The current through the long wire is 20A.
What is a magnetic field in simple terms?
The magnetic field is the area around a magnet in which the effect of magnetism is felt. We use the magnetic field as a tool to describe how the magnetic force is distributed in the space around and within something magnetic in nature.
What causes a magnetic field?
Magnetism is caused by the motion of electric charges. Every substance is made up of tiny units called atoms. Each atom has electrons, particles that carry electric charges. Spinning like tops, the electrons circle the nucleus, or core, of an atom.
How do you find current in a wire in a magnetic field?
The strength of a magnetic field, , some distance away from a straight wire carrying a current, , can be found using the equation = 2 , where is a constant known as “the permeability of free space”
What happens when a wire with a current is placed in a magnetic field?
The wire will bend away from the poles of the magnet.
[tex]i=\frac{2\pi RB}{m_{0}}[/tex]
Given : [tex]R=0.50m, B=8*10^{-6}[/tex]
[tex]i=\frac{2\pi *0.50*8*10^{-6}}{4\pi *10^{-7}}[/tex]
[tex]i=20A[/tex]
Thus, the current flowing in the wire is 20A.
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a steel ball is dropped onto a very hard floor. over and over again, the ball rebounds to its origional height (assume that no energy is lost during the collision with the floor). is the motion of the ball simple harmonic motion?
Yes, the motion of ball is following simple harmonic oscillation.
An equilibrium position exists for harmonic motion. No force is present there. The force acting on the mass attempts to bring the mass back to equilibrium if it is deflected from its equilibrium position. Given that the displacement from equilibrium is measured by x and the force is linear, F = -k * x. K is equal to newtons/meter for springs because k = force/distance. Because of linearity, force and displacement are inversely proportional. Small force, small displacement. Strong force, strong displacement. The period of the simple harmonic oscillator is independent of amplitude because of this proportionality.No matter where the ball is, there is a constant downward force applied by the bouncing object. Only at the bottom of the bounce is there a significant upward force. Nearly all of the damping is at the bounce point. The amplitude has a strong bearing on the period.
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in our milky way galaxy, the orion spur is the select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a closest arm to the central bulge. b closest arm to our sun. c farthest arm from the central bulge.
According to the given information in our milky way galaxy, the orion spur is closest arm to our sun.
Where is the central bulge?A vast disc of stars has an element of stars in the centre. Even though there are many spiral galaxies that share this characteristic, researchers have spent decades trying to figure out how and when the Way Way for sure central bulge may have developed. A spiral galaxy is the Spiral Galaxy. We think it has four large arms, several lesser arm segments, and a central bulge.
What type of galaxy has a central bulge?A spiral known universe structure is intricate; it consists of a revolving disc with a spiral architecture that originates at a dense central bulge. Halos, which are roughly spherical regions along each plane of the discs, encircle spiral galaxies and are sparsely inhabited.
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the nuclear force is group of answer choices long range and charge independent electromagnetic in nature. short range and charge dependent. short range and charge independent. long range and charge dependent
The term "short range forces" refers to nuclear forces. Due to the fact that nuclear forces only work over relatively short distances, such as 1 fermi or 10-15 m.
This means that option a) is the appropriate response.
What is the nature of nuclear force?
The nuclear force is electromagnetic in nature, with a vast range and no charge. charge dependent and limited range. limited range and independent of charging. extended and charge-dependent
A force known as the nuclear force interacts with the protons and neutrons of atoms. The force that holds protons and neutrons in a nucleus together is known as the nuclear force. Protons and protons, neutrons and neutrons, or neutrons and neutrons can all be affected by this force.
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I understand that the question you are looking for is:
The nuclear force is:
a) short range and charge independent electromagnetic in nature.
b) long range and charge dependent.
c)short range and charge independent.
d)long range and charge dependent
suppose an experiment determines that the amount of work required for a force field f to move a particle from the point s1, 2d to the point s5, 23d along a curve c1 is 1.2 j and the work done by f in moving the particle along another curve c2 between the same two points is 1.4 j. what can you say about f? why?.
The force of moving a particle is 0.00262 N.
