In a car crash test, whether you let the car slam the wall or let the car plow into a tub of gelatin, the impulses are the same. However, you and your car will experienced greater force if the car slam the wall.
The impulse is defined as the change in momentum.
I = Δp = m . Δv
Where:
I = impulse
p = momentum
m = mass
v = velocity / speed.
From the Newton's second law of motion:
m = F/a
Where:
F = force
a = acceleration
Hence,
I = F / a . Δv
I = F . Δv/a = F . t
Where t = time period of the exerted force.
The initial and the final velocities of the car are the same for both cases. Hence, from the definition of impulse as the change of momentum, the impulses on both cases are the same. However, if the car experienced sudden stop, which means the force exerted on it in only a very short time, the exerted force on the car will be very large.
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two cars collide inelastically and stick together after the collision. before the collision, the magnitudes of their momenta are p1 and p2 . after the collision, what is the magnitude of their combined momentum?
the magnitude of their combined momentum is p=p1+p2
In Newtonian mechanics, an object's mass and velocity are combined to create momentum, more precisely linear momentum or translational momentum. It is a vector quantity with a magnitude and a direction. When an object's mass (m) and velocity (v), which is also a vector quantity, are known, the result is the object's momentum.
The kilogram meter per second (kg m/s), which is equated to the newton-second in the International System of Units (SI), is the unit used to measure momentum.
According to Newton second law of motion, a body's rate of momentum change is equal to the net force acting on it. While momentum varies depending on the frame of reference, it is a conserved quantity in every inertial frame.
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Using the data collected from the motion detector, the group of students is
able to calculate both initial and final velocities. The initial velocity is
measured when the mass is released, and the final velocity is measured just
as the mass hits the floor. Using these velocities, they calculate the initial and
final kinetic energies. They also calculate the initial gravitational potential
energy by measuring the initial height when the mass is released. The final
gravitational potential energy is taken to be zero at the floor. When they
compare the final (kinetic) energy value to the initial energy value (that is, the
sum of the initial kinetic and gravitational potential energies), which of the
values is greater...
if the assumptions presented in the previous problem are true?
The initial and final energies a
if the assumptions presented in the previous problem are not true?
[ Select ]
Unless the above assumptions are clear, the initial and final energies are equal.
What is kinetic energy?Kinetic energy is the form of energy that an object or a particle possess due to its motion. If work, that transfers energy, is done on an object by applying a net force, the object accelerates and thereby gains kinetic energy. Kinetic energy is a property of a moving object or particle and depends on its motion as well as its mass. The type of motion may be translational (or motion along a path from one place to another), rotational, vibrational, or any combination of motions. Translational kinetic energy is one-half the product of its mass (m) and the square of its velocity (v) or 1/2mv².
Given,
Initial and final velocities = v₁ and v₂
Initial kinetic energy = [tex]\frac{1}{2} mv_{1} ^{2}[/tex]
Final kinetic energy = [tex]\frac{1}{2} mv_{2} ^{2}[/tex]
Gravitational potential energy is calculated = mgh
As the assumptions are not clear, this question assumes no air resistance. As a result, no energy is consumed by work.
then
Initial Kinetic Energy = Final Kinetic Energy
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Which of the following objects have kinetic energy?
An elephant walking 1.5 m/s along the ground.
A jet flying across the sky 4,000 m above the ground.
A car traveling 20 m/s along a flat road.
A concrete block sitting on the ground.
An apple on a tree branch 3.0 m above the ground.
Which statement best shows that waves can carry energy?
Sounds can be recorded.
A rainbow shows a spectrum of colors.
You feel vibrations if loud sounds are played.
Light shining through some trees makes shadows.
The statement that best shows that waves can carry energy is option d: light shining through some trees makes shadows.
What is the most accurate way to define sound waves?A sound wave is the pattern of disruption brought on by the movement of energy moving through a medium as it propagates away from the source of the sound (such as air, water, or any other liquid or solid matter). Pressure waves are produced when an object vibrates, such as a ringing phone, and these waves are known as sound waves.
Therefore, note that the energy of a sound wave is transferred through particle contact. A vacuum cannot be traversed by a sound wave. Sound is now a mechanical wave as a result.
