of a proton moving in a magnetic field changes, so does the momentum of the proton.
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A force is applied to stop a moving shopping cart. Increasing the time interval over which the force is applied.
We are given with a case of a moving shopping cart.
We are asked , how to increase the time, change the force.
For that, if we reduce the applied force in order to increase the time interval.
Generally, if we know the force applied and time taken, we can calculate the change in momentum.
As, Force, F = dP/dt
i.e. Rate of change of momentum w.r.t. time is Force.
So, dP = F.dt
Unit of Force is Newton, N in MKS (metre kilogram second) system.
Unit of Force is Dyne in CGS (centimetre gram second) system.
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projectile motion: if you launch a cannon at 15 degrees above horizontal, and another cannon at 75 degrees above horizontal, which one will reach farther horizontal range? explain your answer.
If you launch a cannon at 15 degrees above horizontal, and another cannon at 75 degrees above horizontal, both will have same horizontal range
In a projectile motion , horizontal range can be calculated using formula
Range = [tex]u^{2}[/tex] sin ( 2 theta) / g
where
u = initial velocity
theta = angle along the horizontal
g = acceleration due to gravity
if we substitute the value of 15 and 75 in formula , we get
sin ( 2 * theta_1 ) = sin ( 2*15 ) = sin 30 = 1/2
sin ( 2* theta_2 ) = sin ( 2 * 75 ) = sin (150) = 1/2
both the values are coming out to be equal
hence , will have equal value of horizontal range
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if a radiograph is done using an 80 inch ffd and 12 mas and a second image is done using a 40 inch ffd, what is the new mas that should be used?
The new mas that needs to be applied reduces mAs 1 devided by 4 , which is 3.
How do you locate fresh mAs?Milliamperage and time are multiplied to get the unit mAs (mA). A typical technique setting for imaging a hurt hand, for instance, may be 60 kVp, 100 mA, and 1/100 of a second (0.01). In this case, 100 milliamperes times 0.01 secondes = one milliampere (or 1 milliampere-second).Usually, the word "más" is used as an adverb to denote "more" or "most." Más, which means "more," can also be used as an adjective or pronoun. The term mais, which is a literary word that means "but," is not the same as the word más.To learn more about unit mAs (mA) refer to:
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two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). the smaller flywheel of radius 12 cm has a cord that has a pulling force of 50 n on it. what pulling force (in n) needs to be applied to the cord connecting the larger flywheel of radius 19 cm such that the combination does not rotate?
The pulling force (in N) that needs to be applied to the cord connecting the larger flywheel is 31.58 N.
Force is a push or pulls upon an object because of the item's interaction with some other object. A pressure can purpose an object with mass to exchange its speed, i.e., to boost up. stress additionally can be described intuitively as a push or a pull. A force has each importance and route, making it a vector amount.
calculation:-
Net torque on the system = 0
τ = r × F
So, here
r₁ × F₁ = r₂
12 × 50 = 19 × F₂
F₂ = 12 × 50 / 19
= 31.58 N
The phrase force has a very particular which means that. At this degree, it is really suitable to describe a pressure as a push or a pull. A pressure isn't always something that an item consists of or 'has in it. A pressure is exerted on one object thru some other. The concept of a force is not restrained to dwelling subjects or non-residing matters.
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What about the Model of Static Electricity makes it mechanistic?
The material that is attracted to the electron which is negatively charged and the material from which the electron was lost is considered as positively charged that makes the Mechanism of Static Electricity.
What is Model of Static Electricity?Static Buildup apparatus. The static build up is the phenomenon in which electric charges are traded between the surfaces of two objects that come into contact with each other. In this procedure, one object static takes on a positive charge and the other a negative charge. The material that interested the electron is negatively charged and the material from which the electron was lost is positively charged. This is the appliance for the Generation of Static Electricity. Static electricity is the result of a disparity between negative and positive charges in an object.
So we can conclude that Static electricity is an variance of electric charges within or on the surface of a material or between materials.
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an airplane has a mass of 26900 kg and takes off under the influence of a constant net force of 38700 n. what is the net force that acts on the plane's 106 kg pilot?
The net force that acts on the plane's 106 kg pilot is 151.58N.