The electric field exerts force on a charged particle when it shifts from one position to another while moving through the same electric field. We can define a potential energy for the force produced by an electric field because it is conservative work. This enables us to analyze physical processes involving charged particles and electric fields using the concepts of work, energy, and the conservation of energy.displacement is (1,2) to (5,23)
Work is 1.2 J
[tex]Work =Force * Displacement\\\\Force= Work/Displacement[/tex]
F=1.2/[(X-x)²+(Y-y)²]
F=1.2/457
F=0.00262 N
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if you pull them back together the same distance and release them to start them swinging, what will you notice about the oscillations of the two children?
The motion of the lighter child would look faster than that of the heavier child, but both have the same period of oscillation.
Oscillation is a type of simple harmonic motion which involves the to and fro movement of an object. The oscillation takes place at a required time called the period of oscillation.
Since the swings are similar, the period of oscillation of the two children are the same and they would complete one oscillation in the same time. Though the oscillation of the lighter child seems faster than that of the heavy child, their masses does not affect the period of oscillation.
When a heavy object oscillates, its mass increases the drag or damping force, but not the period of oscillation. Thus, it oscillate slowly.
Therefore, we can notice about the oscillation that the motion of the child having light weight will be faster than the motion of child having heavy weight.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS :
At a playground, two young children are on identical swings. One child appears to be about twice as heavy as the other. Part A If you pull them back together the same distance and release them to start them swinging, what will you notice about the oscillations of the two children]
A bowler rolls a 5 kg ball down a frictionless bowling alley. The ball accelerates at an average rate of 2 m/s. How much force did the bowler apply to the ball
A force of 10N was applied to the ball by the bowler.
What is a force?A force is any interaction that, when unopposed, will change the motion of an object. It can be a push or a pull. What are the Effects of Force?
Typically, motion can either be described as:
Change in speedChange in directionEffects of a forceForce can make a body that is at rest to move.It can stop a moving body or slow it down.It can accelerate the speed of a moving body.It can also change the direction of a moving body along with its shape and size.It is determined by the formula; F = ma
Where m = mass
a = acceleration
From the question;
m = 5kg
a = 2m/s2
F = ma
F = 5 x 2
F = 10N
Hence, the bowler applied a force of 10N to the ball.
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Which factor is most important to keep the same when looking at the meniscus to compare the surface tension of different liquids?.
Temperature and impurities are most important factors to keep the same when looking at the meniscus to compare the surface tension of different liquids.
Define surface tension.
Surface tension is a characteristic of liquids brought on by an imbalance in molecular forces at their surfaces. The surface tension is also impacted by factors that influence the molecular forces. The liquid's nature, the environment it is in, and its purity all affect how much surface tension there is.
Impurities:
Impurities that are soluble: The surface tension may rise or fall if the contaminants are soluble. If the contaminants are less soluble, the surface tension of the liquid will be reduced. For instance, camphor lowers the surface tension of water because it is less soluble in water. On the other hand, when the contaminants are more soluble, the liquid's surface tension will rise.
Insoluble impurities :Dirt, grease, and other insoluble contaminants will reduce a liquid's surface tension.
Temperature:
As the temperature rises, the molecular attraction between liquid molecules weakens. As a result, liquid surface tension falls as liquid temperature rises.
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determine force p on the cable if the spring is compressed 0.025 m when the mechanism is in the position shown. the spring has a stiffness of k
Force P on the cable if the spring is compressed 0.025 m when the mechanism is in the position shown is 0.198 kN.
The force applied by a spring on objects joined to its finishes is corresponding to the spring's adjustment of a length away from its balance length and is constantly coordinated toward its harmonious position. F = - kx. The proportional constant k is known as the spring steady. It is a proportion of the spring's solidness. Assuming x is positive (uprooting to the right), the subsequent power is negative (toward the left), as well as the other way around. As such, the spring force generally acts to reestablish mass back toward its harmony position. Hence the force P on the cable is 0.198 kN if the spring is compressed 0.025 m when the mechanism is in the position shown.
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in this class we will mostly analyze systems where each microstate equally probable. does a coin flip system have equally probably microstates? explain why or why not. come up with examples of systems where the contrary is true.
