Rachel is correct because she said that is body receive equal magnitude of impulse which completely satisfy the law of conservation of linear momentum.
According to law Conservation of Linear Momentum, if there is no external force working on the system, then the linear momentum remains conserved before and after the collision.
We know that,
Momentum is nothing but the product of force and the time taken for the contact period of the colliding bodies.
We assume that during the head on collision of the body, the body is remain in contact for such a short period of time that there is no external force all the impulse created due to the external force is neglected.
So, because the impulse imparted on both the bodies are equal to each other.
We know that impulse is nothing but the change in momentum.
So, from here we conclude that bodies received equal magnitude of impulse.
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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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magnus has reached the finals of a strength competition. in the first round, he has to pull a city bus as far as he can. one end of a rope is attached to the bus and the other is tied around magnus's waist. if a force gauge placed halfway down the rope reads out a constant 1550 newtons while magnus pulls the bus a distance of 2.15 meters, how much work does the tension force do on magnus? the rope is perfectly horizontal during the pull.
The Work done by tension force on Magnus is
- 3225 Joule .
In the given question we have, one end of rope is tied around magnus waist and other attched to bus and he pulls the bus. The direction of tension force is just work done.
constant force = 1550 Newton
displacement = 2.15 meters
The direction of tension force is opposite to work done due to the tension force is reaction force to force of work done for pulling the bus.
work done by tension = W = - W₀
where W₀is horizontal work done by magnus during pulling.
so, W₀ = Fdcosθ
where , F---> force , d--> displacment and θ ---> angle between force and displacement
As we see whole work done in horizontal direction. So, angle between force and displacement is zero.
put all the vales in above formula we get ,
W₀= 1550× 2.15 cos0 = 1550×2.15 = 3225 Joule
W = - W₀ = - 3,225J
Hence, work done by tension force on Magnus is
- 3,225 Joule.
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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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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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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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bird bones have air pockets in them to reduce their weight. this also gives them an average density significantly less than that of the bones of other animals. suppose an ornithologist weighs a bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g (the bone is watertight). what mass of water is displaced?mass of water displaced:kg what is the volume of the bone?volume of the bone:m3 what is its average density?average density of the bone:kg/m3 question credit: openstax college physics
a) Mass of displaced water is 41.4 g or 0.0414 kg
b) Volume of the bone is 41.4 mL or 41.4 × 10⁻⁶m³
c) Average density of the bone is 1.09 g/ mL or 0.00109 × 10⁻⁶ Kg /m³
In the given question we have, the weight of some bird bones is measured in air outside of some water and the weight is 45.0 grams and the apparent weight in water is 3.60 grams. Now, we shall find out the weight of the displaced water? So the buoyant force is this difference between the weight of the bones out of the water and in the water, so the weight out of the water times g minus the weight in the water times g and then the g can be factored in and the buoyant force is also equal to the weight of the displaced fluid from Archimedes' principle
i.e., 45 × g - 3.60× g = weight/ mass of displaced water
weight of displaced water = 41.4 × g
g× mass of displaced water = 41.4 ×g
=> mass of displaced water = 41.2 grams
a) Mass of displaced water = 0.0414 Kg
b) the volume of the bones is going to be equal to the volume of water displaced.
We know that the density of water is the mass of water displaced divided by the volume of water. So the volume of water displaced is the weight of the water displaced divided by the density of the water.
Volume of water displaced = 41.4 grams / density of displaced water
density of water displaced = 1 grams / milliliters
So, the density of water is 41.4 milliliters or 41.4 ×10⁻⁶ m³
c) The average density of the bone is the weight of the bone divided by its volume,
Average density of bone = 45 grams / 41.4 mililitres
so it's value is 1.09 grams per milliliter or 0.00109 × 10⁻⁵ m³
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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.
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 phase angle between the voltages of the inductor and capacitor in a rlc series circuit?.
Answer: at least 180 degrees
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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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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what conditions must occur for the two carts to move in different directions after the collision? (assuming that a moving cart collides elastically with a stationary cart).
As a result of the collision, the cart, which had a velocity of 1, comes to rest. The cart then accelerates with velocity v1 from rest. assuming that a moving cart collision elastically with a stationary cart.
We are aware that both the linear momentum and the kinetic energy are conserved in completely elastic velocity. However, only the kinetic energy of an inelastic impact is conserved. Any situation in which two or more bodies quickly exert forces on one other is referred to be a collision. The scientific definition of the word "collision" makes no reference to the magnitude of the force involved, despite the fact that the most frequent usage of the word relates to instances in which two or more objects clash violently.
The instantaneous speed could be compared to the speed shown by the speedometer.
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.
a 65 kg bungee jumper drops from a 60 ledge. the bungee cord has an unstretched length of 20 m, meaning that for the first 20 m the only force on the jumper is gravity. the bungee cord acts like a linear spring. the jumper comes to rest 0.5 m above the surface of the water. what is the stiffness constant of the cord?
