The expression for [tex]v^{2}_t[/tex] is equal to √5 times of [tex]v^{2}_b[/tex] where [tex]v_t[/tex] and [tex]v_b[/tex] are the velocities of ball at top and bottom of the circle respectively.
Consider the centripetal force at any point.
T – mg cosθ = m v² ⁄ r
T = mg cosθ + m v² ⁄ r
From figure, cosθ = (r – h) ⁄ r
Substitute in the equation of T.
T = m g (r – h) ⁄ r + m v² ⁄ r
= m ⁄ r (g (r – h) + v²)
But v² = u² – 2 g h
T = m ⁄ r (g r – g h + u² – 2 g h)
= m ⁄ r (u² – 3 g h + g r)
This is an equation for tension in string.
Now, when ball is at the top of circle
We have,
v = √(u² – 2 g h)
= √(5 g r – 2 g ×(2 r))
= √(5 g r – 4 g r)
= √(g r)
And, when ball is at the bottom of the circle,
T[tex]_H[/tex] > 0
m ⁄ r ×(u² – 5 g r) > 0
u² – 5 g r > 0
u² > 5 g r
u > √(5 g r)
Hence,[tex]v^{2}_t[/tex] is equal to √5 times of [tex]v^{2}_b[/tex]
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Calculate the specific heat of a metal. in J/kg.K, from the following data. A container made of the metal has a mass of 3.6 kg and contains 13.5 kg of water, a 1.8 kg of the metal initially at temperature of 175.0 °C is dropped into the water. the container and the water have a initial temperature of 16.0°C and the final temperature of the entire system is 18.0°C.
The specific heat of a metal is 54.89J/kg.K
What does "specific heat" mean?
Specific heat is the amount of energy needed to raise a substance's temperature by one degree Celsius per gram. Typically, the units of specific heat are calories or joules per gram per degree Celsius.
Given: The bottle weighs 3.6 kg and holds 13.5 kg of water.
The weight of the metal is 1.8 kg, and its initial temperature is 175 C.
From 16 to 18 degrees Celsius, the temperature rises.
The container and water both received the same amount of heat from the metal object.
Qp = Qw +Qc
(mp)cΔT= (mw)(cw)ΔT + (mc)cΔT
where, respectively, p, w, and c stand for a metal object, a liquid, and a container.
c = [(mw)(cw)ΔT] / [(mp)cΔT - (mc)cΔT]
=[ 13.5*4187*(18-16) ] / [1.8*(175-16) - 3.6* (18-16)]
= 54.89J/kg.K
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estimate the sea-level landing ground roll distance for the airplane in problem 6.4 assume the airplane is landing with a weight of 2900 pounds. The maximum lift coefficient with flaps at touchdown is 1.8 . After touchdown, assume zero lift.
At touchdown, the flaps' lift coefficient reaches its maximum of 1.8. Upon touchdown, there is a 279-meter zero lift drag.
Vt = 1.8 Vtotal = 1.8 [tex]\sqrt{2w/PSc}[/tex]
Pg = 1.225 kg/m³
1.8 [tex]\sqrt{2* 105000/1.225*50*3}[/tex] = 61.02
V = 0,7 Vt = 0.7 *61.02 = 42.714
After touch down L = 0,
Drag = 1/2 *1.225 *30 *30 *50*0.05 = 1448
Sl = 1.69 * 105000² / 9.81 * 61.02*50*3[1448 + 0.02*105000]
Sl = 279m
The zero-lift drag coefficient and the lift-induced drag coefficient factor, respectively, are denoted by CD0 and k. Under a particular aircraft aerodynamic configuration, the values of both parameters are taken to be constants. Flight can be accomplished without drag. However, without removing air, it is impossible to completely eliminate drag during flight. Although it is not entirely necessary for flight, an airplane that achieves lift will always experience some form of drag because air is required to produce lift. Increasing the zero-lift drag coefficient Cd0 has the effect of raising (TR)min while lowering the velocity at which it occurs. When the drag-due-to-lift factor K is raised, the result is an increase in (TR)min and an increase in the velocity at.
