The speed of the 1.50-kg ball just before impact is 5.557 m/s . After assuming that the collision is elastic, the velocities of both balls just after collision is -2.873 m/s and 2.684 m/s. After ignoring the air resistance, the ball swings up to the height of 0.420 m and 0.367 m.
(a) Initial speed = u = 5 m/s
Height = h = 0.3 m
Using the principle of conservation of mechanical energy, find the speed of the 1.50-kg ball just before impact,
= V = √ (2gh + u²)
= V = √ (2 X 9,81 X 0.3 + 5²)
= V = 5.557 m/s
(b) Initial speed = u = 5 m/s
Height = h = 0.3 m
Weight of the ball = 4.6 Kg
Velocity of 1.50 Kg ball = u'
Velocity of 4.60 Kg ball = v
Now, assuming that the collision is elastic, find the velocities (magnitude and direction) of both balls just after the collision,
= 1.50(5.557 - u) = 4.60v
= 5.557 - u = 3.14v [let this be equation 1]
and,
= 1.50(5.55² - u²) = 4.60v²
= 5.557² - u² = 3.14v² [let this be equation 2]
By dividing 1 and 2,
= 5.557 + u = v [let this be equation 3]
Now, adding 1 and 3,
= 11.114 = 4.14v
Substituting this in equation 3,
= u = -2.873m/s
Thus, for 1.50 kg ball, velocity is -2.873 m/s and that of 4.60 Kg ball is 2.684 m/s.
(c) To find the height,
For a 1.50 Kg ball, h =
= h = u² / 2g
= h = -2.873² / 2 X 9.8
= h = 0.420 m
For a 4.60 Kg ball, h =
= h = u² / 2g
= h = 2.684² / 2 X 9.8
= h = 0.367 m
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An old version of stellar evolution, popular at the beginning of the twentieth century, maintained that stars begin their lives as large, cool spheres of gas, like the giant stars on the H-R diagram. They then contract and heat up under the pull of their own gravity to become hot, bright blue O stars. For the remainder of their lives they lose energy, becoming dimmer and redder with age. As they slowly move down the main sequence, they eventually end up as cool, dim red M stars. Explain how observations of stellar clusters, plotted on the H-R diagram, contradict this idea.
Every star goes through distinct evolutionary stages that are determined by its internal structure and method of energy production depending on its initial mass. The temperature and luminosity of the star change with each of these stages, and as the star develops, it can be seen moving to various locations on the HR diagram.
One of the most crucial tools for studying stellar evolution is the HR diagram, also known as the Hertzsprung-Russell diagram. It was independently created by Ejnar Hertzsprung and Henry Norris Russell in the early 1900's and plots either the colour of stars against their absolute magnitude or the temperature of stars against their luminosity.
The HR diagram is dominated by the main sequence, which extends from the upper left to the bottom right. In their cores, stars spend about 90% of their lives converting hydrogen to helium.
Low-mass stars reach their final evolutionary stage as white dwarf stars.
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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 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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suppose astronomers built a 140-meter telescope. how much greater would its light-collecting area be than that of the 10-meter keck telescope? express your answer using two significant figures. nothing request answer
The light-collecting surface of the 140-meter telescope will be 25 times larger than that of the Keck II telescope, which stands at 10 metres. A telescope is a tool for observing far-off objects through their radiation.
electromagnetic radiation's absorption or reflection. originally exclusively referring to an optical device that observes far-off objects using lenses, curved mirrors, or a combination of the two. A telescope's capacity to focus is referred to as its " light-collecting function." a telescope's capacity to simultaneously focus on several objects.
A 140-meter telescope's 50-meter light-collecting diameter.
A 10-meter telescope has a 10-meter diameter for light gathering.
Pi*(D^2)/4 is the formula for a telescope's light-collecting area.
Light collecting area ratio = (pi*(140^2)/4)/pi*(100)/4 = 25
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Which of the following best reduces atmospheric distortion?
adaptive optics
The best reduces atmospheric distortion is through adaptive optics.
Optical aberrations can be fixed using a technology called adaptive optics (AO). The work that led to the Nobel Prize-winning discovery of a supermassive compact object at the center of our galaxy was made possible by a method that was initially devised to account for the blurring effect of atmospheric turbulence on images in ground-based observatories. We can research the functioning of the visual system and evaluate ocular health in the microscopic domain when AO is employed to compensate for the eye's defective optics.
