Comets are small asteroid-like bodies when they are far from the Sun, traveling in highly ellipical orbits about the Sun. Comets go around the Sun in a highly elliptical orbit
How to find speed of a comet?
Speed of the comet can be determined by using conversation of energy = initial kinetic energy + initial potential energy of comet = final kinetic energy + final potential energy of comet
We know,
M = mass of sun = 1.989 x 1030 kg
m = mass of comet
vi = initial speed of comet = 20000 m/s
ri = initial distance from center of sun = 2.4 x 1011 m
vf = final speed of comet = ?
rf = final distance from center of sun = 5.2x 1010 m
Using conservation of energy
initial kinetic energy + initial potential energy of comet = final kinetic energy + final potential energy of comet
(0.5) m vi2 - GMm/ri = (0.5) m vf2 - GMm/rf
(0.5) vi2 - GM/ri = (0.5) vf2 - GM/rf
(0.5) (20000)2 - (6.67 x 10-11)(1.989 x 1030)/(2.4 x 1011) = (0.5) vf2 - (6.67 x 10-11)(1.989 x 1030)/(5.2x 1010)
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The expansion of the universe after its origin takes place by a phenomenon called.
The expansion of the universe after its origin takes place by a phenomenon called Big bang
What is Big bang theory ?As the universe widened, it cooled and matter began to form. Neutrons, protons, electrons, anti-electron, photons, and neutrinos were all present in the universe one second after the Big Bang. The Big Bang nucleosynthesis, which took place during the first three minutes of the universe, produced the light elements.
The big bang theory is the most commonly accepted explanation. Learn about the initial explosion and how the universe expanded from the size of an atom to include everything that exists today.
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in the pictorial system, what indicates that an extinguisher is not suitable for a particular class of fire?
An extinguisher is not suitable for a certain class of fire if it has a red diagonal line through it on a black background.
With an illustration, define a symbol.Other concepts and beliefs can be conveyed using symbols. Words, music, gestures, ideas, or visual images could all be used to describe them. For example, on maps, rivers are commonly represented by blue lines, and a red rose is frequently associated with compassion and love. A typical symbol for "STOP" is a red octagon.
How do you recognize a symbol?When an image in a text seems to suggest something beyond its exact meaning, symbolism is present. Although authors don't always do this, it could be repeated or seem startling, as if the author is purposefully drawing attention to it.
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if 4 different amplitudes are used, how many bits can be transmitted with each amplitude change? qizzlet
if 4 different amplitudes are used, the numbers of bits that can be transmitted with each amplitude change is 2 bits.
What in physics is the amplitude?Distance between the wave's resting position and its highest displacement is known as amplitude. Frequency is the quantity of waves that pass by a particular place each second.
The distance between the center line (or the still position) and the top or bottom of a wave's crest or trough is known as the amplitude (). Be cautious when using this amount because a diagram may not always show the center line. Meters are used to measure amplitude ( ).
For example:
If there is 4 amplitudes, it will be: 00,01,10,11 then 2 bits
If there is 8 frequencies it will be: 000,001,010,011 ,100,101,110, 111 and then 3 bits
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See full question below
With Amplitude Shift Keying (ASK), if 4 different amplitudes are used, how many bits can be transmitted with each amplitude change?
the scattering of sunlight by the mixture of gas molecules in air results in the blue color of the sky. calculate the energy (in joules) of a single photon of blue light with a frequency of 7.30 × 10¹⁴ hz. (h
The energy (in Joules) of a single photon of blue light = [tex]4.83 * 10^-^1^9 J[/tex]
What is the energy of photon?
The energy that a single photon carries is known as photon energy. Energy is inversely correlated with electromagnetic frequency of the photon.
The energy of a photon is given by the formula
E = h*v
where,
h = planks constant
v = frequency
Given,
h = [tex]6.626 * 10^-^3^4 J s[/tex]
v = 7.30 × [tex]10^1^4[/tex] Hz
1 Hz = 1 [tex]s^-1[/tex]
v = 7.30 × [tex]10^1^4 s^-1[/tex]
E = [tex]6.626 * 10^-34 * 7.30 * 10^1^4[/tex]
E = [tex]48.36 *10^-^2^0 J[/tex]
E = [tex]4.83 * 10-19 J[/tex]
The energy (in Joules) of a single photon of blue light = [tex]4.83 * 10^-^1^9 J[/tex]
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a particle with charge +4.20 nc is in a uniform electric field e⃗ directed to the left. the charge is released from rest and moves to the left; after it has moved 6.00 cm, its kinetic energy is +2.20×10−6 j.