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In a normal distribution, which of the following statements is true about the area that falls between one standard deviation above and one standard deviation below the mean?
If a person's strength test standard score is 0.0, assuming a normal distribution, that person is stronger than 50% of the population.
Does a normal curve's area beneath it always equal 1?The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. A normal curve's undercut area is always equal to one.
What proportion of scores deviates more than one standard deviation from the mean?Approximately 68 percent of the observations (or 68 percent of the area under the curve) will always fall within two standard deviations (one above and one below) of the mean, regardless of how a normal distribution appears or how large or small the standard deviation is.
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identify the statement that is true about ocean water. group of answer choices it has an average salinity of 1.0%. it contains negative ions (anions) like chloride and sulfate derived from volcanic gases. cold ocean water can hold more salt than warmer water can. its salinity and temperature are mostly the same in surface waters; deeper water tends to be more heterogeneous. flag question: question 7
The ocean water contains different types of ions.
The increase in the salt concentration results in the higher density of the ocean water. This salt concentration in the ocean is the result of different ions present in it.
The water is mostly present in the oceans and in some parts it is in the form of running water in the rivers. The oceans are salty due to the presence of the dissolved ions.
The salty nature of the oceans is also due to the ions carried by the rain water and other form of running water on the surface of the Earth. The amount of salt present in the ocean water in a particular region varies as compared to the other.
This variation in the concentration of the salt in the water leads to the variation in the density of the ocean water because if the concentration of the salt is low, then less amount salt is present in unit volume and therefore it has less density whereas if the concentration of the salt is more, it will lead to the higher density of the ocean water.
Therefore, the correct statement about ocean is that it contains different ions that are responsible for its salinity.
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taipei 101 (a 101-story building in taiwan) is sited in an area that is prone to earthquakes and typhoons, both of which can lead to dangerous oscillations of the building. to reduce the maximum amplitude, the building has a tuned mass damper, a 660,000 kg mass suspended from 42-m-long cables that oscillates at the same natural frequency as the building (figure 1). when the building sways, the pendulum swings, reaching an amplitude of 75 cm in strong winds or tremors. damping the motion of the mass reduces the maximum amplitude of oscillation of the building.
The period of oscillation of the Taipei 101 building is 13 seconds .
In the question ,
it is given that ,
the length of the cables(L) is = 42 m
the mass of the mass damper is = 660000 Kg ,
the amplitude is = 75 cm = 0.75 m
we know that the acceleration due to gravity(g) is = 9.8 .
the formula for the Time Period (T) is
T = 2π√(L/g)
Substituting the values ,
we get ,
T = 2π√(42/9.8)
Simplifying further ,
we get ,
T = 13.00079 seconds
T ≈ 13 seconds .
Therefore , the period of oscillation is = 13 seconds .
The given question is incomplete , the complete question is
Taipei 101 (a 101-story building in Taiwan) is sited in an area that is prone to earthquakes and typhoons, both of which can lead to dangerous oscillations of the building. to reduce the maximum amplitude, the building has a tuned mass damper, a 660,000 kg mass suspended from 42-m-long cables that oscillates at the same natural frequency as the building . when the building sways, the pendulum swings, reaching an amplitude of 75 cm in strong winds or tremors. damping the motion of the mass reduces the maximum amplitude of oscillation of the building .
What is the period of oscillation of the building?
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the generation of heat from the sun drives the hydrologic cycle by providing the energy for the evaporation of water from various water sources on the planet's surface. True or False
It is true that the hydrologic cycle is powered by heat from the sun, which is used to energize the water to evaporate from the planet's surface's many water sources.
The hydrologic cycle: what is it and why is it significant?The water balance is crucial because it determines how water gets to people, plants, and other species. In addition to supplying water for people, animals, and plants, it also transports nutrients, diseases, and sediment to and from aquatic habitats.
