A certain transformer doubles input voltage. if the primary coil draws 10 a of current, then the current in the secondary coil is 5a
What is Voltage?The voltage represents the potential energy of an electrical charge at a certain location, if one were to place an electrical charge unit there. To put it another way, it is a measurement of the energy present in an electric field or an electric circuit at a certain location. It is equivalent to the amount of labour required to complete each unit of payment.The voltage can be mathematically stated as, where work is measured in joules and charge is measured in coulombs. The voltage is the difference in potential energy between two places in a circuit, according to our definition. The potential of one point is higher than that of the other points.To learn more about Voltage refer to:
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If the bond energies of X2 and C-X are 151.9 kJ and 2763 kJ, respectively, and the bond energies of C-C and C-c are 338 kJ and 604 kJ, respectively, give an estimate of AE for the reaction below: C2H4 + X2 => c2H4X2 (in kJ). (Enter your answer as the nearest whole number without units)
= [ 4 (C-H) + 1 (C=C) + 1 (X2) ] - [ 2 (C-X) + 1 + (C-C) + 4 (C-H)
= [ (C=C) +(X2) ] - [ 2 (C-X) + 1 (C-C) ]
= [ 604 +151.9 ] - [ 2 (276.3) + (338)]
= -134.7 KJ
= -135 KJ
Bond energies depend on the number of bonds between atoms. Even though π bonds are weaker than σ bonds, a double bond, which consists of a σ and π is bond, is stronger than a single bond because there are bonds.
A quantity of strength, equal to the distinction among the energies of the Bond energies depend on the number of bonds between atoms. Atoms and the energies of the separated atoms, is released, usually as warmness. that is, the bonded atoms have a lower strength than the character atoms do.
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You are asked to find the index of refraction for an unknown fluid, using only a laser and a Michelson interferometer. A Michelson interferometer consists of two arms--paths that light travels down, which end in mirrors--attached around a beam splitter. (Figure 1)The beam splitter separates the incoming light into two separate beams and then recombines them once they return from the ends of the arms. The recombined beams are sent to a telescope, where their interference pattern may be observed in detail.
Part A
Part complete
First, you must find the wavelength of the laser. You shine the laser into the interferometer and then move one of the mirrors until you have counted 100.0 fringes passing the crosshairs of the telescope. The extremely accurate micrometer shows that you have moved the mirror by 0.03164 millimeters. What is the wavelength λ of the laser?
Express your answer in nanometers, to four significant figures.
Part B
You now immerse the interferometer in a tank filled with some unknown liquid and carefully align the laser into the interferometer. You move the mirror until you count 100.0 fringes passing the crosshairs of the telescope. The micrometer indicates that the mirror has moved 0.02381 millimeters. What is the index of refraction for this mystery fluid?
Express your answer to four significant figures.
The wavelength λ of the laser is 632.8 nm and the index of refraction for this mystery fluid is 1.329.
What is wavelength and index of refraction?Refraction can change the wavelength of light or sound as it travels through a medium with a density greater than that of air. The wavelength reduces as a result of the wave's decreasing speed as it moves through the denser medium. If the wave travels faster when in a rarer medium, the wavelength rises. Because the speed and, consequently, the wavelength of the wave are lowered while traveling through the denser media, the index of refraction is greater for the denser medium than the rarer one.
An interferometer is a device that employs the interference phenomena to calculate the wavelength of light in terms of a standard length or the distance in terms of the wavelength of light that is already known. Through partial reflection and transmission, light from an extended source is split into two halves. The two directions in which these two beams are transmitted are at right angles to one another. They are noticed and studied as interference fringes that are created when they are reflected off the mirror.The angle between mirrors M1 and M2 determines how the fringes in the Michelson interferometer are shaped. Let S' be the replica of the source S, and let M2 be the virtual replica of mirror M1.Let D represent the distance between the mirror M1 and its virtual counterpart, M2'. As a result, the air film that is enclosed between M1 and M2' is what will cause the interference pattern to appear. Let S1' and S2' represent the respective Saras M1 and M2's photos.As a result of the amplitude division process, we are able to produce two coherent sources, S1' and S2'.
A)
2D = nλ
2 x 0.03164 x 10^-3 = 100 x λ
Wavelength, λ = 632.8 nm
B)
2D = n λ
2 x 0.02381 x 10^-3 = 100 λ
Wavelength,λ = 476.2 nm
Refractive index =λ₁/λ₂
Thus,
Refractive index = 632.8/476.2 = 1.329
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which of the following graphs represents the relationship between the gravitational force that two objects exert upon one another and the distance between the two objects?