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a skier traveling 11.0 m/s reaches the foot of a steady upward incline and glides 15 m up along this slope before coming to rest. what was the average coefficient of friction?
The average coefficient of friction of the track on which the skier is travelling is 0.59.
According to work energy theorem, the work done by conservative forces and the non conservative forces on the body is equal to the change in kinetic energy of the body.
So here, we know that the skier is travelling with a speed of 11m/s and he glide a distance of 15 m.
Here, we can write,
Mgd + uMgd = ∆K
Where M is the mass of the body,
g ji is the acceleration due to gravity,
d is the distance travel by the glider,
K is the change in kinetic energy,
U is the coefficient of friction.
Putting values,
Mgd + uMgd = 1/2Mv²
2(gd + ugd) = v²
u = (v²/2-gh)/gd
u = ((11)²/2 -10×15)/10×15
u = 0.59
So, the average coefficient of friction is 0.59.
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the hanging mass is referred to as m and it sets the centripetal force. group of answer choices true false
The answer is True
When we do not have the numerical value of mass.
The answer is False
By choosing a value of hanging mass it becomes false.
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a 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. the safe hits the spring and, in coming momentarily to rest, compresses it 50 cm. what is the spring constant of the spring?
The value of the spring constant of the spring is 156800N/m.
As per the work energy theorem, the work done in making the safe go down will be equal to the work done by the spring.
So it can be written
1/2kx² = mgh
K is the spring constant,
x is the compression,
m is the mass of the safe,
g is the acceleration due to gravity which is 9.8m/s²,
H is the height above the ground at which the safe is kept which is 2m.
Now, putting all the values,
1/2(k)(0.5)² = 1000(2)(9.8)
K = 156800 N/m.
So, the value of the spring constant is 156800 N/m.
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What is the phase angle between the voltages of the inductor and capacitor in a rlc series circuit?.
Answer: at least 180 degrees
9-3 is it possible for a small force to produce a larger impulse on a given object than a large force? explain.
It is possible for a smaller force with a longer time to be stronger than a larger force with a shorter time since impulse equals force x time.
Is it possible for a small force to produce a larger impulse?Yes, since impulse is defined as the product of the applied force and the applied time (J=Ft J = F t), a smaller force acting over a longer period of time may produce a larger impulse than a larger force acting over a shorter period of time. Force times time equals impulse.In comparison to a bigger force that acts over a much shorter period of time, a tiny force acting over a long period of time can easily produce more impulse (change in momentum). An object's momentum is a function of its mass times its velocity.An item can be propelled at the same speed by a tiny force applied over a long time as it can by a high force applied quickly.To learn more about larger impulse refer
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you toss a ball straight upward so it leaves your hand at a speed of 10.1 m/s. if the 3.3 kg ball started at rest and the tossing action lasted 0.33 s, what was the strength of the force exerted on the package by your hand?
The strength of the force exerted on the package by your hand: 101 N
We know v = u+at
v =10.1 m/s
u = 0
t =0.33 s
10.1 = 0+a*0.33
10.1 = a*0.33
a = 30.6 m/s^2
Force exerted F = ma
= 3.3*30.6
= 101
F = 101 N
What is Force ?A force is an effect that can change the motion of an object. Under the influence of a force, an object with mass can change its speed (e.g. move from standstill), i.e. to speed up A force can also be intuitively described as a push or a pull. A force has both magnitude and direction, so it is a vector quantity. It is measured in SI units Newton (N). Power is represented by the symbol F (formerly P).
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suppose you have two identical socks that exert a force of 10 n on each other. now you move them so they are three times as far apart as they were originally. (a) calculate the new force between the objects. (b) will this force be attractive or repulsive? please explain
(a) Since the separation is being tripled the force would go to 1/9 its original value if the charges remained constant because Coulomb's Law is an inverse square law. So, the new force is 10/9 N.
(b) because the pressure remains the equal and it became repulsive, initially, it will remain repulsive. One could also deduce this for the reason that the socks are equal.