Why is the hydrological cycle called that?The hydrologic cycle, another name for the water cycle, describes where and how water is kept on Earth. In the sky, on the surface of the land, and underground, water is kept in reserve. It can be either a liquid or a solid.
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Over the last 600,000 years, the highest pre-industrial concentration of carbon dioxide in the atmosphere was _____.
Over the last 600,000 years, the highest pre-industrial concentration of carbon dioxide in the atmosphere was approximately 300 ppm.
One carbon atom is covalently doubly linked to two oxygen atoms in every carbon dioxide molecule, giving it the chemical formula CO2. At room temperature, it exists. in. the gaseous. state. Carbon dioxide functions as a greenhouse gas in the atmosphere by being transparent to visible light while absorbing infrared radiation. As of May 2022, it was a trace gas in the Earth's atmosphere, rising from pre-industrial levels of 280 ppm to 421 ppm (or around 0.04%) by volume. [9] [10] These elevated carbon dioxide concentrations and climate change are mostly brought about by the burning of fossil fuels. [11] Groundwater, lakes, ice caps, and ocean all contain carbon dioxide because it is soluble in water. Upon dissolving in water, carbon dioxide
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a snowstorm, Anna tracked the amount of snow on the ground. When t regan, there were 3 inches of snow on the ground. Snow fell at a constan h per hour until another 2 inches had fallen. The storm then stopped fo nd then started again at a constant rate of 2 inches per hour for the nex Make a graph showing the inches of snow on the ground over time usin at Anna collected
The graph representation is attached below:
What is a graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
In the common case where x and f(x) are real numbers, these graph pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
The range in the graph is the set of possible output values, which are shown on the y-axis.
Therefore, The graph shows the inches of snow on the ground over time as Anna collected the snow.
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How are natural levees formed? a. Cementing action occurs at the sides of streams as a result of the high velocity of the water
b. Suspended load is deposited when the river covers the floodplain
c. Minerals precipitate at the sides of rivers when the water is at bankfull level
d. Bedload rises up over riverbanks during high floods
Option B; Natural levees formed Suspended load is deposited when the river covers the floodplain.
Usually, earth is used to construct levees. Sediment is forced to the side by the natural flow of a body of water, forming a natural levee. Frequently, a river's banks rise up from the river bed just a little bit . Sediment, silt, and other materials pushed aside by the rushing water are accumulated along the banks to form levees. A natural levee may be the intersection of the flood plain and the channel (a broad, low ridge of built along the side of a channel by debris- laden floodwater). When floodwater that is clogged with debris overflows a channel and goes into a floodplain, a levee is formed.
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Hint : solar panels generate an average (day and night) of about 200 Watt/m2.
1. Estimate the annual USA energy consumption (in joule).
2. What is the average power (in watt) required for the USA over one year?
3. Using the hint provided, estimate the total area (in meter2) needed to provide this power.
4. Estimate the surface area of the USA (in meter2)
According to the given hint, solar panels generate an average about 200 Watt/m2.
1. The annual USA energy consumption is 103,108,904,000,000,000,000J.
2. The average power required for the USA over one year is 3.2 trillion watt.
3. The total area needed to provide this power is 32.6 billion [tex]m^{2}[/tex].
4. The surface area of the USA is 9.834*[tex]10^{12}[/tex] [tex]m^{2}[/tex].
Solar energy originates from the sun. Solar panels (also called "PV panels") are used to convert light from the sun, which consists of energetic particles called "photons", into electricity that can be used to power electrical loads increase.
Solar panels can be used in a variety of applications including remote power systems for cabins, telecommunications equipment, remote sensing and, of course, power generation for residential and commercial photovoltaic systems.
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A coin and a ring roll down an incline starting at the same time. The one to reach the bottom first will be the
A) ring.
B) coin.
C) Both reach the bottom at the same time. coin
Option B;A coin and a ring roll down an incline starting at the same time. The coin will be the one to descend first.