Yes, a coin flip system has equally probable microstates because the probabilities of heads and tails are both 50%.
What is microstate?
A microstate is a particular microscopic configuration of the a thermodynamic system which the system may occupy with a specific probability throughout its thermal fluctuations, according to statistical mechanics. The macroscopic characteristics of a system, including its temperature, pressure, volume, and density, are referred to as its macrostate. A specific set of values for the energy, the number of particles, as well as the volume of the an isolated thermodynamic system is thought to specify a specific macrostate of it, according to statistical mechanics treatments. Microstates are depicted in this description as various ways the system might be able to reach a specific macrostate.
Examples of systems where the microstates are not equally probable include rolling a dice, where each side has a different probability of being rolled, and the stock market, where the outcomes are not predetermined and are affected by many variables.
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A 80 g , 35-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 11 g ball of clay traveling horizontally at 2.3 m/s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
The maximum angle measured from vertical is [tex]\theta=57^{o}}[/tex]
Calculation:-
Substituting values:
[tex]\small (1-\cos\theta)=\frac{\left (\frac{1}{3}(0.08\;kg)+(0.011\;kg) \right )\left (0.67168\;m/s \right )^{2}}{(0.011\;kg\times 9.8\;m/s^{2\times } 0.35\;m)}\small (1-\cos\theta)=0.4503\small \cos\theta=1-0.4503\small \cos\theta=0.5496\small \therefore \theta=\cos^{-1}\left (0.5496 \right )\small \boldsymbol{\therefore \theta=56.66^{o}}ROUNDING TO 2 SIGNIFICANT FIGURES:\small \boldsymbol{\therefore \theta=57^{o}}[/tex]
The maximum angle at which a given quantity of bulk goods can be conveyed in a given time even if the conveyor is tilted. Bulk material throughput generally decreases as the maximum angle is approached. The sum of the three angles of a triangle is 180 degrees.
Maximum Permissible Slope means the steepest slope of excavation that can be tolerated to prevent collapse under the most favorable field conditions, expressed as the ratio of horizontal distance to the vertical slope. The maximum elevation angle at solar noon is a function of latitude and declination.
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a small artery has a length of 1.6 ✕ 10−3 m and a radius of 2.4 ✕ 10−5 m. if the pressure drop across the artery is 1.8 kpa, what is the flow rate (in mm3/s) through the artery? (assume that the temperature is 37°c.)
The flow rate through the artery is 7.03*10-11 m3/s (measured in mm3/s). What is the flow rate through the artery in mm3/s if the pressure drop across the artery is 1.8 kpa?
How can I calculate flow rate?
To determine the flow rate represented as Q, which is equal to Q = V/t, we must define both the volume V and the instant in time that it is passing past represented by t. In addition, the relationship between flow rate and velocity is shown by the equation Q = Av, where A is the flow's cross-sectional area and v is its average velocity.
What three different flow rates are there?
Vacuum technology primarily deals with three forms of flow: viscous or continuous flow, molecular flow, and at the interface between these two.
Briefing:
Given,
Pressure Δp = 1.8 kPa
Viscosity μ = 2.03*10-3Pa
Subsituting the values in equation,
Δp = 8μLQ / π
Q = Δp × π / 8μL
Q=7.03*10-11 m3/s
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the swirling gas that collects around a compact object, as its binary companion transfers material to it, is called
The swirling gas that collects around a compact object, as its binary companion transfers material to it, is called NOT an event horizon.
NOT an event horizon is its binary counterpart, which transports matter to it.
What is an object in a sentence?
To refer to the item or person that is the target of an action, we typically use the word "object." Alternatively, the recipient. In a sentence, a verb's action is transferred to a noun or pronoun as a direct object. It typically responds to the what- or whom-questions regarding the verb.
What is a picture or an object?
Icons, cursors, buttons, sprites, and other complicated artworks can be made from a collection of simple visual pieces called image objects. Without having to sketch a single pixel, Image Objects let you express creativity.
The object we are talking about here is the death of the star.
Starlight is impacted by atmospheric winds, as well as regions with varying temperatures and densities, when it enters our atmosphere. The night sky appears to sparkle because of the impact of the Earth's atmosphere.