Electrostatic repulsion can also be observed, for example, with an electroscope. It's a simple device consisting of a piece of metal sticking out of a glass jar and a thin metal leaf hanging inside. When the outer piece of metal touches the charged body, the Coulomb force causes the sheet to expand.
The repulsive force between oppositely oriented magnets. A compression material that repels the body on both sides. Repulsion is associated with involuntary vomiting such as in response to the ingestion of toxins.
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an ac adaptor for a telephone answering unit uses a transformer to reduce the line voltage of 80 v (rms) to a voltage 9.8 v. the rms current delivered to an answering system is 392 ma. if the primary (input) coil in the transformer in the adaptor has 170 turns, how many turns are there on the secondary (output) coil? answer in units of turns.
The secondary coil of the transformer is 21 turns.
We need to know about transformers to solve this problem. The transformer is a device that changes the output voltage by using different turns on its coil. The ratio of output voltage and input voltage should follow this equation
Vo / Vi = Ns / Np
where Vo is output voltage, Vi is input voltage, Ns is secondary turns and Np is primary turns.
From the question above, the given parameters are
Vi = 80 V
Vo = 9.8 V
Np = 170 turns
By using the equation, we can calculate the secondary turns
Vo / Vi = Ns / Np
80 / 9.8 = 170 / Ns
Ns = 170 . 9.8 / 80
Ns = 20.825
Thus we can round the secondary turns to 21.
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an elevator is moving down at a constant rate of 4 m/s. a person is standing on ascale that says the person weighs 80 n. when it reaches the bottom, it comes to a stop in 2 seconds. during the stopping process, what is the reading on the scale? (a picture of what is happening during the stopping of the elevator will help.)
The reading on the scale is 96.31 N.
What is meant by reading on the scale?The Reading Scale describes how people progress through the difficult process of learning to read. It provides teachers with methods for viewing and analyzing their observations of children's developing reading skills, knowledge, and comprehension.
When the elevator stops, its speed decreases from 4 m/s to 0 m/s.
This suggests a slowing down. The amount of force being applied to the
F= mass times acceleration
Assuming the deceleration is constant, we have the following equation:
V = U + at
Where V = Final speed = 0
U = initial speed = 4
a = acceleration
t = time
Solving, we get:
0 = 4 + 2a
a = -2 m/s^2
Solving, we get:
0 = 4 + 2a
a = -2 m/s^2
Thus the object decelerates at 2 m/s^2
The mass of the person = 80 / 9.81 = 8.155 kg
F = 8.155 * 2
F = 16.31 N
Weight in total: 80 + 16.31 = 96.31 N (This is the reading on the scale).
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A car (mass 1 000 kg) uses 50 000 J of energy (from fuel) to accelerate the car from rest to 5.5 m/s (about 20 km/h). How efficient is the car’s engine? ( Think, Eff = Eout/Ein x 100/1)
The energy output from the car is 15125 J and the input energy is given 50000 J. Thus, the efficiency of the car is 30.25 %.
What is engine efficiency?The efficiency of an engine is the ratio of its energy output to the energy input multiplied by 100. The efficiency of a heat engine can be found similarly using the input heat and output heat.
Given the mass of the car is 1000 Kg and it is accelerated to 5.5 m/s. Therefore the kinetic energy output is is calculated as follows:
KE = 1/2 mv²
= 1/2 1000 kg × (5.5 m/s)²
= 15125 J
The input energy is 50000 J. Therefore, the energy efficiency is :
efficiency = output energy / input energy × 100
= ( 15125 J/ 50000J ) × 100
= 30.25 %
Hence, the energy efficiency of the car is 30.25 %.
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a 40-kg crate is being lowered with a downward acceleration is 2.0 m/s 2 by means of a rope. (a) what is the magnitude of the force exerted by the rope on the crate? (b) what would be the magnitude of the force exerted by the rope if the crate were being raised with an acceleration of 2.0 m/s 2?
a) Force exerted by the rope on the crate is equal to 312 N.
b) Force exerted by the rope if the crate were being raised with an acceleration of 2.0 m/s² is 472N.
What is force?In science, a force is a push or a pull in a specific direction. When one object interacts with another object, forces are created.
In physics, arrows are used to represent forces. An arrow pointing in the same direction will indicate the force's direction.