(a) The work done is 1.50 x 10^-6 J
(b) The potential of the starting point with respect to the endpoint is 357.14 V.
(c) The magnitude of E is 5952.38 N/C.
Given that,
Charge = 4.20 nC
Distance = 6.00 cm
Kinetic energy K.E = 1.50 x 10^-6 J
The particle start from rest. So, the initial kinetic energy i zero.
(A) We need to calculate the work by the electric force
Using formula of work done
W = ∆K.E
W = K.Ef - K.Ei
Put the value into the formula
W = 1.50 × 10^-6 - 0
W = 1.50 x 10^-6 J
The work done is 1.50 x 10^-6 J
(B). We need to calculate the potential of the starting point with respect to the endpoint
We know that.
Change in potential energy = change in kinetic energy
∆P.E = ∆K.E
So, U = 1.50 x 10^-6
Using formula of potential
V = U/q
Put the value into the formula
V = 1.50 × 10^-6/4.20 x 10^-9
V = 357.14 V
The potential of the starting point with respect to the endpoint is 357.14 V
(C) We need to calculate the magnitude of E
Using formula of work done
W = F x r (1)
Using formula of force
F = qE
Put the value in the equation (1)
W = qE x r
E = W/q x r
Put the value into the formula
E = 1.50 x 10^-6/4.20 x 10^-9 x 6.00 x10^-2
E = 5952.38 N/C
Hence, The magnitude of E is
5952.38 N/C
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Two kindergartners are having a game of tug-of-war. The kid on the left has a mass of
27 kg and the kid on the right is 31 kg. As the game progresses, neither kid is going
anywhere. What is the momentum of the kid on the right?
The momentum of the kid on the right having a mass of 31 kilograms is 0 Kg.m/s
How do I determine the momentum?Momentum is defined as the product of mass and velocity. It is expressed mathematically as:
Momentum = mass × velocity
With the above formula, we can obtain the momentum of the kid on the right as follow:
Mass of kid on the right = 31 kilogramsVelocity of kid on the right = 0 m/sMomentum of kid on the right =?Momentum = mass × velocity
Momentum = 31 Kg × 0 m/s
Momentum = 0 Kg.m/s
Thus, the momentum of the kid on the right is 0 Kg.m/s
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a collection of logic gates for which the static power dissipation is zero, and the dynamic power dissipation is 10 mw is operating at 1 ghz with a 1.2-v supply. by what fraction could the power dissipation be reduced if operation at 1.0 v were possible? if the frequency of operation is reduced by the same factor as the supply voltage (i.e., 1.0/1.2), what additional power can be saved?
Additional Saving in power is 1.48mw.
What exactly is power dissipation?As a result of primary action, power dissipation is the process by which power is lost as heat. The process of power dissipation happens naturally. The power will be dissipated by each resistor in the circuit that has a voltage drop across it.
Since Pdyn = fc v²oo is proportional to v²oo reducing power supply
from 5v to 3v reduces the power dissipation by a factor of
(3.3)²/5² = 0.436
The power dissipation now become 0.436×10×10⁻³ = 436×10⁻³ = 4.36mw.
Since Pdyn is proportional to reducing f by the some factor as the supply voltage 3.3/5 = 0.66results in reducing the power dissipation
further by factor of 0.66
Additional Saving in power = (1.0.66) X(4.36 × 10⁻³ )
Additional Saving in power = 1.48mw.
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a 500 kg motorcycle accelerates from rest to 25 m/s over a time interval of 5.5 s. find the force exerted on the motorcycle by the road due to friction.
The force exerted on the motorcycle of mass 500 kg is 2272.72 N.
How to calculate for force?Force can be calculated by multiplying the mass of a body to its acceleration. The S.I Unit of force is Newton (N).
To calculate the force exerted on the motorcycle, we use the formula below.
Formula:
F = m(v-u)/t.......... Equation 1Where:
F = Force on the motorcyclem = Mass of the motorcyclev = Final velocity of the motorcycleu = Intial velocity of the motorcyclet = Time taken to change its velocity.From the question,
Given:
m = 500 kgv = 25 m/su = 0 m/st = 5.5 sSubstitute these values into equation 1
F = 500(25-0)/5.5F = 2272.72 NHence, the force acting on the motorcycle is 2272.72 N.