Its rotational inertia will be higher. Because of this, it accelerates more slowly than a coin. First to the bottom, the coin makes it. Any item that can be turned possesses rotational inertia. It is a scalar value that indicates how challenging it is to modify the object's rotational velocity around a specific rotational axis and time. Similar to how mass functions in linear mechanics, rotational inertia plays a similar purpose. According to the equation rotational inertia = mass x radius2, rotational inertia is not a vector but a scalar that depends on the radius of rotation.
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A satellite is in circular orbit about the Earth at an altitude at which air resistance is negligible. Which of the following statements is true?
a. There is only one force acting on the satellite.
b. There are two forces acting on the satellite, and their resultant is zero.
c. There are two forces acting on the satellite, and their resultant is not zero.
d. There are three forces acting on the satellite.
e. None of the preceding statements are correct.
(a is supposed to be the answer, however give me a clear explanation why and brief explanations on why the other options don't work)
At each point in its course, the satellite's velocity would be perpendicular to the circle. The satellite would accelerate in the direction of the circle's centre, or the body around which it is orbiting. Thus, option A is correct.
What satellite is in circular orbit about the Earth at an altitude?Because the satellite orbits the earth, the gravitational pull of the planet on the satellite supplies the necessary centrifugal force. In a circular orbit, the gravitational force is constant, hence the satellite's velocity is also constant.
Therefore, A satellite in a circular orbit around the earth moves at a constant speed and maintains the same height above the planet.
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if all volcanic activity were to stop tomorrow, there would be a reduction in carbon flux into the atmosphere.
if all volcanic activity were to stop tomorrow, there would be a reduction in carbon flux into the atmosphere. is 99%
A carbon flux is the volume of carbon that is transferred across carbon stocks during a certain period of time. 1. To put it simply, it is the transfer of carbon from the land to the seas, the atmosphere, and living things. For instance, the atmosphere receives inflows from decomposition (CO2 emitted by the breakdown of organic matter), forest fires, and the burning of fossil fuels, while the atmosphere also receives outflows from plant growth and ocean absorption. The ocean operates as a net sink of 1.7 GtCyr, which is where the highest natural flow occurs between the atmosphere and the ocean. A significantly smaller net sink exists in the terrestrial ecosystem.
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Earth became internally differentiated, with a metallic core distinct from the rocky mantle, during the...
A) Archean Eon
B) Haedan Eon
C) Proterozoic Eon
D) Paleozoic Eon
Earth became internally differentiated, with a metallic core distinct from the rocky mantle, during the Hadean Eon.
About Hadean EonHadean is the name of the oldest geological era (Eon) which ranges from 4.0 to 4.6 billion years ago. The Hadean Age itself is an unofficial unit on the chronostratigraphic chart which has been accepted by the International Stratigraphic Commission (ICS), and ratified by the International Association of Geological Researchers (IUGS).
The name Hadean is taken from the Greek word meaning God of Hell, to describe the condition of the earth which is full of glowing rocks due to the cosmic impact during the big bang. At the beginning of this era the atmosphere had not yet formed, so it is thought that there was no life.
The Hadeans are characterized by the early formation of Earth from accretion of dust and gas. Throughout the Earth, impacts from space objects released large amounts of heat that probably prevented most rock from solidifying on the surface.
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You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 78.2 kg hop on board for a ride through the woods and the springs (one for each wheel) each compress by 6.37 cm. When you pull the trailer over a tree root in the trail, it oscillates with a period of 1.29 s. Determine the following.
(a) force constant of the springs
N/m
(b) mass of the trailer
kg
(c) frequency of the oscillation
Hz
(d) time it takes for the trailer to bounce up and down 10 times
s
a) let k be combined spring constant...