What is a net force?The net force acting on an object is the result of all pushing and pulling forces acting on the object collectively (the sum). If there is an imbalance in the pushing and pulling forces acting on an object, the object will accelerate in the direction of the net force.
All forces acting on an object are added together to form the "net force." If the object is not moving, then this net force must be equal to zero, according to Newton's First Law.
acceleration a = F/m
a = 38700/ 26900
a = 1.43m/s²
F = ma
F = 106×1.43
F = 151.58N.
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a cylindrical rod has equal and opposite forces applied parallel to the surface of its circular ends. the forces are directed toward the center of the rod. what type of stress is this rod subject to?
The force that results in a material's deformation and subsequent reduction in volume is known as compression stress.
What exactly are tensile and compressive stress?Tensile Stress: When a body is subjected to an equal force that is applied perpendicular to its cross-sectional area, it deforms. Definition of Compressive Stress: The solid is compressed by the application of an external force. The body, which is known for compressive stress, responds by producing the restoring force.The force that results in a material's deformation and subsequent reduction in volume is known as compression stress. A material shrinks in volume as a result of the stress it experiences. The failure of the material is caused by high compressive stress.To learn more about compression refer to:
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Evaluate the sentence.
“Before the current can flow, the battery must first fill the wire with electrons.”
Correct or incorrect? Why?
Current is generated from the flow of electrons. To generate current the circuit must be complete. Hence, the battery must fill with the wire of electrons.
What is battery?A battery is an electrical component to power electronic devices. It is working with the principle of electrolysis. Where an electrolyte is used in which the two electrodes are dipped.
A redox reaction taking place there generate a chemical energy and which then converted to the electrical energy.The electron flow must be connected to a complete circuit.
Hence, without filling the electron in the battery it may not work. When it is connected with the wire to the external circuit it will passes the current to the devices.
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the mechanical energy and amplitude of a block-spring oscillator are 7.50 j and 9.40 cm respectively. let the maximum speed be 4.70 m/s. what is the mass of the block?
The mass of the block is 0.655 kg
What is mechanical energy?The combination of kinetic energy, or energy of motion, and potential energy, or energy stored in a system as a result of the arrangement of its components, is known as mechanical energy. A system with solely gravitational forces or one that is otherwise idealized—that is, a system without dissipative forces like friction and air resistance or a system in which such forces may be fairly neglected—has constant mechanical energy.A swinging pendulum has its highest kinetic energy and lowest potential energy in the vertical position, where its speed is greatest and height is lowest, and its highest Energy is constantly moving back and forth between the two forms as the pendulum swings. The mechanical energy of the pendulum, which is the total of its kinetic and potential energies, is constant when air resistance and friction at the pivot are taken into account.Calculation
The mechanical energy of block system,
[tex]E=\frac{1}{2} mv_{max} ^{2}[/tex]
The mass of the block is
[tex]m=\frac{2E}{v^{2} _{max} }[/tex]
[tex]\frac{2(7.50)}{4.70^{2} } =0.6550 kg[/tex]
Hence, the mass of the block is 0.655 kg
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The mass of the block is 0.655 kg
What is mechanical energy?The combination of kinetic energy, or energy of motion, and potential energy, or energy stored in a system as a result of the arrangement of its components, is known as mechanical energy.A system with solely gravitational forces or one that is otherwise idealized—that is, a system without dissipative forces like friction and air resistance or a system in which such forces may be fairly neglected—has constant mechanical energy.A swinging pendulum has its highest kinetic energy and lowest potential energy in the vertical position, where its speed is greatest and height is lowest, and its highestEnergy is constantly moving back and forth between the two forms as the pendulum swings.The mechanical energy of the pendulum, which is the total of its kinetic and potential energies, is constant when air resistance and friction at the pivot are taken into account.The mechanical energy of block system,
[tex]$E=\frac{1}{2} m v_{\max }^2$[/tex]
The mass of the block is
[tex]$m=\frac{2 E}{v_{\max }^2}$[/tex]
[tex]$\frac{2(7.50)}{4.70^2}=0.6550 \mathrm{~kg}$[/tex]
Hence, the mass of the block is 0.655 kg
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explain how your observation of the experiment either agreed with galileo or led you to a different conclusion. answer with three to five complete sentences and use proper grammar and mechanics.
My experiment disagreed with Galileo because Galileo's explanation for the tides was incorrect; the hypothesis that Earth orbits the Sun is right.