When starlight reaches the atmosphere, it is affected by winds in the atmosphere and areas with different temperatures and densities. This causes the star's light to sparkle when seen from Earth.
But when they run out of fuel, they die and supernova happens.
Therefore here, the object, we are talking in context with star and the swirling gas that collects around a compact object, as its binary companion transfers material to it, is called NOT an event horizon.
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A car, mass 1225 kg, traveling at 105 km/h, slows to a stop in 53 m. What is the size of the force that acted on the car
The force acting on the car is 9700N.
First, the speed has to be converted to m/s units (SI)
105 km/h x 1000m/3600s ≅ 29 m/s
Then, using kinematics, we must determine the acceleration to determine the force. Kinematics is the area of mechanics that studies pure motion without taking into account the masses or forces at play, likewise known as applied kinematics. The concept of mechanical devices that change one type of motion into another.
[tex]V_{final^{2} } = V_{intial^{2} } + 2ax[/tex]
[tex]29^{2} = 0^{2} + 2 * a * 53[/tex]
a ≅ [tex]7.9\frac{m}{s^{2} }[/tex]
Using equation,
F = ma
F = 1225 x 7.9
9677 N ≅ 9700 N
Therefore, The force acting on the car is 9700N.
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consider two objects moving in uniform circular motion around two circular tracks of the same radius. if the linear speed of object 2 is 50\p% greater than the linear speed of object 1, then how does centripetal acceleration of object 2 compare to the centripetal acceleration of object 1?
Centripetal acceleration of object 2 with 1 is [tex]& a c_2=2.25 a c_1[/tex]
What is Centripetal Acceleration ?The pace at which a body moves through a circle is known as centripetal acceleration. When a body travels in a circle, its direction is constantly changing, which results in a change in velocity, which generates an acceleration because velocity is a vector quantity (i.e., it contains both a magnitude, the speed, and a direction).
By applying the formula for the Centripetal acceleration :
[tex]& a_c=\frac{v^2}{R} \\& a_{c_1}=\frac{v_1^2}{R} \\& a_{c_2}=\frac{v_2^2}{R} \\[/tex]
[tex]& \frac{a c_2}{a c_1}=\frac{v_2^2}{v_1^2}=\left(\frac{1.5 v_1}{v_1}\right)^2=2.25 \\[/tex]
[tex]& \left.a_{c_2}=2.25 a c_1\right) \\[/tex]
By Comparing the centripetal acceleration of two objects
Centripetal acceleration of object 2 with 1 is [tex]& a c_2=2.25 a c_1[/tex]
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what is the magnetic field in the middle of the capacitor plates at a distance d from the center, as a function of time t ? give your answer in terms of d , r , i0 , t , r , c , and any necessary constants.
That completely depends on the voltage wave-form that's being impressed across the capacitor
What is magnetic field and capacitor ?The area in which the force of magnetism acts around a magnetic material or a moving electric charge is known as the magnetic field. Moving electric charges and magnetic dipoles combine to form a magnetic field, which acts as a force field on other adjacent moving charges and magnetic dipoles.
A two-terminal electrical device known as a capacitor is capable of storing energy in the form of an electric charge. It is made up of two electrical wires that are spaced apart by a certain amount. Vacuum may be used to fill the space between the conductors, or a dielectric, an insulating substance, may be used instead.
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what is the lift (in newtons) due to bernoulli's principle on a wing of area 89 m2 if the air passes over the top and bottom surfaces at speeds of 260 m/s and 180 m/s , respectively?
The lift in newtons due to Bernoulli's principle on a wing of area 89 m² is 22,704 N.
How to calculate lift force?According to this question, the following information are given:
Area of the wing = 89m²
Density of air = 1.29kgm³
Speed at the top surface (V2) = 260m/sec
Speed at the bottom surface (V1) = 180m/sec
According to Bernoulli's principle, force is given by the following expression: F = A × d × V2 - V1/2
Where;
F = force
A = area
d = density
F = 89 × 1.29 × (260² - 180²)/2
F = 1.29 × 17,600
F = 22,704 N
Therefore, the lift in newtons due to Bernoulli's principle on a wing of area 76 m² is 22,704 N.