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A heat engine has a cold reservoir of 250 k and a hot reservoir of 715 k. What is the maximum efficiency of the engine? a. 65. 0% b. 60. 8% c. 73. 6% d. 58. 6% e. 69. 1%.
Answer:
Heat in = 715 K
Heat out = 250 K
Heat converted to work = 715 - 250 = 465 K
Efficiency = 465 / 715 = .65
(a) Maximum efficiency = 65%
You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20 m/s to the right and an acceleration of 8.40m/s2 to the left.
How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?
The oscillating and regular motion of an object is known as the SHM. The object must move 0.532 meters from x(t) = 0.65 meters to x(t) = A = 1.182 meters.
It is a periodic and oscillating movement that moves in a rectilinear fashion.
Knowing that there will always be a restoring force (F) that tends to return the motion to its initial location when it moves an amount called an amplitude is important when thinking about simple harmonic motion.
There are some important factors to take into account with this motion,
The movement's position, X (m), in its initial, equilibrium, and other positions.
The speed is a (m/s2).
Speed, V (m/s)
The volume, A (m)
The periodicity, w (rad/s),
The distance that the object needs to move from x(t) = 0.65m to x(t) = A = 1.182m is 0.532m.
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if the moon were five times more distant from earth than it is now, how would the gravitational force that earth feels from the moon be different?
If the moon were five times more distant from earth than it is now, the gravitational force would decrease.
How are distance and gravitational forces related?Inversely related to the square of the distance between the two objects is the gravitational force, which is directly proportional to the masses of the two objects. In other words, as objects get heavier, their gravitational pull is stronger; however, as objects get farther apart, their pull is weaker.Gravity's pulling power weakens as a pair of objects are separated by more space.As one gets farther away from a planet, the gravitational field weakens. Distances measured from the Earth's centre have a clear inverse square relationship with the dilution of gravity that occurs as you move away from the planet's surface.For, masses [tex]{M_{1},M_{2}}[/tex] , the gravitational constant G, and the increasing distance R ,the gravitational force F is given by,[tex]F= G\frac{M_{1}M_{2}}{R^{2} }[/tex]
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Two charged particles repel each other with a force f. If the charge on only one of the particles is doubled and the distance between them is also doubled, then the force will be.
The resultant force will be f/2. This means that the resultant force is half of the original repulsive force between the two charged particles.
What is Coulomb's law?According to B, the electrical force between two charged objects is inversely proportional to the square of the separation distance between the two objects and directly proportional to the product of the charges on the objects.
Mathematical expression of Coulomb's law:
[tex]F=\frac{kQ_{1}Q_{2} }{d^{2} }[/tex]
Here,
F = Electrical force
Q1 = Charge on the first object (in Coulombs)
Q2 = Charge on the second object (in Coulombs)
d = Distance between the two objects (in meters)
k = A proportionality constant (Coulomb's law constant)
According to the problem given, the force would double if one of the charges were doubled. The force would be four times lower if the distance were doubled. These two variations working together would result in a two-fold reduction in force thus resulting into f/2.
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a long, straight wire carries a current i (see figure below). which of the following statements is true regarding the magnetic field due to the wire? more than one statement may be correct.
For a long straight wire carrying conductor the magnitude of the magnetic field produced around it is proportional to I/r, and the direction is out of the page at P.
A magnetic field is produced by moving charges. Charges are constantly moving in a conductor carrying current; as a result, magnetic fields are created all around the conductor.
The right-hand thumb rule indicates the direction of this magnetic field. The thumb of the right hand is used in this rule to indicate the current's direction. The direction of the magnetic field surrounding the wire is indicated by the curled fingers.
The magnitude of the magnetic field produced by the current carrying conductor depends on the following factors:
The magnitude of the current flowing through the conductor
The distance to the point where the field value is calculating.
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A red ball with a velocity of +3. 0 m/s collides head-on with a yellow ball of equal mass moving with a velocity of -2. 0 m/s. What is the velocity of the yellow ball after the collision?.
After collision velocity of yellow ball become 3 m/s.
What is collision velocity?
Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in velocity).
Velocity of red ball = 3 m/s
Velocity of yellow ball = -2m/s
Red ball and yellow ball both have same mass
So, after head on collision their velocity will be exchanged.
So after collision velocity of yellow ball become 3 m/s.
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If you drop the sand bag out of the cart right at the equibrium location, what effect will that have on the amplitude of your oscillation?.