The graph that best represents the relationship between the gravitational potential energy of a freely falling object and the object's height above the ground is the last graph.
What is Gravitational potential energy ?
Gravitational potential energy is the energy possessed by a body by virtue of its position. The formula is expressed as:
E = mgh
m is the mass of the object
g is the acceleration due to gravity
h is the height of the object
Note that the formula shows that the gravitational potential energy is directly proportional to the height of the object
This direct proportionality shows that the required graph will have a positive slope.
This shows that the graph that best represents the relationship between the gravitational potential energy of a freely falling object and the object's height above the ground is the last graph.
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What is the bouncing back of a ray of light sound or heat when the ray hits a surface that it does not go through?; Is the bouncing back of a light ray from a surface?; What is the bouncing back of the wave as it hits a surface?; What is the bouncing back of light when it hits?
When something bounces off a wall or other object, reflection happens. Following the rule of reflection, waves are reflected off of straight boundaries.
When light strikes a surface without being absorbed, what is the term used to describe the bounce back?Reflection
When light reflects off of something, it does so. The light will reflect at the same angle it struck the surface if the surface is smooth and shining, such as glass, water, or polished metal.
What does it mean for a sound to repeatedly bounce back to its source?Echoes. A sound that is repeated as a result of sound waves being reflected back is known as an echo. The way a rubber ball bounces off the ground is the same way that sound waves can bounce off smooth, hard things.
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A hopper jumps straight up to a height of 1.3 m. With what velocity did he leave the floor
The velocity with which the jumper leaves the floor is 5.1 m/s.
What is the initial velocity of the jumper?
The initial velocity of the jumper or the velocity with which the jumper leaves the floor is calculated by applying the principle of conservation of energy as shown below.
Kinetic energy of the jumper at the floor = Potential energy of the jumper at the maximum height
¹/₂mv² = mgh
v² = 2gh
v = √2gh
where;
v is the initial velocity of the jumper on the floorh is the maximum height reached by the jumperg is acceleration due to gravityv = √(2 x 9.8 x 1.3)
v = 5.1 m/s
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in a certain 2-slit combined interference and diffraction experiment, the fifth interference maximum and the first diffraction minimum are located at the same angle relative to the center of the screen.
In a two-slit interference and diffraction experiment, the fifth interference maximum and the first diffraction minimum can occur at the same angle relative to the center of the screen under certain conditions.
In a diffraction experiment, light waves passing through the two slits can also diffract and spread out, producing a pattern of bright and dark fringes on the screen. The position of the dark fringes, also known as diffraction minima, is determined by the wavelength of the light and the size of the slits.
If the fifth interference maximum and the first diffraction minimum occur at the same angle relative to the center of the screen, it means that the path difference between the waves passing through the two slits is equal to the wavelength of the light. This can be achieved by adjusting the separation between the slits, the distance between the slits and the screen, and the wavelength of the light.
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What’s the temperature 32 degrees Fahrenheit in degrees Celsius?
water flows at a rate of 2.5 m/s over a flat plate that is parallel to the oncoming flow. (a) determine the approximate location downstream of the front of the plate where the boundary layer becomes turbulent. assume that this occurs at a reynolds number rex
The boundary layer thickness is 7.92 x 10^(-3) m.
A) Formula for Reynolds number to reflect this question is given as;
R_e = Vx/v
Where;
V is velocity
x is polar coordinate where the boundary layer will become turbulent.
R_e is reynolds number.
Reynolds number for turbulent flow of flat plates has a value of 5 x 10^(5)
v is kinematic velocity
From water tables at standard conditions, kinematic viscosity is 1.12 x 10^(-6) m²/s
Now, R_e = Vx/v
We are looking for x, so let's make x the subject.
x = v•R_e/V
Thus, plugging in the relevant values to obtain;
x = [1.12 x 10^(-6) x 5 x 10^(5)]/0.5
x = 1.12m
The boundary layer thickness at the point where the flow becomes turbulent is given by;
δ = 5√(vx/V)
Where;
V is velocity
x is polar coordinate where the boundary layer will become turbulent.
R_e is reynolds number.