Given,
mass of a crate, m = 40 kg
Acceleration of crate, a = 2 m/s²
a) As carte is falling down, net force exerted by rope on the carte is given by : F = m(g-a)
F = 40(9.8-2)
F = 312 N
∴ required force exerted by the rope on the crate is equal to 312 N.
b) If the crate was raised with an acceleration of 2.0 m/s², than:
F = m(g+a)
F = 40 (9.8 + 2)
F = 472 N
∴ required force exerted by the rope if the crate were being raised with an acceleration of 2.0 m/s² is 472N.
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the lift piston base and the input piston base are at the same height. what input force, , is required to maintain this system in equilibrium?
Input force = (Output force/Output area) × Input area
By Pascal Law,
Input force / input area = Output force / output area
By re-arranging,
Input force = (Output force/Output area) × Input area
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what measure do seismologists use to calculate the distance from a seismic receiving station to the epicenter of an earthquake? group of answer choices the time interval between the first p wave and the last surface wave the magnitude of the ground acceleration of surface wave passing a receiving station the time elapsed between the first p wave arrivals from the first and last aftershocks the time interval between the arrivals of the first p and s waves the amplitude of the strongest s wave
Option A - the time interval between the first P-wave and first S-wave arrivals is correct.
Determine the difference between the first P-wave and the first S-arrival wave's periods, and then use that information to calculate the distance of the epicenter from the seismic recording station.
The study of elastic wave motion through the ground is known as seismology. Seismology of earthquakes is the finest method for investigating the earth's core. A portion of the energy released after an explosion or earthquake is transported through the earth as elastic waves. Stresses increase in the crust as the lithospheric plates of the Earth continue their sluggish motion, particularly close to the plate borders. Compression, tension, and shear stresses increase in the crust until they exceed the resistance of the rock or the friction along an existing fault. Then, an abrupt rock slide along a fault happens. The rocks lurch to their new location in a matter of seconds, and the ground trembles as the stress energy is released. Similar to growing ripples from a pebble thrown in still water, seismic waves propagate outward from the area of the fault that ruptured.
To clarify the options an image is attached.
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How can we statistically study the evolution of galaxies many billions of years ago?.
We can contrast distant galaxies with nearby galaxies.
The cosmos is 13.7 billion years old, but how can they know that?Although scientists are unsure of the universe's actual age, we estimate that it is somewhere between 13 and 14 billion years old. In order to determine the age of the universe, astronomers use two different methods: (a) searching for the earliest stars; and (b) measuring the universe's rate of expansion and projecting it back to the Big Bang.
How can the age of galaxies be determined?The amount of time it took for the galaxies to get to their current distances is therefore t=D/v. However, we know that v=H0D because to Hubble's Law. Therefore, t=D/v=D/(H0D)=1/H0. Thus, 1/H0 can be used as a rough estimate for the age of the Universe.
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6. what is the origin of the acceleration cue when in hover mode at 4 ktgs? in hover mode at 7 ktgs? in transition mode at 50 ktgs?
When the velocity vector is less than its maximum scale, the tip of the vector serves as the origin of the acceleration cue (6 KTGS). When the velocity vector is at or above maximum scale, the center of the LOS reticle serves as the origin of the acceleration cue.
Where does maximal velocity occur?Knowing that the system is in equilibrium at y=0, or when displacement and acceleration are both equal to zero, is known as the velocity maxima. As a result, the maximum velocity in simple harmonic motion at a given place can be calculated using the formula v=A. A velocity vector shows the rate of change in an object's position. The magnitude of a velocity vector represents an object's speed, whereas the vector's direction represents an object's direction. The apex—the highest point on any trajectory—is reached when vy=0. Given that we are aware of the initial location, initial and final velocities, and initial position, we may determine y using the equation v2y=v20y2g(yy0).
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Within free market economies, what role does self interest play? What role does competition play?
Economic activity is driven by self-interest, and competition helps to drive down costs and increase the quality, diversity, and creativity of goods and services.
What kind of activity is self-interested?Seeking your own personal gain is the definition of self-interest. You attend work in order to earn money to spend on the things you want. You attend school so that after you graduate, you'll be able to find a better career and get more money to spend on the things you desire.