By detecting retinal changes at the cellular level, AO allows us to adjust for the eye's imperfect optics. AO has expanded the capabilities of imaging in thick tissue specimens, such as when examining neuronal processes in the brain, by correcting for sample-induced blur in microscopy.
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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 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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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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three particles are fixed in place. the mass of b is greater than the mass of c. can a fourth particle (particle d) be pplaces somewhere so that the net gravitational force on particle a from particles b, c, and d is zero?
Its position of this particle D must be near the positive y-axis in the second meiotic division of the aforementioned equations.
What is gravitational force and example?This attraction that earth has on an object is referred to as gravitational force. Examples of motion brought on by gravitational force also include upwards motion of a ball being thrown, the downward motion of water moving through a stream, and the pull of gravity on river flow.
Briefing:When two bodies are separated by a distance R and have masses M and m, the gravitational attraction between them is:
F= GMm/R²
The gravitational force is a result of the interaction between the gravitational forces exerted by particle B and particle C on particle A.
We can claim that because particle B has a larger mass than particle A does, the gravitational force was closer to and roughly equal to the mass of the bodies.
The net gravitational force on particle A would be zero if particle D force is exerted that is equal to it and opposite to the normal Force that results.
As a result, particle D need to be positioned close to the positive y-axis in the second quadrant.
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f a force of 120 n acting 0.29 m from the axis of rotation is balanced by another force of 92 n (causing no motion), what is the moment arm of the second force?
The moment arm of the second force is 0.29 m.
What is moment?
A moment is just a mathematical expression used in physics that involves the product of a physical quantity and a distance. Moments refer to the physical quantities that are dispersed from the reference point and are typically defined with regard to a fixed reference point. The moment thus explains the position or arrangement of the quantity. For instance, the moment of force, also known as torque, is the result of the force acting on an object and the object's distance from of the reference point. In theory, a moment can be created by multiplying any physical quantity by a distance. Forces, masses, and electrically charged distributions are frequently used units.
The moment arm of the second force is the distance from the axis of rotation to the point at which the force is acting.
Since the two forces are in equilibrium, meaning that they have cancelled each other out, the distance from the axis of rotation to the point at which the second force is acting (the moment arm) must be equal to the distance from the axis of rotation to the point at which the first force is acting (0.29 m).
Thus, the moment arm of the second force is 0.29 m.
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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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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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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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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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how do these meteorites support the nebular theory's scenario about for the formation of the terrestrial planets?
These meteorites' appearance and makeup exactly match what we would anticipate if, as the nebular theory predicts, metal and rock condensed and accreted.
What three sorts of meteorites are there?varieties of meteorites The number of meteorites discovered on Earth exceeds 60,000. These meteorites can be classified as either stony, iron, or stony-iron by scientists. Many sub-groups exist within each of these kinds.
Where can you locate meteorites?The American Southwest, the African continent's northwest desert, and Antarctica are among the best locations for meteorite searching. Being a snow and ice desert, Antarctica is very cool (no pun intended), as it would be simple to notice a strange-looking, dark rock from space.
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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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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]
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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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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A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. Its maximum cruising speed is 90 mi/h. (a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?(c) Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart.(d) The trip from one station to the next takes at minimum 37.5 minutes. How far apart are the stations?
The train can go a maximum distance of 119671.2 feet if it starts off at a slow speed, accelerates until it reaches cruising speed, and then maintains that speed for 15 minutes.
The train travels 117057.6 feet when it starts off at rest and must come to a complete halt in 15 minutes. Between two consecutive stops that are 45 miles apart, the train travels in 30.22 minutes overall. The distance between the stations is 55.92 miles.
This condition can be broken down into two kinematic equations:
d = 1/2*10*t2 for acceleration (No initial velocity) UNITS: foot, s
Knowing the ultimate velocity allows us to calculate t as follows: v=90mph=132ft/s=10*t, which equals t=13.2s.
d = 5*(13.2^2) = 871.2 ft
Constant speed for 15 minutes = 900s
d = 132ft/s * 900s = 118800 ft
Total Distance: 119671.2 ft = 22.665 mi
Split this situation up into 3 parts, Maximum distance would be maximum cruising time:
Accelerating to cruising speed: d = 871.2 ft, t = 13.2s
Decelerating from cruising speed:
d = 5*(13.2^2) = 871.2 ft
900 seconds at constant speed for 15 minutes
d = 132 feet per second multiplied by ninety seconds equals 118,800 feet.