Reynolds number for turbulent flow of flat plates has a value of 5 x 10^(5)
v is kinematic velocity
Plugging in the relevant values to get ;
δ = 5√(1.12 x 10^(-6)•1.12/0.5)
δ = 5√(2.5088 x 10^(-6)
δ = 7.92 x 10^(-3) m
Therefore, the boundary layer thickness is 7.92 x 10^(-3) m.
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Stars are defined to be on the main sequence if they are burning hydrogen in their cores (hydrogen is combining into helium through nuclear fusion). Eventually, a star will run out of hydrogen fuel in its core, nuclear fusion will stop, and the star will enter a new stage of its lifetime. What is true?
More massive stars emit more energy and run out of hydrogen fuel in their cores faster. More massive stars have shorter main-sequence lifetimes because they burn through their fuel at a faster rate
More massive stars emit more energy and run out of hydrogen fuel in their cores faster.
What is the role of hydrogen in stars?In order to create helium and energy, hydrogen nuclei must fuse. The procedure uses hydrogen as its fuel. As the hydrogen is depleted, the star's core condenses and warms up further. As a result, all the elements up to iron are formed through the fusing of heavier and heavier elements.
Nuclear fusion is how stars generate their energy. This process, known as the "proton-proton chain," which involves a series of events that turns four hydrogen atoms into one helium atom, dominates for the majority of stars.
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The coefficient of static friction between the incline and the 200-1b crate in (Figure 1) is pe = 0.3. Part A Determine the force P that must be applied to the rope to begin moving the crate up the incline. Express your answer in pounds to three significant figures. Figure < 1 of 1> IVO AEO J1 vec ? P = lb Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining
The force applied due to friction is 32.2 N.
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact.
Coefficient of friction, ratio of the frictional force resisting the motion of two surfaces in contact to the normal force pressing the two surfaces together. It is usually symbolized by the Greek letter mu (μ). Mathematically, μ = F/N, where F is the frictional force and N is the normal force.
To solve for the minimum force, let us assume it to be F (N)
So
F=mg sin A
But
=>>>> coefficient of static friction x (F + mg cos A
=>3 x 9.8 x sin35 = 0.3 x (F + 3 x 9.8 x cos35)
So making F subject of formula
F + 24.0 = 56.2
F = 32.2N
Therefore, the force applied due to friction is 32.2 N.
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In what type of wave interaction does the wave bounce off of an object?; What happens when waves bounce off objects and interact?; What is it called when waves interact with each other?; What is the reflection of waves?
The wave bounces off an item when there is a reflection kind of wave interaction.
When waves strike a surface and rebound, reflection occurs. When a wave encounters a surface, it might reflect in all directions. For instance, visible light bounces off the surfaces it encounters. Your eyes receive the reflected light, which makes it possible for you to see the objects.
What occurs when waves come into contact?When two or more waves collide, interaction occurs. Wave interference is the term used to describe how waves interact with one another. Wave interference may occur when two waves that are traveling in opposite directions meet. The two waves pass through each other, and this affects their amplitude.
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1. A compact car, with mass 725 kg, is moving at 115 km/h toward t
on the east. Sketch the moving car.
a. Find the magnitude and direction of its momentum.
Draw an arrow on your sketch showing the momentum.
b. A second car, with a mass of 2175 kg, has the same
momentum. What is its velocity?
The magnitude and direction of its momentum are 23259.5 kg*m/s. and eastward direction respectively.
Its velocity is 10.66 m/s
How can one determine the magnitude and the direction of the momentum?To find the magnitude and direction of the momentum of the compact car, we can use the formula for momentum, which is defined as the product of an object's mass and velocity:
momentum = mass * velocity
In this case, the mass of the compact car is 725 kg and its velocity is 115 km/h. Converting the velocity to meters per second (m/s) by dividing by 3.6 gives us a velocity of 31.94 m/s.
Plugging these values into the formula above gives us a momentum of 23259.5 kg*m/s.
The direction of the momentum is the same as the direction of the velocity, which in this case is toward the east. Therefore, we can represent the momentum of the compact car as an arrow pointing eastward.
To find the velocity of the second car, we can use the formula for momentum and solve for velocity:
velocity = momentum / mass
In this case, the mass of the second car is 2175 kg and its momentum is the same as that of the compact car, which we calculated to be 23259.5 kg*m/s. Plugging these values into the formula above gives us a velocity of 10.66 m/s.
Note that the velocity of the second car is much lower than that of the compact car, despite having the same momentum. This is because the second car has a much larger mass, so it takes a larger force to change its momentum by a given amount.