What part of Galileo's theory is incorrect?Galileo discovered evidence in 1595 that he believed supported the idea that Earth orbits the Sun. Galileo believed that the irregular motion of Earth around the Sun was the primary cause of the tides. Galileo's explanation for the tides was incorrect, even though the idea that Earth orbits the Sun is true.
Galileo presents his three top justifications for his contention that the earth revolves around the sun. One of these is his claim that "the ebbing and flowing of the ocean tides" supports his position.
There are high and low tides. Galileo thought that the earth's rotation was what created the tides. One of his absolute worst theories is this one.
The sun and moon's actions cause "the ebb and flow of the sea," as we now understand. That is the correct explanation for the tides, as stated by Newton. They result from gravitational forces, as Newton demonstrated.
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a 5.0- kg box is pulled by a horizontal force f applied to the top of the box. when the box meets a low doorstep, it begins to rotate around it. the box is 60 cm wide and 100 cm high. what minimum magnitude of the force f is needed to cause this movement?
The minimum magnitude of the force f is 21 N needed to cause the movement of a 5 kg box pulled by a horizontal force.
What is force and how is the magnitude of force comes out to be 21 N ?Force is the newtonian quantity which represents the product of mass and acceleration.The mass of the box is given to be 5 kg and the box is 60 cm wide and the height is 100 cm .When the block about to rotate normal shifted to the edge of the cube , mg(w/2) = Fh, F = mgx (w/2)= Fh taking g as 9.8 m/s^2.Substituting the values , F = (5 × 9.8 ( 60/2)) / 70Then the force would be , F = (5 × 9.8 × 30 ) / 70,F = 1470 / 70,F = 21 N.Hence the magnitude of the force comes out to be 21 N.Therefore when a 5 kg box is pulled by a horizontal force f applied to the top of the box, the minimum magnitude of the force f needed is 21N.To know more about force visit:
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The schroedinger wave equation relates the energy of an atom to its electrons in terms of the.
The Schrödinger wave equation relates the energy of an atom to its electrons in terms of the wave function.
What is the Schrödinger wave equation?The Schrödinger wave equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Schrödinger's model of the atom assumed the electrons could be treated at matter waves. The Schrödinger equation is conceptually the quantum counterpart of Newton's second law in classical mechanics.
Since electrons are identical to one another, the wave function of an atom with more than one electron must satisfy special conditions. The wave function of a system of identical particles depends on the coordinates of all the particles. The wave function must remain unaltered or at most undergo a change of sign if the coordinates of two of the particles are interchanged.
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Resonant standing waves are excited on a string that is fixed at both ends. The speed of the superposed traveling waves that yield the standing wave increases if.
When the tension in the string is reduced, the speed of the traveling waves that combine to form the standing wave accelerates.
What does conflict between people mean?When people are uneasy, distrustful of one another, and there is a chance of an unexpected act of violence or conflict, tension is the result. There is a good chance that the two nations' conflict will persist. Synonyms include conflict, animosity, uneasiness, and antagonism. More words for tension.
What's a good instance of tension?The force of compression opposes the tension. Each object in the scene that is in contact with another one applies a force to the other. Pulling a rope provides the best demonstration of a tension force. There is a large amount of tension created in the rope when a pull force is applied.
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What is the potential difference measured if the following voltmeter (refer to picture) is used and connected to the circuit via the 3V terminal?
Since the meter's 3V terminals are connected to the circuit, we have to read the "zero-to-3" scale on the meter to get our measurement. That's the scale under the marks.
On that scale, the needle points to 1.4 DC Volts. That's the potential difference between the two points the meter probes are touching.
What accounts for the light and dark bands produced when monochromatic light reflects from a glass pane atop another glass pane?.
The waves that are reflected off the glass on the top and bottom surfaces of the air wedge interfere, which results in these bands. Interference between light waves reflected from the thin film's two sides.
Define monochromatic light.Electromagnetic radiation of a certain wavelength, whether visible or invisible, is monochromatic light.
Although in theory monochromatic light has exactly one wavelength, this is not practical, hence monochromatic light always comprises of a (relatively) narrow bandwidth of wavelengths. The color that the human eye can see when monochromatic light is in the visible spectral range is referred to as the spectral color. Lasers produce monochromatic light directly; a monochromator separates monochromatic light from a broadband light source.