To find the stiffness constant of the cord, learn gravity and force.
What is gravity?
By means of gravity, a planet or other body pulls objects toward its center. All the planets are maintained in their orbits around the sun by the force of gravity.
What is force?
An object with mass changes its velocity in response to a push or pull. Force is an external agent that has the power to alter a body's resting or moving state. It has a size and a movement.
Enot=Eat start= Ug =mgh
=(65kg)(10m/s²)(60m)
=39,000J
Eat lowest point =Usp+Ug
=1/2K(Δy²)+mgh
=1/2k(39.5m)² + (65kg)(10m/s²)(0.5m)
from conservation of energy, solve to get K= 49.6N/m.
Therefore, the energy function can be written ( for y<40).
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a 1.92 kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 4.77 n/m. the object is displaced 5.31 m to the right from its equilibrium position and then released, which initiates simple harmonic motion. what is the magnitude of the force acting on the object 3.72 s after it is released? answer in units of n.
The magnitude of the force acting on the object of mass 1.92 kg, 3.72 s after it is released is 23.414 N in negative direction.
ω = √ ( k / m )
ω = Angular frequency
k = Force constant
m = Mass
k = 4.77 N / m
m = 1.92 kg
ω = √ 4.77 / 1.92
ω = √ 2.48
ω = 1.58 rad / s
F ( t ) = - m d ω² cos ω t
F ( t ) = Force wrt time
d = Displacement
t = Time
t = 3.72 s
d = 5.31 m
F ( 3.72 ) = - 1.92 * 5.31 * 1.58² cos ( 1.58 * 3.72 )
F ( 3.72 ) = - 25.45 cos 5.88
F ( 3.72 ) = - 23.414 N
Therefore, the magnitude of the force acting on the object is 23.414 N in negative direction.
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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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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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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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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 are skiing and you push off from the top of the hill, giving yourself an initial velocity of 1 m/s. You accelerate down the hill at a rate of 2 m/s/s. What will your speed be after 10 seconds? How far will you have traveled after 10 seconds?
Using Equations of motion, speed after 10 seconds will be 21 m/s and the distance travelled after 10 seconds will be 110 m.
What are Equations of motion?
Equations of motion are thought of as the relationships that assist us in relating the physical quantities, such as distance traveled, time spent traveling there, acceleration, and initial and final velocities.
First equation of motion
The velocity-time relation is the name given to the fundamental equation of motion, v = u + at.Second equation of motion
The position-time relation can be defined as s = ut + 1 / 2at2 in the second equation of motion.Third equation of motion
v2 = u2+ 2as, the position-velocity relation, is the third equation of motion.Given, initial velocity, u = 1 m/s
acceleration, a = 2 m/s/s
time = 10 s
Using First equation of motion, we find the speed after 10 seconds.
v = u + at
v = 1 + 2 x10
v = 1 + 20
v = 21 m/s
Using Second equation of motion, we find the distance travelled after 10 seconds,
s = ut + 1 / 2at2
s = 1 x 10 + ( 2 x 10 x 10)/2
s = 10 + 100
s = 110 m.
Hence, after 10 seconds speed will be 21 m/s and distance will be 110 m.
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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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What is the normal force acting on a 50kg dog? A)540N b)570N c)490N d)440N
Answer:
C) 490
Explanation:
Normal force = mass × gravitational acceleration
50kg × 9.8
490 N
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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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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Calculator
O
A speaker, rated at 4V, draws a current of 13A. It is left switched on for 3 seconds. How much electrical work is done on a speaker?
Answer:
16C
Explanation:
since current=CHARGE/TIME
THEREFORE CHARGE=TIME X CURRENT
=2X8
=16C
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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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 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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A van accelerates from a velocity of 2 m/s to a velocity of 20 m/s in 12 s.
Calculate the acceleration of the van.
Answer:
Explanation:
Given:
V₀ = 2 m/s
V = 20 m/s
Δt = 12 s
__________
a - ?
The acceleration of the van:
a = ΔV / Δt = (V - V₀) / Δt
a = (20 - 2) / 12 = 18 / 12 ≈ 1.5 m/s²
Projectile motion is a combination of _______________ motion in the horizontal direction, and ________________ motion in the vertical direction.
A. accelerated, accelerated
B. constant, constant
C. accelerated, constant
D. constant, accelerated
Projectile motion is a combination of constant motion in the horizontal direction, and accelerated motion in the vertical direction. Therefore, the correct answer option is: D. constant, accelerated.
What is projectile motion?Projectile motion can be defined as a form of motion which is experienced by a physical object (body) that is projected near the surface of planet Earth, while moving along a parabolic (u-shaped curve) path, and under the influence of a gravitational force only.
Based on scientific research and records by scientists such as Galileo, we can infer and logically deduce that the initial horizontal velocity of a physical object undergoing a projectile motion is always equal to its final horizontal velocity.
Additionally, Galileo stated that projectile motion combines constant or uniform motion in the horizontal direction and accelerated motion in the vertical direction.
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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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