Therefore, the correct answer is as given above
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find the speed se of the spacecraft when it crashes into the earth. express the speed in terms of me , re , and the universal gravitational constant g .
Speed of the spacecraft right before the collision:[tex]\sqrt{} \frac{2G.Me}{Re}[/tex] .
Assumption: the earth is exactly spherical with a uniform density.
What is the magnitude of the gravitational force acting on the Earth due to the sun?The magnitude of the gravitational force acting on the Sun due to the Earth is 3.52×1022 3.52 × 10 22 Newtons.This question could be solved using the conservation of energy.
The mechanical energy of this spacecraft is the sum of:
the kinetic energy of this spacecraft, and
the (gravitational) potential energy of this spacecraft.
Let denote the mass of this spacecraft. At a distance of from the center of the earth (with mass ), the gravitational potential energy () of this spacecraft would be:[tex]GPE=\frac{G.Me.M}{R}[/tex]
Initially, (the denominator of this fraction) is infinitely large. Therefore, the initial value of will be infinitely close to zero.On the other hand, the question states that the initial kinetic energy () of this spacecraft is also zero. Therefore, the initial mechanical energy of this spacecraft would be zero.Right before the collision, the spacecraft would be very close to the surface of the earth. The distance between the spacecraft and the center of the earth would be approximately equal to , the radius of the earth.The of the spacecraft at that moment would be:Subtract this value from zero to find the loss in the of this spacecraft:Assume that gravitational pull is the only force on the spacecraft. The size of the loss in the of this spacecraft would be equal to the size of the gain in its .Therefore, right before collision, the of this spacecraft would be:On the other hand, let denote the speed of this spacecraft. The following equation that relates and to :Rearrange this equation to find an equation for :It is already found that right before the collision, . Make use of this equation to find at that moment:[tex]\sqrt{} \frac{2KE}{M}[/tex]=[tex]\sqrt{\frac{2G.Me}{Re} }[/tex]
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.
if you know the car's potential energy and its kinetic energy, you can determine its mechanical energy through the formula .
The formula to calculate mechanical energy is ME=PE+KE. If you are aware of the kinetic and potential energies of the vehicle.
Simply put, what is kinetic energy?The energy an entity has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.
What makes kinetic energy so crucial?The capacity to perform work is arguably the most significant characteristic of kinetic energy. Force flowing on an object while it is moving is referred to as work. Energy and work are interchangeable because of their tight relationship.
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What are acceleration vs. time graphs?
The acceleration versus time graphs are the mathematical representation of the variation of acceleration with time.
There are several methods of representing the variation of two quantities one such method is graphs.
When the variation of the acceleration of the object and the time taken by the object to reach at acceleration are plotted on a graph the provides us with a few certain quantities.
For an example the slope of the acceleration-time graph tell us about the sudden change in acceleration at that particular instant.
Also the area under the acceleration vs. time graph represents the change in velocity of the object.
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What physical quantity does the slope of the v2/2 v/s h graph represent: #Hint: The algebraic statement of the conservation of Mechanical Energy is FEequals 1 half m v squared plus m g h where E,m, and g are constants. Solve for v2/2and determine what the slope would be if 'h' was on the horizontal axis. slope--g slope=-Elm slope-E slope-h
The physical quantity that does the slope of the v2/2 v/s h graph represent is the slope-g. The slope is representing the change in v over the change in time.
By definition, that is the acceleration. Also extra than only a gimmick, it is geometry's manner of displaying us how variables now no longer most effective relate to 1 another, however how they are able to constitute the fee of alteration among the variables.
The slope of the displacement time graph offers us the bodily amount called pace. The slope of a pace graph represents an object's acceleration. As a result, the cost of the slope at a given time represents the object's acceleration at that time. The fee of changing of an object's pace with admire to time is described as acceleration.
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❧ What are the images formed by a plane mirror?
The following are some properties of images formed by a plane mirror are; virtual, upright, left-right reversed, the same distance from the mirror as the object's distance, and the same size as the object.
What is a plane mirror?When a ray of light hits a surface, then it can undergo one of the following reflection, refraction, or absorption. So mirrors are polished surfaces coated with mercury such that they reflect most of the light hitting them.
Characteristics of the image formed by a plane mirrorThe image is virtual.The image is laterally inverted.The image is erect.The size of the image is the same as the size of the object.The distance between the image obtained from the mirror is the same as the distance between the object from the mirror.Learn more about plane mirrors:https://brainly.com/question/1126858
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What does gravitational potential energy depend on?; What three things does gravitational potential depend on?; Does the gravitational potential energy of an object depends on the path?