At maximal displacement, the speed is zero, the kinetic energy is zero, and the only source of energy is the potential energy held in the spring. E = 1/2 kA² is the energy at the greatest distance.
What is meant by oscillation?The process of any variable or measure fluctuating repeatedly about its equilibrium value in time is known as oscillation. A periodic change in a substance's quality between discrete choices or around its central value is another way to describe oscillation.
Briefing:Here, A represents the oscillation's amplitude.
Dropping the sandbag won't change the system's overall energy since all of the energy is derived from the energy stored of spring.
Therefore, the amplitude won't be affected.
The square of oscillation's intensity determines the system's energy in an exact correlation. The energy in the system remains constant, hence the oscillation's amplitude does not vary.
Hint:
Utilize the energy at balance to ascertain whether the maximum speed for dropping the sandbag at the cart's maximal changes in any way.
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If log 3 4=1. 2619, evaluate log3 0. 25. Give your answer to four decimal places
PLEASEEEEEEEEEE HELPPPPPPPPPP I HAVE BEEN STUCK ON THIS SAME QUESTION FOR ABOUT 2 -4 HOURS NOW
If log 3 4 = 1. 2619, then the solution to the equation above, which evaluates log 3 0, 25, is -1. 2619.
What does evaluate mean example?When one assess something or someone, then take them into account in order to form an opinion on them, such as whether or not they are good or terrible. It's challenging to assess the state of the market. Synonyms: evaluate, rank, value, and decide More alternatives to analyze. to evaluate or determine the degree, significance, scope, or worth of something: Doctors assess the patient's health. He was only genuinely content while working alone since then he had complete control over the strategy and the dangers.
Briefing:Convert decimal to fraction:
log₃ 25/100
Reduce the fraction:
log₃ 1/4
Round the number:
=-1.2619
hence, its evaluate -1.2619 when If log 3 4=1. 2619.
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it has been suggested that extraterrestrial civilizations (if they exist) might try to communicate by using electromagnetic waves having the same frequency as that given off by the spin flip of the electron in hydrogen, which is 1.43 ghz . to what wavelength should we tune our telescopes in order to search for such signals?
In order to search for the signal, we would need to tune our telescopes to a wavelength of 208.3 cm.
If an extraterrestrial civilization were to transmit a signal using the spin-flip of the electron in hydrogen, the frequency of the signal would be 1.43 GHz, now to determine the wavelength of the signal, we can use the formula (λ = c/f), where c is the speed of light and f is the frequency. The speed of light is 299,792,458 meters per second, so the wavelength of the signal would be 208.3 cm.
In order to search for the signal, we would need to tune our telescopes to a wavelength of 208.3 cm. This is because radio telescopes detect electromagnetic radiation in the radio frequency range, which is measured in wavelengths.
By tuning our telescopes to the wavelength of 208.3 cm, we will be able to detect any signals transmitted by an extraterrestrial civilization using the spin-flip of the electron in hydrogen.
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question 91 pts a 0.6 kg squirrel falling at 14 m/s hits in a pile of leaves and comes to rest in 2 s. find the normal force of the leaves on the squirrel as it comes to rest.
If a 0.6 kg squirrel falling at 14 m/s hits a pile of leaves and comes to rest in 2 s , the normal force of the leaves on the squirrel as it comes to rest would be 4.2 Newtons.
What is Newton's second law?
Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
As given in the problem a 0.6 kg squirrel falling at 14 m/s hits in a pile of leaves and comes to rest in 2 s.
The change in the moment of the squirrel = 0.6 × 14
=8.4 Kg - m/s
The normal force = rate of the change of the momentum
= 8.4 / 2
= 4.2 Newtons
Thus, the normal force of the leaves on the squirrel as it comes to rest would be 4.2 Newtons.
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solar radiation can be absorbed by the earth's surface or reflected back into space. the ratio of reflected radiation to absorbed radiation is known as albedo. which of the following surfaces has the lowest albedo?
When solar energy is transmitted straight backward from a surface, reflection takes place. Albedo is the portion (or percentage) of radiation that is reflected back.
As more solar energy is received, more heat is reflected back into space, raising the temperature of the atmosphere. The Earth system does not become hotter as a result of solar radiation that Earth's surface or atmosphere reflect back into space. Heat is produced as a result of absorbed radiation. Only a small portion of the energy that reaches the Earth's surface is reflected. Around 30% of the incoming radiation is reflected back to space and does not heat the surface, leaving the remaining 70% to be absorbed by the atmosphere and the Earth's surface.