Total distance: 22.665 miles or 119671.2 feet.
Divide this circumstance into three pieces. The maximum distance corresponds to the maximum cruising time:
Cruising speed acceleration: d = 871.2 ft, t = 13.2 s
Deceleration from cruise: d = -5*t2 + 132*t, v = 0 = -10*t + 132, t = 13.2s, d = 871.2ft
We know that while cruising, t = 900s - 13.2s - 13.2s = 873.6s, and d = 132*873.6 = 115315.2ft.
117057.6 feet or 22.17 miles total.
Similar to part b, but with the cruise distance known and the requirement to solve for time now (minimum time is maximum speed, so maximum cruising time).
d = 871.2 feet, t = 13.2 seconds, accelerating
d = 871.2 feet, t = 13.2 seconds, decelerating
When cruising, the distance is 45 miles and the altitude is 871.2 feet. The altitude is then multiplied by 1742.4 feet to get the total altitude, which is 235857.6 feet.
t = 235857.6/132 = 1786.8s
Total time: 1786.8 + 12.2 + 12.2 = 1813.2s or 30.22 minutes.
This portion is identical to part c, except that the order is reversed:
d = 871.2 feet, t = 13.2 seconds, accelerating
decreasing: d = 871.2 feet, t = 13.2 seconds
Traveling: t = 2250 - 26.4 = 2223.6s d = 132*2223.6 = 293515.2ft
Total distance: 293515.2 plus 1742.4 feet, or 55.92 miles.
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Which forms as a result of compressional stress? anticline and synclinenormal faultstrike-slip faultfault-block mountain.
Compressional stress causes synclines and anticlines to develop. Thus, the correct option is A.
What is Anticline ?When previously horizontal strata are folded upward and the two limbs diverge from the surface, anticlines emerge.
Instead of shattering to create faults or joints, when rocks deform in a ductile way, they may bend or fold, and the resulting structures are known as folds. Folds are brought about by long-lasting compressional or shear stresses. These folds result from typically brittle rocks acting ductility under conditions of low strain rate and/or high temperature.
According to the definition
We get to know that
Compressional stress causes synclines and anticlines to develop. Thus, the correct option is A.
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I need help
Tell us what activity is engaged in malala yousafiza what he is fighting for. Her life.
What a reward she got.
Express opinions about it
Answer:
the activity in this is not an easy way to do it in my mind and the heart of the city is not a bad day to get to a new report from the University of Texas I think that it was not until you are looking for a way that it would have been a great job in the world and is not intended to limit the scope of this invention to provide a method and system and a lot of people are going to get.
write the rate law that you determined from the experimental data. include the numerical value for k, and the appropriate orders for each reactant.
[tex]v_{0}[/tex]= k [A]^x [B]^y is the general rate law or rate law equation for any chemicals reaction where A and B means concentration of the species.
What is rate law?Rate law or rate law equation is the equation linking the initial and final or forward reaction rate in any chemical reaction taking place. the general rate law equation is [tex]v_{0}[/tex]= k [A]^x [B]^y.
Description of [tex]v_{0}[/tex]= k [A]^x [B]^y.[tex]v_{0}[/tex]= k [A]^x [B]^y. here in the given equation A and B represents the concentration of the species reacting in the given chemical equation.
the data id find or calculated experimentally.
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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 square coil, enclosing an area with sides 7.9 cm long, is wrapped with 2,786 turns of wire. a uniform magnetic field perpendicular to its plane is turned on and increases to 0.11 t during an interval of 0.5 s. what average voltage is induced in the coil? express the answer with two decimal places.
The average voltage induced in the coil is 97.00 V.
What is voltage?