The Gravitational potential energy depends on mass , acceleration and path and potential also as G=V/m.
a). As you can imagine, gravitational energy is the energy associated with gravity. This is the potential energy stored due to an object being in a higher position compared to a lower position. (e.g. far from the ground or close to the ground).
Gravitational energy is the energy associated with gravity.
b). Systems can increase their gravitational energy as their mass moves away from the center of the Earth and away from other bodies (such as the sun, planets, and stars) large enough to generate a large amount of gravity. there is.
Potential energy can be defined as the amount of work expended to lift an object from the ground to its current height. In another sense, this is the amount of work the body does before returning to ground level (the position of maximum stability) when translated from its current level. Therefore, potential energy can be related to work.
c). A negative sign indicates that gravity is doing positive work as the mass approaches. A negative potential indicates a bonding state. That is, when mass is placed under its influence, it becomes trapped in its potential, and if something can provide the energy to escape the clutches of gravity, it must not escape.
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in today's demonstration, a nonmoving ball placed at the top of the ramp is an example of question 5 options: chemical energy gravitational potential energy elastic potential energy kinetic energy
Gravitational Potential Energy is demonstrated by a stationary ball put at the top of a ramp. The energy that a body has or acquires is known as gravitational potential energy.
because when something is in a gravitational field, it changes position. It is, to put it simply, energy that results from gravitational force or gravity. Taken two pencils is the most typical illustration. If one pencil is set down on a table and the other is raised above it, the pencil raised will have more gravitational potential energy than the pencil set down on the table. The equation U = mgh is used to compute it. The mass, m, is expressed in kilograms.
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find the sae's for the assigned nodal voltages. solve for the nodal voltages. round answer to 2 decimal places, add 0's as needed. express magnitude as positive number and angle between . ±180∘.
v1 = ∠ ∘ V
v2 = ∠ ∘ V
v3 = ∠ ∘ V
An express magnitude is a positive number and angle between. ±180∘. v1 = ∠ ∘ V.
Nodal stress analysis complements the previous mesh analysis in that it is equally powerful and based on the same concepts as matrix analysis. As the name suggests, node voltage analysis uses Kirchhoff's first law node equation to find the voltage potential around a circuit.
When we use the term node voltage, we are referring to the potential difference between two nodes in a circuit. Select one of the nodes in your circuit as the reference node. All other node voltages are measured with respect to this one reference node.
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ight with a frequency of 5.9 x1014 hz travels in a block of glass that has an index of refraction of 1.51. A) What is the wavelength of the light in vacuum ? | B) What is the wavelength of the light in the glass?
The wavelength in a vacuum is 5.08 x 10-7 m and the wavelength of the light in the glass is 3.367 x 10-7 m
As we know that
Velocity = wavelength x frequency
So, wavelength = Velocity / frequency
If the light travels in a vacuum,
Then, wavelength = speed of light/frequency
Here the frequency is 5.9 x1014 Hz
And the speed of light = 3 x 10 8 m/s
So, wavelength in vacuum = 3 x 10 8 / 5.9 x1014
= 5.08 x 10-7 m
Again, the wavelength of the light in the glass
λ=c/μn where μ is a block of glass that has an index of refraction
Then λ=(3 x 10 8 )/(1.51x5.9 x1014 )
= 3.367 x 10-7 m
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match the feature on mars with the best terrestrial analogy. be sure to think broadly. the analogy can be geological, chemical, or conceptual.
The two planets are similar in size, inclination, structure, composition, and the presence of water on their surfaces. They also have many key differences.
While Earth has 23h 56m and 4 s period of rotation, Mars's period of rotation is about 24 hours and 40 minutes. Mars is inclined on its axis, similar to Earth., It is inclined at 25.19° to its orbital plane.
They are both terrestrial planets. This means that both have a dense metallic core and also an overlying mantle and crust, which is composed of less dense materials (like silicate rock).
Mars also has a surface covered by a mountain range. Ice water exists beneath much of the Martian surface. Radar data and soil samples have confirmed the presence of shallow subsurface water at the middle latitudes as well.
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you have a horizontal grindstone (a disk) that is 87 kg, has a 0.35 m radius, is turning at 95 rpm (in the positive direction), and you press a steel axe against the edge with a force of 15 n in the radial direction. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone. (b) How many turns will the stone make before coming to rest?