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What are two things that happen when a home computer scanner uses electromagnetic waves.
When a home computer scanner employs electromagnetic waves, two things happen:
A silicon chip inside the charge-coupled device releases electrons via the photoelectric effect, creating an image.
A charge-coupled device needs to receive visible light after it has bounced off an object.
Electromagnetic waves: what are they?
By varying the wave's amplitude, frequency, or phase, electrical signals can be transmitted across electromagnetic waves. To transfer music and video between televisions and mobile devices, the signal is converted into a series of binary ones and zeros.
A type of radiation that moves in waves at the speed of light is called electromagnetic energy. Light, electromagnetic radiation, electromagnetic waves, radiant energy, or the movement of radiation are some other names for it. Electromagnetic field radiation can be used to transfer heat.
An electric field and a magnetic field oscillate to create electromagnetic waves, or EM waves. In other words, the oscillation of the magnetic and electric fields results in electromagnetic waves.
At the speed of light, they all move. In the process of transferring energy via a medium, the material's atoms absorb and emit wave energy .Mechanical waves. require a medium to pass through in order to transmit their energy from one location to another.
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Kieran is driving his chevrolet spark around a level turn with a radius of curvature of 70. 9 m at a speed of 22. 4 m/s. Calculate the acceleration of the car.
The Chevrolet Spark accelerates at 7.1 m/s around a flat turn with a radius of curvature of 70.9 m at a speed of 22.4 m/s.
Describe acceleration.The rate at which the speed and direction of a moving object vary over time. A point or object going straight forward is accelerated when it accelerates or decelerates.
A is the centripetal acceleration, and V is the linear velocity.
Radius v = 22.4 m/s
Radius = 70.9 m
a = 22.42 / 70.9 m a
a = 7.1 m/s / s
Centripetal acceleration is the term used to describe the speed of a body rotating in a circle. A vector quantity, that is. It is represented as m/s2.
Consequently, the car's acceleration is 7.1 m / s
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does it take the same amount of time for something at a steeper angle to fall than something at a less steep angle
The starting vertical velocity determines the time in the air. Increasing the relevant results lengthens the duration in the air because higher release degrees have a better and improve velocity component.
Why does physics recommend a launch angle of 45 degrees?
We see that for the lengthiest punts 2 = 90 degrees and, consequently, = 45 degrees because the sine function has an intake average of 90 degree that results in its highest output value, 1. In other words, a projectile moves and furthest when it is fired at a 45-degree angle.
Which direction has lowest range?
Range reduces with increasing projection angle.
The reach will be at its narrowest when the projected angle is extremely distant from 45 degrees.
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what was the key discovery that led to the identification and definition of the intense radio emitters known as quasars?
Strong emission lines in their visible spectra were found to be hydrogen lines with very high redshifts.
What is quasars ?A nearly disastrous attempt to observe a far-off radio source results in the discovery of the first quasar, also known as a quasi-stellar astronomical phenomenon.
Quasars produce as much energy from a volume as small as our solar system as more than 100 regular galaxies.
According to NASA, "quasars are some of the most brilliant and energetic objects in the entire universe, with the ability to emit hundreds or even thousands of times the energy output of our galaxy.
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For a hydrogen atom, calculate the wavelength of light (in m) that would be emitted for the orbital transition of n(initial) = 3 to n(final) = 1. Submit an answer to four significant figures. The Rydberg constant is 1.09678 x 10⁷ m⁻¹.
The wavelength of the light emitted for the orbital transition from n = 3 to n = 1 is 0.975m.
For hydrogen, the wavelength of the light emitted for the orbital transition of n = 3 to n = 1 is given by,
1/λ = R(1/n²-1/n'²)
Where,
R is the Rydberg's constant,
n is the initial orbital,
n' is the final orbital,
Putting values,
1/λ = 1.097(1/1-1/9)
1/λ= 1.097 x 8/9
λ = 0.975 m.
Hence, the wavelength of the light emitted is 0.975m.
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if quasars often resemble little blue stars, what was it about them that so surprised astronomers when they were discovered?