How can self-interest be developed?Pick some fresh endeavors that promote goodwill in your career, family, and leisure life. Likewise, be adamant in your actions. When appropriate, communicate your thoughts and feelings to others by asking for what you want, declining what you don't want, and saying No to requests. For a while, make it a point to treat yourself to something every day.
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three objects are at the top of an inclined plane: a disk, a sphere, and a ring. all of the objects have the same radius and the same mass. which object would finish last in a race down the incline if they are all released from rest? (hint: use conservation of energy methods, and note that at the bottom there is both translational and rotational energy)
The ring would finish at last in the race down the incline.
Incline is a a plane surface tilted at some angle from the horizontal.
The moment of inertia of the ring = [tex]mr^{2}[/tex]
The moment of inertia of the disc = ( [tex]mr^{2}[/tex] ) / 2
The moment of inertia of the solid sphere = 2( [tex]mr^{2}[/tex] ) / 5
Since the moment of inertia is the resistance to rotational motion, we see that the object with the smallest moment of inertia will reach the bottom first.
The gain in total kinetic energy is equal to the loss in gravitational potential energy, which in turn is the same for all the objects and is equal to 'mgh'
where h is the height of the inclined plane.
So the order of reaching the bottom is Sphere, disc and ring.
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what is the point in the sky directly overhead called? which constellation is closest to this point tonight?
The answers include the following:
The point in the sky which is directly overhead is called Zenith.The constellation which is closest to this point tonight is Polaris.What is Constellation?This is referred to as a group of stars that form a perceived pattern or outline and are usually given names and an example is hydra.
The Zenith as the name implies is known as the overhead point in the sky which is usually hardly seen while the constellation which is closest to this point tonight is Polaris due to the position thereby making it the most appropriate choice.
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Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. the vertex of the parabola is at the origin. where should gabe place the bulb to ensure a perfect beam of light? (0, 1) (0, 4) (1, 0) (4, 0)
Gabe should place the bulb to ensure a perfect beam of light at (C) (1,0).
A reflective surface used to gather or project energy like light, sound, or radio waves is known as a parabolic, paraboloid, or paraboloidal reflector, dish, or mirror. Its form is a component of a circular paraboloid or the surface produced by a parabola rotating around its axis.
Suppose the equation of parabolic mirror is Y2 = 4ax
The given data in the problem is x = 1 and y = 2
So the subject value is y2 = 4ax
4 = 4 a (1)
4 = 4a
a = 1
So x = 1
thus focus is at (x, y) = (1,0)
Thus option C is the correct answer.
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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 if a primordial black hole with the mass of our moon and a schwarzchild radius of 0.01cm approached, passed through, and exited the earth? what might happen to our planet and to life here?
When it will pass through our Earth, it will contain the whole of our earth as its gravitational field is so high.
What is a primordial black hole?A hypothetical type of dark gap that formed soon after the Big Bang is known as primordial dark openings. High densities and inhomogeneous circumstances in the early cosmos may have caused sufficiently thick regions to experience gravitational crumpling, which would have framed black openings. Supermassive dark gaps can be distinguished from bring down mass clusters by certain characteristics. Firstly, due to some SMBHs, the usual thickness of an SMBH (defined as the mass of the dark opening divided by the volume inside its Schwarzschild range) may be less than the thickness of water.Given that the volume of a round question, such as the occasion skyline of a non-pivoting dark opening, is specifically relative to the 3D square of the span, and that a dark gap's thickness is. On the other hand, conversely relative to the square of the mass, higher mass dark gaps have lower normal thickness, this is the reason. As with thickness, the tidal power of a body at the occasion of skyline is counterintuitively related to the square of the mass, Therefore, the tidal powers in the region of the occasion skyline are essentially weaker for monstrous dark apertures. It's a slow-moving event.When it will pass through our Earth, it will contain the whole of our earth as its gravitational field is so high.To learn more about primordial black hole, refer to
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When it will pass through our Earth, it will contain the whole of our earth as its gravitational field is so high.