The angular acceleration is 0.19 and the number of turns is 41.07 revolutions.
m = 87 kg be the mass of the grindstone,
r = 0.35 m be the radius of the grindstone,
I = mr²/2 be the grindstone's moment of inertia,
ω = 95 revolution/min = 95 2π/60s = 9.9 s-1 be initial angular velocity,
F = 15 N be the force pressing radially,
f = 0.2 be the coefficient of friction,
α (unknown) be the grindstones angular acceleration.
a)The tangential force slowing the grindstone is
fF
Its torque is
rfF
By Newton's Second Law
rfF = Iα
Therefore
α = rfF/I = 2rfF/mr² = 2fF/mr
Substituting actual numbers
α = 2×0.2×15/(87×0.35) = 0.19 s-2
Note that the above is the absolute value of the acceleration.
Depending on which direction is considered positive or negative,
the answer may need to be negated.
b)
Let
t be the time it takes the grindstone to come to rest,
θ be the total angle by which the grindstone will turn before coming to rest.We have the following identities, which follow from the definition of acceleration:
ω = αt
θ = αt²/2
From the first
t = ω/α
Plug into the second
θ = α(ω/α)²/2 = ω²/2α
Substitute actual numbers
θ = 9.9²/2×0.19 = 257.92
The above result is in radians.
Since the result is supposed to be given in revolutions,
we need to divide by the number of radians per revolutions:
257.92/2π = 41.07 revolutions
Therefore, the angular acceleration is 0.19 and the number of turns is 41.07 revolutions.
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the loop is in a magnetic field 0.40 t whose direction is perpendicular to the plane of the loop. at t=0, the loop has area A=0.285 m2
The emf induced in the loop at t = 0 is
Part a)
[tex]$$\text { EMF }=14 \times 10^{-3} \mathrm{~V}$$[/tex]
The emf induced in the loop at t = 1.00 s
Part b)
[tex]$$E M F=15.67 \times 10^{-3} \mathrm{~V}$$[/tex]
What is emf induced ?
As we know that magnetic flux through the loop is given as [tex]$\phi=B . A$[/tex]
now we have
[tex]$$\phi=B \pi r^2$$[/tex]
now rate of change in flux is given as
[tex]\frac{d \phi}{d t}=B(2 \pi r) \frac{d r}{d t}$$[/tex]
now we know that
[tex]$$\begin{aligned}& A=\pi r^2 \\& 0.285=\pi r^2 \\& r=0.30 m\end{aligned}$$[/tex]
Now plug in all data
[tex]$$\begin{aligned}& E M F=(0.20) \times 2 \pi \times(0.30) \times(0.037) \\& E M F=14 \times 10^{-3} V\end{aligned}$$[/tex]
Now the radius of the loop after [tex]$t=1 \mathrm{~s}$[/tex]
[tex]$$\begin{aligned}& r_1=r_0+\frac{d r}{d t} \\& r_1=0.30+0.037 \\& r_1=0.337 m\end{aligned}$$[/tex]
Now plug in data in above equation
[tex]$$\begin{aligned}& E M F=(0.20) \times 2 \pi \times(0.337) \times(0.037) \\& E M F=15.67 \times 10^{-3} V\end{aligned}$$[/tex]
Complete question:The loop is in a magnetic field 0.40 T whose direction is perpendicular to the plane of the loop. At t = 0, the loop has area A = 0.285 square m.Suppose the radius of the elastic loop increases at a constant rate, dr/dt = 3.70 cm/s .
A) Determine the emf induced in the loop at t = 0.
B)Determine the emf induced in the loop at t = 1.00 s .
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the vectors d and e are [-4,1] and [1,4] respectively .find the angle b/n and e (Use dot product )
The angle between the two vectors is 59 degrees.
What is the angle between the two vectors?
The angle between the two vectors is calculated by applying the following equation as shown below.
Mathematically, the formula for angle between two vectors is given as;
tan θ = Vy / Vx
where;
Vy is the resultant vertical vectorVx is the resultant horizontal vectorThe resultant vertical vector is calculated as follows;
∑ Vy = ( 1 + 4 ) = 5 y
The resultant horizontal vector is calculated as follows;
∑ Vx = ( -4 + 1 ) = -3x
The angle between the two vectors is calculated as follows;
tan θ = Vy / Vx
tan θ = 5 / 3
tan θ = 1.667
θ = arc tan ( 1.667 )
θ = 59 degrees
Thus, the angle between the two vectors is a function of the resultant vertical and horizontal vector.