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In which type of transistor does current flow from the base to the emitter?
In an PNP transistor, the base controls the amount of current passing through it while allowing current flow from the base to the emitter.
The goal of the NPN transistor is to allow electrons to move from the emitter to the collector (so conventional current flows from collector to emitter).The base, which regulates the number of electrons the emitter "emits," receives electrons from the emitter.A PNP operates in a similar but reverse manner. The base still regulates the current flow, but it now goes from emitter to collector in the reverse direction.The emitter emits "holes" (a hypothetical absence of electrons), which are gathered by the collector, rather than electrons.PNP transistors, on the other hand, are made to allow current to flow from the collector to the emitter.To know more about transistors visit:
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if the human body has an average density of 973 kg/m3, what fraction of a person is submerged when floating gently in fresh water?
The fraction of the person submerged when floating gently on the freshwater is 0.973.
The average density of the human body = 973 kg/m³.
According to the Archimedes' principle, when a body floats in a fluid it experience is an upward force on it which is called buoyancy the buoyancy on an object is equal to the weight of the fluid that is displaced by the body.
If a body floats than the buoyancy must be equal to the weight of the body.
therefore buoyancy B can be given as
B = Vρg
V is the volume of the body,
ρ is the density of the body.
Also
B = V'xg
V' is the portion of the body submerged in fresh water,
x is the density of the fresh water.
Density of fresh water is 1000kg/m³.
Equating both the equations of 'B'
Vρ = V'x
ρ/x = V'/V
V'/V = 973/1000
So, the fraction of the human body submerged in freshwater is 0.973.
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Hydroelectric power plants are most commonly located nearA. coal-powered plants.B. nuclear-power plants.C. artificial reservoirs.D. estuaries.
Answer:
C. Artificial Resevoirs
Explanation:
For two main reasons; the first is the capacity of water of water they contain, and the second one is for mainteinance purpouse.
an inventor designs a machine that he claims will lift a 30 kg object with the application of only a 25 n force. if the inventor is correct, what is the shortest possible distance through which the force must be applied for each meter that the object is raised?
The shortest possible distance through which the force must be applied must be 0.83 meters.
What is force?
A force is indeed an influence that can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both magnitude and direction. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.
The shortest possible distance through which the force must be applied for each meter that the object is raised is 0.83 meters.
This is because the force needed to lift the object is 25 N,
and the mass of the object is 30 kg (30 x 9.8 = 294 N).
Therefore, the amount of work done for each meter of lifting is 25 N x 0.83 m = 20.75 Joules (J).
This means that each meter of lifting requires 20.75 J of work, and therefore the shortest possible distance through which the force must be applied must be 0.83 meters.
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2) Which type of bond will form between these elements?
WHICH BOND?
a heuristic device in which a solution to a problem is found by evaluating the difference between the current situation and the goal is the:
A heuristic device in which a solution to a problem is found by evaluating the difference between the current situation and the goal is the mean end analysis.
Heuristics are mental shortcuts that are frequently utilized to streamline issues and prevent cognitive overload. Heuristics, which enable people to arrive at rational conclusions or answers to complex situations rapidly, are a function of how the human brain evolved and is wired.
This designates a notion or idea that is employed more because it facilitates our thinking about the issue than because it is strongly supported by the data. A heuristic tool is Max Weber's ideal type. The three heuristics that attracted the most attention were representativeness, anchoring and adjustment, and availability.
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A magnetic field near the floor points down and is decreasing. Looking down at the floor, which option best describes the direction of the non-Coulomb electric field A. Clockwise B. Counter Clockwise C. Into the page D. Out of the page E. There is no curly electric field
Answer: B: counter clockwise
Explanation: I learned about this in the 9th grade!
7.121 Solve Prob. 7.120, assuming that the magnitude P of the two forces is increased to 120 kN 7.122 A torque of magnitude T 12 kN m is applied to the end of a tank containing compressed air under a pressure to 8 MPa. Knowing that the tank has a 180-mm inner diameter and a 12-mm wall thickness,. Determine the maximum normal stress and the maximum shearing stress in the tank.
Maximum normal stress and the maximum shearing stress in the tank are 60MPa and 18.277 MPa respectively.