What is a primordial black hole?A hypothetical type of dark gap that formed soon after the Big Bang is known as primordial dark openings.High densities and inhomogeneous circumstances in the early cosmos may have caused sufficiently thick regions to experience gravitational crumpling, which would have framed black openings.Supermassive dark gaps can be distinguished from bring down mass clusters by certain characteristics.Firstly, due to some SMBHs, the usual thickness of an SMBH (defined as the mass of the dark opening divided by the volume inside its Schwarzschild range) may be less than the thickness of water.Given that the volume of a round question, such as the occasion skyline of a non-pivoting dark opening, is specifically relative to the 3D square of the span, and that a dark gap's thickness is.On the other hand, conversely relative to the square of the mass, higher mass dark gaps have lower normal thickness, this is the reason.As with thickness, the tidal power of a body at the occasion of skyline is counterintuitively related to the square of the mass,Therefore, the tidal powers in the region of the occasion skyline are essentially weaker for monstrous dark apertures.It's a slow-moving event.When it will pass through our Earth, it will contain the whole of our earth as its gravitational field is so high.To learn more about primordial black hole, refer to
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a thin oil slick (index of refraction 1.50) floats on water (index of refraction 1.33). when a beam of white light strikes this slick at normal incidence from air, the only enhanced reflected colores are red (650nm) and violet (390 nm). what is the minimum thickness of the oil
The oil slick measures 325 nm thick, at the very least. There are a few methods for measuring slicks between 0.1 and 10 m (0.0001-0.001 mm), but these aren't helpful for oil spill cleanup.
What is an oil slick known as?An oil spill is the inadvertent release of a liquid petroleum hydrocarbon to the environment as just a consequence of human activity (also known as an oil slick). This is the typical definition of an oil slick; alternative definitions are covered in the article.
What does oily hair refer to?A combination of dark blue, green, or purple tones are applied to darker hair in this style, which is also known as oil spill hair because it gives the hair a shimmering appearance. It resembles the pastel hair style, but instead of using ultra-pale colors, deeper colours are blended to create the iridescent look..
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what has more kinetic energy an object of mass 2m moving with speed 3v or an object of mass m moving with speed 4v
Kinetic energy The height of an object of mass m moving at speed 4v will be greater than that of an object of mass 2m moving at speed 3v. Kinetic energy = 0.5 m v2
A mass of 2 m moving at a speed of 3 v has kinetic energy of 9 m, while a mass of m moving at a speed of 4 v has kinetic energy of 8 m. The ability of an object to move another object is known as its kinetic energy. It is effective for a force to move an object. Furthermore, we are aware that an object in motion can cause a stationary object to move if it collides with it. It can therefore perform a function. The ability of an object to perform work as a result of its motion is how we define kinetic energy.
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a digital thermometer can make readings to the tenth of a degree at either the celsius setting or the fahrenheit setting. which reading would be more precise?
The Fahrenheit setting, since 1 degree Fahrenheit is smaller than 1 degree Celsius.
For general use, a straightforward formula exists to convert temperatures from Fahrenheit to Celsius. Just subtract 30 from the Fahrenheit value, and then divide that result in half.
Most objects we measure including length, width, time, and other dimensions—have one thing in common: their values all begin at zero. Zero of any of those units may be converted into another sort of unit quite easily because we all know exactly how long zero centimeters or inches are. Inches, metres, and centimetres all equal zero. As an illustration, let's use inches and centimetres. To move from 0 inches to 1 inch, we need to add 1 inch. This much is clear.
Similarly, we just need to add 1 centimetre to go from 0 centimetres to 1 centimetre. The quantity of space we are adding is the only distinction between adding one inch or one centimetre. One inch is 2.54 centimeters, according to the connection between the two units.
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a spherical shell with radius r and uniform surface charge density spins with angular frequency w around the diameter. find the magnetic field
The magnetic field is [tex]\vec{m}=\frac{Q}{3} R^2 \vec{\omega}[/tex]
How to calculate magnetic field?The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is moving through a magnetic field.