Quasar is famous for being an intergalactic object which is billions of years away from the earth yet can still be seen, unlike the other star body, unlike giant galaxies.
Hence, the fact that quasars can be detected from distances where even the biggest and most luminous galaxies cannot be seen means that "they must be intrinsically far more luminous than the brightest galaxies."
This condition, including other related evidence gotten in recent years concerning our galaxy, has shown that quasars are probably the central nuclei of very distant, very active galaxies.
The surprising thing was that quasars and active galaxies have a lot of mass in the center of the very small volume of the space.
Therefore, the surprising thing about quasars was that due to this mass and energy they are 100 times more luminous than Milky Way which means they have high recession velocity and a very large amount of red-shifting.
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what is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (we can neglect the volume of the capillary tubing connecting the bulbs.)\
Through a stopcock, this bulb was connected to a 0.5 liter evacuated bulb. When the stopcock was opened, the pressure at each location increased to 530 mm, but the temperature stayed the same.
The relationship between temperature and pressure for a given volume of gas is direct. Pressure increases in systems as temperature increases and vice versa. The Gay-Lussac's law specifies the relationship between a gas's pressure and temperature. the relationship between a gas's temperature and the force it applies to its container. Gay-Lussac's Law or Amontons' Law of Pressure-Temperature are two names for this. A gas will press more forcefully against its container as its temperature rises. By heating a gas, you can hasten the motion of its molecules. The pressure will rise and there will be more impacts on the container's walls.
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when the frequency of an ac circuit is decreased, the current in the circuit increases. which combination of elements is most likely to comprise the circuit?
The correct answer is resistor, inductor and capacitor.
Impedance of an LCR circuit is given by
Z = √[R² + (X₁ - X(C))²]
Z = √[R² + {2πνL - (1/2πνC)²]
The variation of Z with ν is shown in the figure.
As ν increases , Z decreases and hence current increases.
At ν = ν(r), Z is minimum, current is maximum
Beyond
ν = ν(r)
Z increases and current decreases.
Therefore, the combination of circuit elements is most likely to comprise
the circuit are R, L and C .
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a 140 nf capacitor is used in a standard 120 volt ac circuit with a frequency of 60 hz, what is the capacitive resistance?
The capacitive resistance [tex]x_c[/tex] = 18956 ohms
as per given in the question,
a capacitor having a capacitance (c) is 140nf
the standard voltage of the ac circuit (v) is 120 volts
the frequency of the circuit (f) is 60 hertz
we need to find the capacitive resistance of the given circuit
The opposition offered by a capacitor to the flow of ac current in the ac circuit is known as capacitive resistance.
the formula to find capacitive resistance of the circuit is
[tex]x_c = \frac{1}{2\pi fc}[/tex] ----(1)
where
[tex]x_c[/tex] is the capacitive resistance
[tex]\pi[/tex] is a constant value 3.14
[tex]f[/tex] is the frequency
[tex]c[/tex] is the capacitance of the capacitor
[tex]c =140nf[/tex]
[tex]f=60hz[/tex]
[tex]v=120\ volt[/tex]
substitute all the values in equation (1) we get
[tex]x_c = \frac{1}{2(3.14)(60)(140\times10^{-9}) }[/tex]
=> [tex]x_c = \frac{1}{6.28(60)(140\times10^{-9}) }[/tex]
=> [tex]x_c = \frac{1}{376.8(140\times10^{-9}) }[/tex]
=>[tex]x_c = 1.8956\times10^{4}[/tex]
=>[tex]x_c[/tex] = 18956 ohms
the capacitive resistance is 18956 ohms
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The capacitive resistance of the capacitor is 18947 ohms.
The capacitive resistance of a capacitor is given by the formula:
Xc = 1 / (2πfc)
where:
Xc is the capacitive resistance in ohms
π is a constant with the value of 3.14
f is the frequency in hertz
c is the capacitance in farads
In this case, the capacitance is 140 nf, which is equal to 140 * 10^-9 farads. The frequency is 60 hz.