Monochromatic light should only have one wavelength, according to theory. Monochromatic light is actually defined as having a narrow bandwidth.
A monochromator can be used to separate monochromatic light from polychromatic light.
In the visible wavelength range, monochromatic light is regarded as having spectral color.
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at what frequency would the reactance of a 15 mu or micro ff capacitor equal that of a 1.5 mh inductor?
The capacitor's reactance decreases as the frequency being applied to it rises. Similarly, the reactance value of the capacitor increases as the frequency across it decreases. The complex impedance of the capacitor is the name of this variation.
Because capacitance equals inductive reaction
Xc = XL
2*pi*frequency*L = 1/(2*pi*frequency*C)
frequency^2 = 1/(4*pi^2*L*C)
frequency = 1/2 * pi * sqrt(L*C)
frequency = 1/ (2*3.142*sqrt(1.1*10^-3*11*10^-6))
frequency = 1446.67 Hz
Reactance is the resistance that a capacitor and an inductor provide to an AC current in a circuit. Reactance and resistance are relatively similar, although reactance changes depending on the frequency of the ac voltage source. Ohms are used to measure it.
Either an increase in frequency or capacitance causes a reduction in capacitive reactance. As the frequency approaches zero in the limit, the capacitive reactance reaches an infinite value. Zero frequency for the generator implies the presence of a battery or other dc source.
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a light plane attains an airspeed of 500 km/h. the pilot sets out for a destination 800km due north but discovers that the plane must be headed 20o east of due north to fly there directly. the plane arrives in 2.0 h. what were a) the magnitude b) the direction of the wind velocity?
a) The magnitude of the wind velocity([tex]V_{ag}[/tex]) is 185 km/h
b) the direction of the wind velocity ([tex]V_{ag}[/tex]) is [tex]22.3^{o}[/tex] southwest
What is relative velocity?Understanding frame of reference is key to understanding relative motion or relative velocity. A frame of reference can be compared to the observer's current motion while they watch an event. For instance, you would consider yourself to be in a stationary frame of reference if you were sitting in a lawn chair and watching a train pass you at 50 meters per second from left to right. From your perspective, the train is moving while you are at rest. If you have excellent vision, you may even see a glass of water on a table inside the train move 50 meters per second from left to right.Calculation
Let east be + x-axis and north be + y-axis
The destination is D= 800 km
This takes 2 hours, so the constant velocity of the plane (relative to ground) is [tex]V_{pg}[/tex] is 400 km
The vector sum of the plane's velocity with respect to the air, which has (x, y) components (500cos70, 500sin70)
and the velocity of the wind relative to the ground ([tex]V_{ag}[/tex]). Thus, (400 km/h) = (500 km/h) cos70i +(500 km/h) sin70j + [tex]V_{ag}[/tex].
Which yields
[tex]V_{ag}[/tex] = (-171 km/h) i – (700 km/h) j
a) The magnitude of the wing velocity is
[tex]V_{ag}[/tex] = [tex]\sqrt{(-171 km/h) i - ( 700 km/h) j}[/tex] = 185 km/h
b) The direction of the wind velocity is
Θ = [tex]tan^{-1} =\frac{-70.0 km/h}{-171 km/h} = 22.3^{o}[/tex] southwest
Hence, the magnitude of [tex]V_{ag}[/tex] is 185 km/h and direction of the [tex]V_{ag}[/tex] is [tex]22.3^{o}[/tex] Southwest.
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two parallel metal plates are 5 cm apart and have equal surface charge densities of 9 nc/m2 of opposite signs on their inner surfaces. what is the electric field between the plates?
1.01 x 10³ C/m² is the electric field present between the two metal plates.
The electric field is defined as the region around a charged particle or charged body in which if another charge is placed experiences an electrostatic force.
The electric field inside two equal and opposite charged plates is given by
E = σ / ε ------ equation 1
here σ is the surface charge density = 9 x 10⁻⁹ C/m²
ε = Dielectric permittivity = 8.85 x 10⁻¹² C²/Nm²
Putting the values in equation 1
E = 9 x 10⁻⁹ / 8.85 x 10⁻¹²
=> 1.01 x 10³ N/C
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