Uniformly charged spherical shell of radius R carries a total charge =Q
Hence it has surface charge density
[tex]\sigma=\frac{Q}{4 \pi R^2}[/tex]
It rotates about its axis with frequency=f
∴ Its angular velocity ω=2πf
Suppose the angular velocity [tex]\vec{\omega}=\omega \hat{z}[/tex]
To find the magnetic moment of spinning shell we can divide
it into infinitesimal charges. Using spherical polar coordinates (ρ,ϕ,θ) with origin at the center of the spherical shell, we consider infinitesimal area dS of a circular ring of infinitesimal width and of radius r located at a distance R from the origin on the surface of sphere.
Here [tex]\vec{r}=R \sin \theta \hat{r}[/tex] and coordinate ρ=R, is constant for each elemental area.
[tex]d q=\sigma d S=\sigma R^2 \sin \theta d \theta d \phi[/tex]
Current in the ring is given by
[tex]\begin{aligned}&d I=(d q) \times f=\left(\sigma R^2 \sin \theta d \theta d \phi\right) \times \frac{\omega}{2 \pi} \\&\Rightarrow d I=\frac{\omega \sigma R^2 \sin \theta d \theta d \phi}{2 \pi}\end{aligned}[/tex]
Now the magnetic dipole moment of ring is given by the expression in terms of position vector [tex]\vec{r}[/tex]current density [tex]\vec{J}[/tex]
[tex]\begin{aligned}&d \vec{m}=\frac{1}{2} \int_{\text {ring }} \vec{r} \times \vec{J} \\&\Rightarrow d \vec{m}=\frac{1}{2} d I \int_{\text {ring }} \vec{r} \times d \vec{l}\end{aligned}[/tex]
Line integral becomes equal to the circumference of ring
[tex]\therefore d \vec{m}=d I\left(\pi R^2 \sin ^2 \theta\right) \hat{z}[/tex]
Inserting value of dI we get
[tex]\begin{aligned}&d \vec{m}=\frac{\omega \sigma R^2 \sin \theta d \theta d \phi}{2 \pi}\left(\pi R^2 \sin ^2 \theta\right) \hat{z} \\&\Rightarrow d \vec{m}=\frac{\vec{\omega} \sigma R^4 \sin ^3 \theta d \theta d \phi}{2}\end{aligned}[/tex]
Total magnetic moment is integral with respect to both variables within respective limits
[tex]\begin{aligned}&\vec{m}=\frac{\vec{\omega} \sigma R^4}{2} \int_0^\pi \sin ^3 \theta d \theta \int_0^{2 \pi} d \phi \\&\Rightarrow \vec{m}=\frac{\vec{\omega} \sigma R^4}{2} \times \frac{4}{3} \times 2 \pi \\&\Rightarrow \vec{m}=\frac{4}{3} \pi \sigma R^4 \vec{\omega}\end{aligned}[/tex]
Rewriting in terms of charge Q
[tex]\begin{aligned}&\vec{m}=\frac{4}{3} \pi\left(\frac{Q}{4 \pi R^2}\right) R^4 \vec{\omega} \\&\vec{m}=\frac{Q}{3} R^2 \vec{\omega}\end{aligned}[/tex]
The complete question is : A spherical shell of radius R and uniformly charged with charge Q is rotating about its axis with frequency f. Find the magnetic moment of the sphere?
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the earth's atmosphere is transparent tomost waves in thequestion 2 options:visible part of the spectrum.infrared part of the spectrum.ultraviolet part of the spectrum.entire electromagnetic spectrum.
The earth's atmosphere is transparent to most waves is visible part of the spectrum(option -1).
What wavelengths are transparent to the atmosphere of the Earth?To some microwave radiation wavelengths, but not to others, the Earth's atmosphere is transparent. The Earth's atmosphere is more easily penetrated by the longer wavelength microwaves than by the shorter ones (wavelengths more akin to radio waves).
When compared to open, closed, or partially closed windows, the Earth's atmosphere is only transparent to particular wavelengths of light. All of the radio waves, the majority of the IR light, and all of the visible light pass through the atmosphere.
It should be noted that the atmosphere is generally opaque in the infrared spectrum and completely transparent in the visible and infrared bands. In our hypothetical case, this would be entirely transparent (no absorption) in the solar band and uniformly absorb (and emit) throughout the earth emission band.
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