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A wave on a string is described by y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m + t/(0.20 s))], where x is in m and t in s.
In what direction is this wave traveling?
What are the wave speed, frequency, and wavelength?
At t = 0.50 , what is the displacement of the string at x = 0.20 m?
The wave is traveling in the negative x direction.The wave speed is 12.0m/s.The frequency is 5HzThe wavelength is 2.4m.The displacement is 0.029m.
What is the displacement of the string ?The general wave equation is given by;
y(x, t) = y cos (2(x/λ) - 2ft) --------------------------------(i)
y(x, t) is the displacement of the wave at position x and a given time t
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m) + t/(0.20 s))] ------------------(ii)
Which can be re-written as;
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m)) + 2π(t/(0.20 s))] -------------(iii)
Comparing equations (i) and (iii) we have that;
=> 2π(x/(2.4 m) = 2π(x/λ)
=> λ = 2.4m
Therefore the wavelength of the wave is 2.4m
Also, still comparing the two equations;
=> 2π(t/(0.20 s) = 2πft
=> f = 1 / 0.20
=> f = 5Hz
Therefore the frequency of the wave is 5Hz
To get the wave speed (v), it is given by;
v = f x λ
Where f = 5Hz and λ = 2.4m
=> v = 5 x 2.4
=> v = 12.0m/s
Therefore, the speed of the wave is 12.0m/s
At t = 0.50s and x = 0.20m;
The displacement, y(x,t) of the string wave is given by
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m) + t/(0.20 s))]
Convert the amplitude of 3.0cm to m
=> 3.0cm = 0.03m
Carefully solve the equation
=> y(x, t) = (0.03m) × cos[2π((0.20)/(2.4 m)) + 2π(0.50/(0.20 s))]
=> y(x, t) = (0.03m) × -0.9684
=> y(x, t) = 0.029m
Therefore the displacement at those points is -0.029m
Also, the sign of the displacement shows that the direction of the wave is in the negative x direction.
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Let r be the separation vector from a fixed point (x’, y’, z’) to the point (x, y, z), and let r be its length. That is
(a) Refer to part (a)
(b) Refer to part (b)
(c) [tex]nr^{n-1}\bold{\hat{r}}[/tex]
Step-by-step Explanation:To answer the questions, I will show the derivations of each part by applying vector calculus methods such as the gradient operator, denoted by '▽', to the given quantities. I will use the definition of the gradient operator in Cartesian coordinates to solve each part.
Given:
[tex]\bold{r} = (x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}; \ r=\sqrt{ (x-x')^2+(y-y')^2+(z-z')^2}[/tex]
Show that:
(a) [tex]\nabla (r^2)=2 \bold{r}[/tex]
(b)[tex]\nabla (1/r)=- \bold{\hat{r}}/r^2[/tex]
(c) What is the general formula for [tex]\nabla (r^n)[/tex]?
[tex]\hrulefill[/tex]
Part (a): Proving [tex]\Large{\nabla (r^2)=2\hat{r}}[/tex][tex]\hrulefill[/tex]The gradient operator in Cartesian coordinates is:
[tex]\nabla = \hat{\imath}\dfrac{\partial}{\partial x}+ \hat{k}\dfrac{\partial}{\partial y}+ \hat{\jmath}\dfrac{\partial}{\partial z}[/tex]
The square of the vector length is given by:
[tex]\Longrightarrow r^2 = [(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}]^2\\\\\\\\\Longrightarrow r^2 = (x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}[/tex]
Now, applying the gradient operator to 'r²':
[tex]\Longrightarrow \nabla r^2 = \\\\\bullet \dfrac{\partial}{\partial x}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}]=2(x-x')\\\\\bullet \dfrac{\partial}{\partial y}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}] = 2(y-y')\\\\\bullet\dfrac{\partial}{\partial z}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}] =2(z-z')\\\\\\\\\therefore \nabla r^2=2(x-x')\hat{\imath}+ 2(y-y')\hat{\jmath} + 2(z-z')\hat{k}\\\\\\\\[/tex]
Factoring out a 2:
[tex]\Longrightarrow \nabla r^2=2[(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}]\\\\\\\\\therefore \boxed{\nabla r^2=2 \bold{r}}[/tex]
[tex]\hrulefill[/tex]