Plugging these values into the formula, we get:
Xc = 1 / (2π * 60 * 140 * 10^-9)
= 18947 ohms
A 140 nf capacitor is used in a standard 120-volt ac circuit with a frequency of 60 hz. The capacitive resistance of the capacitor is given by the formula Xc = 1 / (2πfc). Plugging in the values for capacitance, frequency, and pi, we get Xc = 18947 ohms. Therefore, the capacitive resistance of the capacitor is 18947 ohms.
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Why do astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system?.
Answer:
Meteorites Contain Magnesium-26
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a 0.40 kg mass is attached to a 0.5 m string and displaced an angle of 12 degrees before it is released. 1. what is the initial potential energy of the pendulum? 2. what is the angular frequency of the pendulum? 3. what is the velocity of the pendulum at the lowest point in its swing? 4. what is the height of its displacement?
A pendulum is a weight released from a starting point so that it can swing freely. When a pendulum is displaced sideways it restores a force due to gravity that will accelerate it back toward the equilibrium position from the resting position.
How to find initial potential energy, angular frequency, velocity and height of displacement of a pendulum?
We know, m= 0.40kg
L=0.5m
Angle = 12°
i) Main answer is : initial potential energy = PE = mgh (1-cos∅)
= 0.9×9.81×0.5×(1-cos12°)
= 0.0429 J
ii)Main answer is: Angular frequency= W= √g/l
=4.43 rad/s
= 0.7 rev/s
iii) Main answer is : velocity of pendulum = V=√2gl(1-cos∅)
=0.46m/s
iv) Main answer is : height of displacement= h=L (1-cos∅)
=0.01m
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The pendulum's angular frequency is 4.42 rad/s, and its potential energy is 0.04 J. the pendulum's lowest in its swings has a speed of 0.44 m/s, a motion time of 0.010905 m, and a lateral distance of 0.1039 m.
What is potential energy, exactly?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is squeezed or strained, its energy increases. If a steel ball is lifted above the ground as contrasted to falling to the ground, it has higher potential energy.
Briefing:Given data:
The associated mass is m=0.40kg.
The string measures L=0.5m in length.
Angle misplaced is equal to 12°.
(1). Calculate the potential energy of pendulum:
PE=mg[L−Lcosθ]
PE=0.40kg×9.8m/s[0.5m−0.5m×cos12°]
PE=0.04J
Consequently, the pendulum's potential energy is 0.04 J.
(2). Determine the pendulum's angular frequency:
[tex]\omega=\sqrt{\frac{g}{L}}[/tex]
Changing every variable in the aforementioned equation:
[tex]\omega=\sqrt{\frac{9.8 \mathrm{~m} / \mathrm{s}^2}{0.5 \mathrm{~m}}}[/tex]
ω = 4.42 rad/s
Consequently, the pendulum's angular frequency is 4.42 rad/s.
(4). Do the vertical displacement calculation:
[tex]x_V=L-L \cos \theta[/tex]
[tex]\begin{aligned}& x_V=0.5 \mathrm{~m}-0.6 \mathrm{~m} \cos 12^{\circ} \\& x_V=0.010905 \mathrm{~m}\end{aligned}[/tex]
Do the horizontal displacement calculation:
[tex]\begin{aligned}& x_H=L \sin \theta \\& x_H=L \sin 12^{\circ} \\& x_H=0.1039 \mathrm{~m}\end{aligned}[/tex]
The height of the horizontal displacement is therefore 0.1039 m, while the height of the deformation is 0.010905 m.
(3).Calculate the pendulum's rock bottom in its swing by using energy balance to determine its velocity.
KE = PE
[tex]\frac{1}{2} 0.40 \mathrm{~kg} \times v^2=0.04 \mathrm{~J}[/tex]
v = 0.44 m/s
Calculate the pendulum's velocity at its rock bottom in its swing, which is 0.44 m/s.
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calculate the orbital period of a comet with a perihelion distance of 0.5 au and aphelion in the oort cloud, at a distance of 50,000 au from the sun.
The value of the major axis of the comet will be [tex]A=50AU[/tex]and the major axis of the comet is the sum of aphelion distance [tex]\left(a_y\right)[/tex] and perihelion distance [tex]$\left(p_y\right)$[/tex] is [tex]49 AU[/tex]
It is given that,
The value of the perihelion distance of 0.5 au and aphelion in the Oort cloud, at a distance of 50,000 au from the sun.