Define hoop stress
A "hoop stress" is a stress distribution that maintains its original shape while the stressed item is rotated around a fixed axis. Any force exerted on the cylindrical pipe wall by a pressure differential in a straight, closed pipe will eventually result in hoop stresses.
According to the definition, shearing stress is "a kind of stress that acts parallel to the cross section of the material." Shear forces result in shear stress. They are a pair of forces that have the same magnitude and are directed in the opposite direction and operate on opposite sides of a body. A vector quantity is shear stress.
Given Data
Diameter: d = 180mm
Wall Thickness: t = 12mm
Torque: T = 12kN.m
Pressure in cylinder: p = 8MPa
Inner Radius ,c1 = d/2
c1 = 180/2
c1 = 90*10^-3 m
Outer radius, c2 = c1+ t
c2 = 90+12
c2 = 102*10^-3m
Polar moment of inertia ,J is 3.14/2*(c2^4- c1^4)
J ≈66.968×10^-6 m^4
The maximum torsional shear stress, τ= Tc/J
τ=18.277MPa
The normal stress due to pressure, σ1 = pr/t
σ1 = 60MPa
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the largest temperature change ever recorded in a 24-hour period occurred in loma, montana, on january 15th, 1972. during this time, the temperature rose from -54 to 49, an increase of 103 degrees fahrenheit. find the magnitude of this change in kelvin.
Loma saw greatest 24-hour temperature fluctuation on January 15, 1972. Temperature rose by an equal 103 degrees from -54 degrees to 49 degrees. This sets global standard for a 24-hour changes in temperature.
Why is 273 at the highest point on the Kelvin scale?The distance here between kelvin (K), a component of kelvin scale, and then a degree on the Temperature scale depends on where zero lies. This melting point seems to be the zero point upon that Celsius scale, whereas absolute zero is really the zero point upon that Kelvin scale. Accordingly, 0oK is equal to -273.15oC and 0oC is equivalent to 273.15 kelvins.
Why not swap the kelvin units for Celsius?The freezing point, boiling point, or any combo of water and a chemical were all taken into consideration when the Celsius and Fahrenheit scales were developed. Scientists adopted the Absolute temperature scale because they desired a scale where 0 depicts the total lack of thermal energy.
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what do we see when white light passes through a cool cloud of gas? what do we see when white light passes through a cool cloud of gas? an emission line spectrum infrared light visible light thermal radiation an absorption line spectrum
When white light passes through a cool cloud of gas an absorption line spectrum is observed.
An absorption line spectrum is made up of frequencies of light transmitted with dark bands when electrons absorb energy in the ground state to reach higher energy states.
This type of spectrum is created when atoms absorb energy.No two types of atoms or molecules give the same patterns.
In other words, any particular gas can absorb or emit only certain wavelengths of light that are typical for that gas.
In contrast, absorption spectra are produced when white light passes through a cold, rarefied gas.
Since cloud of gases are cold and hence when white light passes through a cool cloud of gas an absorption line spectrum can be observed.
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A ball i thrown at a peed of 15m/ at an angle of 30 degree to the horizontal. Reolve the movement of the ball into it horizontal and vertical component. Ue the equation of motion to work out the component of the ball' velocity and diplacement every 0. 5 econd
Here we have to calculate horizontal distance and vertical displacement of a ball thrown at a particular angle and a particular speed.
How to calculate horizontal distance and vertical displacement？
The ball is thrown at an angle, θ=30o.
Initial velocity of the ball, u=15 m/s
Horizontal range of the ball, R=12.3 m
We know that, R=u cosθ t,
where t is the time of flight
⟹t=5317.3=2 secs
using equation of motion we get:-
−h=ut−1/2gt²
=15×2−1/2×9.8×2²=−10.4
⟹ Height at which the ball reaches, h=10.4 m
The vertical distance fallen during each consecutive second will increase. (i.e., there is a vertical acceleration).
The vertical displacement follows the equation above (y = 0.5 • g • t2).
Furthermore, since there is no horizontal acceleration, the horizontal distance traveled by the projectile each second is a constant value -
Formula for horizontal distance is
x= vix × t=20 m/s
Thus, the initial horizontal velocity of 20 m/s. Thus, the horizontal displacement is 20 m at 1 second, 40 meters at 2 seconds, 60 meters at 3 seconds, etc. We can tabulate it as shown in the attachment.
TIME HORIZONTAL DISPLACEMENT
0 s 0 m
1 s 30 m
2 s 60 m
3 s 90 m
4 s 120m
5 s 150 m
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