The difference throughout electric potential between two points is known as voltage, also referred to as electric pressure, electric tension, as well as (electric) potential difference. It translates into the amount of work required to move a charge from one point between two points in a static electric field. Volt is the name of the voltage-derived unit in the International System of Units. 166 Joules per coulomb, or 1 volt equals 1 joule (of work) per 1 coulomb, is how work per unit of charge is expressed in SI units (of charge). Power and current were used in the previous SI definition for the volt, the quantum Hall as well as Josephson effect was introduced in 1990, and as of 2019 fundamental physical values obtained have been used in the definition of any and all SI units as well as derived units.
The average voltage induced in the coil can be calculated using Faraday's Law:
V = (B*A*N*Δt)/t
V = (0.11 T *(7.9 cm)^2 * 2,786 turns * 0.5 s)/0.5 s
V = 97.0 V
Therefore, the average voltage induced in the coil is 97.00 V.
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You measure 48 turtles' weights, and find they have a mean weight of 34 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight.
While measuring the weight of 48 turtles' weights with a mean weight of 34 ounces and a population standard deviation of 4.4 ounces, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is +- 0.634
Given:
The sample size or the number of total turtles, [tex]n=48[/tex]
The mean of the weights of the sample of 48 turtles, [tex]x=34[/tex]
The population standard deviation is the diffference between each value of the sample and the sample mean.
Population standard deviation[tex]=4.4[/tex]
Confidence interval= 90% [tex]=0.90[/tex]
Significance level[tex]= 1- confidence[/tex][tex]=1-0.90=0.10[/tex]
The critical value of a statistical distribution is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test.
The critical value, [tex]z=\frac{n-x}{deviation} =\frac{48-34}{4.4} =3.181[/tex]
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
The closest z value from the z table corresponding to critical value =3.181 is [tex]z=0.99926[/tex]
The margin of error, [tex]E=z*\frac{deviation }{\sqrt{sample size} } =0.99926*\frac{4.4}{\sqrt{48} } =0.634[/tex]
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light of 550 nm illuminates two narrow slits 0.12 mm apart causing an interference pattern on a screen 1.0 m away. how much farther did the light from the left slit travel than the light from the right slit to the m
The light from the left slit travels to the m at 500 nm slower than the light from the right slit. Two tiny openings spaced 0.12 mm apart are illuminated by 550 nm light, creating an interference pattern.
Interference patterns: what are they?
Thomas Young demonstrated that when light from two sources collides while moving through the same medium, an interference pattern is created. It is crucial to go back a few steps and examine the interference of water waves that originate from two sites in order to comprehend Young's experiment.
What kinds of interference patterns are there?
The light reflected from an oil coating floating on water is one of the best illustrations of interference. Another illustration is the thin soap bubble film (illustrated in Figure 1),
Briefing:
r = d*sin(theta)
r = 1m *sin(5.5*10^-7)
r = 9.599^-9m r = 9.6nm
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Purchasing uses information from the _____ to place purchase orders for raw materials with qualified suppliers.
Purchasing uses information from the sales order plan to place purchase orders for raw materials with qualified suppliers.
What is purchasing?The term purchasing has to do with the process of the buying of goods and services. The process of purchasing a very essential part of the business venture such that in some areas, an entire department may be devoted to the coordination of the processes involved in purchasing in the establishment.
A purchasing manager may be given the task of seeing to the coordination of the entirety of all the purchasing activities.
Thus, we could see that purchasing is a chain of activities that is based on the principles of demand and supply.
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the focal length of david's lens is 50 cm . if rebecca stands in front of david at a distance of do and david perceives the position of rebecca at di , what does do equal if the magnification is -0.40?
The distance of do is 83.34 cm for the magnification -0.40.
Magnification is the process of increasing apparent size.
It is usually done to see the object in an enlarged view by increasing its resolutions so that a more clear view of the object can be visualized.Microscopes like light, electron and compound microscopes are used to see a high resolution image of the object.Magnification can be calculated by the formula M = -(l/f₀)(25/f₁)M = magnification = - 0.40
l = distance between the eyepiece and the objective lens
f₀ = focal length of the objective
f₁ = focal length of the eyepiece
the focal length of David's lens is: f = 50 cm.
Distance 'u' between the object is to be calculated
According to the formula;
u =f( 1/m -1)
⇒ u = 50(-1/0.40-1) = 83.34 cm.
Hence, distance do is 83.34 cm.
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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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