Part (b): Proving [tex]\nabla (1/r)=- \bold{\hat{r}}/r^2[/tex][tex]\hrulefill[/tex]The length 'r' is given by:
[tex]r=\sqrt{ (x-x')^2+(y-y')^2+(z-z')^2}[/tex]
Now applying the gradient operator to 1/r:
[tex]\dfrac{1}{r}=((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}[/tex]
[tex]\nabla \dfrac{1}{r} =\\\\\bullet \dfrac{\partial}{\partial x}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(x-x')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2}\\\\\bullet\dfrac{\partial}{\partial y}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(y-y')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2} \\\\\bullet\dfrac{\partial}{\partial z}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(z-z')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2}[/tex]
[tex]\Longrightarrow \nabla \dfrac{1}{r} = - \dfrac{(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}}{[(x-x')^2+ (y-y')^2 + (z-z')^2]^{3/2}}[/tex]
[tex]\Longrightarrow \nabla \dfrac{1}{r} = -\dfrac{\bold{r}}{r^3}; \ \text{Where:} \ \bold{\hat{r}} =\dfrac{\bold{r}}{r} \rightarrow \bold{r}=\bold{\hat{r}}\cdot r \\\\\\\\\Longrightarrow \nabla \dfrac{1}{r} = -\dfrac{ \bold{\hat{r}} \cdot r}{r^3}\\\\\\\\\therefore \boxed{\nabla \dfrac{1}{r} = \dfrac{\bold{-\hat{r}}}{r^2}}[/tex]
[tex]\hrulefill[/tex]
Part (c): General formula for [tex]\nabla (r^n)[/tex][tex]\hrulefill[/tex]The general formula is as follows:
[tex]\Longrightarrow \nabla(r^n)=\dfrac{\partial}{\partial r}[r^n] \bold{\hat{r}} \\\\\\\\\therefore \boxed{\nabla(r^n)=nr^{n-1}\bold{\hat{r}}}[/tex]
a fixed amount of a monatomic ideal gas is taken through the following cyclic process. originally (a) it is near atmospheric pressure (100 kpa) with a volume of 0.50 m3 and a temperature of 375 k. then it is isothermally compressed to half its volume (b). then its volume triples (c) during an isobaric expansion.
The qualitative sketch of the process on the PV plane is attached below:
What is ideal gas equation?The ideal gas law (also called the perfect gas law), the relationship between pressure P, volume V, and temperature T of a gas in the boundary region between low pressure and high temperature. Gas molecules move almost independently. each other. In such cases, all gases obey an equation of state known as the ideal gas law.
PV = nRT, where n is the number of moles of gas and R is the universal (or complete) gas constant, 8.31446261815324 joules/kelvin/mol (the universal gas constant is defined as Avogadro's number NA multiplied by Boltzmann's constant k) . ) In the International System of Units, energy is measured in joules, volume in cubic meters (m3), force in newtons (N), and pressure in pascals (Pa). where 1 Pa = 1 N/m2. A force of 1 Newton moving a distance of 1 meter does 1 Joule of work. Therefore, the dimension of both products PV and nRT is work (energy).
The qualitative sketch of the process is drawn on the PV plane.
At A,
P₁ = 100 kPa
V₁ = 0.50 m³
T₁ = 375 K
At B,
T₂ = 375 K
V₂ = 0.25 m³
P₁V₁ = P₂V₂
So, P₂ = (100× 10³ ×0.50)/ 0.25
= 200 kPa
At C,
P₃ = 200 kPa
V₃ = 0.75 m³
We know, V₂/ T₂ = V₃/ T₃
So,
T₃ = V₃T₂/ V₂
= (0.75 × 375)/ 0.25
= 1125 K
At D,
P₄ = 100 kPa
T₄ = 1125 K
V₄ = P₃V₃/ P₄
= (200 × 0.75)/ 100
= 1.5 m³
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The complete question is:
Why does a light ray bend when it travels from the air to water?
Answer: When the light hits the water, it causes the light to slow down, and when it does this, the light changes directions.
Explanation:
Please help me
Jadee S. pulls a piece of luggage across the airport, notices that she is lagging behind her parents and wants to catch up for a short amount of time. She pulls with a horizontal force of 33.3 N. The force due to friction for the luggage is 12.3 N and the mass of the luggage is 50.0 kg.
Answer:
The acceleration of the luggage is:
a = (33.3 N - 12.3 N) / 50.0 kg = 0.466 m/s²
Explanation:
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