We need to determine the value of the orbital period of a comet
As we know,
Half of the semi-major axis is the radius of the orbit.
[tex]$$\begin{aligned}a & =\frac{50000 \mathrm{~A} \cdot \mathrm{U}}{2} \\& =25000 \mathrm{~A} . \mathrm{U}\end{aligned}$$[/tex]
From the Kepler's third law, the square of the period of a comet is directly proportional to the cube of its radius of the orbit.
So, applying the above concept.
We will get,
[tex]$$\begin{aligned}p^2 & =a^3 \\p & =[a]^{\frac{3}{2}} \\& =[25000 \mathrm{~A} U]^{\frac{3}{2}} \\& \approx 4 \times 10^6 \text { years (or) } 4.0 \text { million years }\end{aligned}$$[/tex]
(2) Using keplers third law calculate the semi major axis of the comet can be calculated as follows
[tex]$$\begin{aligned}p^2 & =a^3 \\a & =[p]^{\frac{2}{3}} \\& =[125]^{\frac{2}{3}} \\& =25 \mathrm{~A} . \mathrm{U}\end{aligned}$$[/tex]
So, the value of the major axis of the comet will be:
[tex]$$\begin{aligned}A & =2 \mathrm{a} \\& =2(25 \mathrm{~A} \cdot \mathrm{U}) \\& =50 \mathrm{~A} \cdot \mathrm{U}\end{aligned}$$[/tex]
Major axis of the comet is the sum of aphelion distance [tex]\left(a_y\right)[/tex] perihelion distance [tex]$\left(p_y\right)$[/tex].
[tex]$$\begin{aligned}A & =a_y+p_y \\p_y & =A-a_y \\& =50 \mathrm{~A} . \mathrm{U}-1.0 \mathrm{~A} . \mathrm{U} \\& =49 \mathrm{A.U}\end{aligned}$$[/tex]
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how much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center is 3.75 kv ?
The excess charge required to reach the given potential is 4.6 x 10-6 C.
What is potential?
Potential typically refers to a skill that is still being developed. The phrase is used in a wide range of disciplines, from physics to a social sciences, to describe things that are capable of changing in a variety of ways, from the straightforward release of energy besides objects to the realisation of abilities in people. In his works Physics, Ontology, Nicomachean Ethics, as well as De Anima, which deals with the human psyche, the philosopher Aristotelian incorporated this idea in to the his theory of potentiality as well as actuality, a pair of interconnected principles he used to analyse motion, causality, ethics, as well as physiology.
The charge required to reach the given potential is given by the formula
Q = 4πεrV
Where Q is the charge, ε is the permittivity of free space, r is the radius of the sphere, and V is the potential.
Plugging in the given values, we get
Q = 4π(8.85 x 10-12 F/m)(0.125 m)(3.75 x 103 V)
Q = 4.6 x 10-6 C
Therefore, the excess charge required to reach the given potential is 4.6 x 10-6 C.
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Which two options are reasons that electromagnetic waves are effective for use in communication devices?.
The two options are reasons that electromagnetic waves are effective for use in communication devices:
1. Electromagnetic waves can travel long distances with minimal energy loss.
2. Electromagnetic waves can easily be modulated to carry information.
What is electromagnetic wave?
In terms of physics, electromagnetic radiation (EMR) is made up of electromagnetic (EM) field waves that travel through space while carrying radiant electromagnetic energy. It consists of X-rays, gamma rays, microwaves, infrared, visible light, ultraviolet, and radio waves. These waves are all a component of a electromagnetic spectrum. Electromagnetic waves, that are synchronised oscillations of the electric and magnetic fields, are the traditional form of electromagnetic radiation. Due to the periodic alteration of the electric or magnetic field, electromagnetic radiation or waves are produced. Different wavelengths of the electromagnetic spectrum are produced depending on the manner in which this periodic change takes place and the power generated. Electromagnetic waves move at the speed of light, commonly abbreviated as c, in a vacuum.
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Answer:
Explanation:
Which two options are reasons that electromagnetic waves are effective for use in communication devices?.