F = kx
k = F/x = 78.2*9.81/0.0637 = 12043.045 N/m
so,
spring constant for each spring = 1/2*12043.045 = 6021.52 N/m
b) w=2*pi/T = 2*pi/1.29 = 4.87 rad/s
so,
w=sqrt(k/m)
m = k/w^2 = 12043.045/4.87^2 = 507.78 kg
so, mass of trailer = m-mass of children = 507.78-78.2 = 429.58 kg
c) frequency of the oscillation = 1/T = 1/1.29 = 0.775 Hz
d) time it takes for the trailer to bounce up and down 10 times = 10*T = 10*1.29 = 12.9 s
Oscillation is defined as the process of repeating fluctuations of a quantity or measure around its time equilibrium value. Oscillation can also be defined as the periodic variation of matter between two values or about their average.
The term vibration describes the mechanical vibration of an object. However, vibrations also occur in dynamic systems. More precisely, it occurs in all areas of science. Even our heartbeats produce vibrations. Objects that move around the equilibrium point are called oscillators.
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A wooden block floats in water, and a solid steel object is attached to the bottom of the block by a string as in the figure below. If the block remains floating, which of the following statements is valid? (Choose all correct statements.)The tension in the string is less than the weight of the steel object.The buoyant force on the block is equal to the weight of the volume of water it displaces.The buoyant force on the steel object is equal to its weight.The buoyant force on the block is equal to its weight.The tension in the string is equal to the weight of the steel object.
Thus, the statement 'the buoyant force on the block exerted by the water is equal to the weight of the volume of water displaced by the block' is correct.
In the figure, (FB)block is buoyant force on block, (FB)steel is buoyant force on steel object, Wsteel is weight of the steel object, Wblock is weight of the steel block, and 7 is tension in the string. is
Weight of an object acts always in downwards.
Buoyant force on an object which is placed in a fluid is always upward direction. When the buoyant force is equal to the weight of the object, then the object floats in the fluid.
From the Archimedes principle, the buoyant force exerted by a fluid on an object which is placed in it is equal to the weight of the fluid displaced by the object.
Thus, the statement 'the buoyant force on the block exerted by the water is equal to the weight of the volume of water displaced by the block' is correct.
When the block is floating, the buoyance force supported by the water is equal to the total weight of the block and steel object. Thus, the statement the buoyant force on the block is equal to its weight is not correct.
As the steel object is at rest in the water, then the net force acting on it is zero.
(F ret )steel =0
T+(F B ) steel -W steel =0 W steel =T+(F B ) steel
Therefore,
T<W steel
Thus, the statement tension in the string is less than weight of the steel object is correct.
If the weight of the steel object is equal to the buoyant force, then the tension in the string should be zero. But the steel object is hanging with the string, so tension never is zero.
Thus, the statement 'the buoyant force on the steel object is equal to its weight' is not correct.
If the tension in the string is equal to the weight of the steel object, then the buoyant force on the steel object should be zero. But any object in a fluid should experiences the buoyant force.
Thus, the statement 'the tension in the string is equal to the weight of the steel object' is not correct.
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From within a rotat- ing frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.
Rotation produces centrifugal force, which is not a component of an interaction. As a result, it is referred to as a fictional force.
What creates gravity?All objects with mass, like our Earth, really bend and curve spacetime, which is what causes gravity to pull you toward the ground. You experience gravity because of that curvature.
What kind of force is gravity?An object with mass attracts another item with mass. The strength of the force is directly proportional here to masses of the two objects and divided by the square of the radius between the two.
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9. An Atwood's Machine consists of a cord passing over a frictionless, massless pulley as shown below. It has a 4.0-kg object tied to one end and a 12.0 kg object tied to the other. Compute the acceleration and the tension in the cord. (4.9m/s/s, 58.8N)
The answer to the question is that the acceleration equals 4.9 m/s² and the cord tension is 58.8 N.
What is the physics of tension?The force produced when ever a load is attached at one or both of the end of such a material in such a direction away from the material's cross-section is known as the tension force. It's frequently referred to a tension force as a "pushing" force.
Briefing:(a) Let's use Newton's Second Law for Movement to our example:
[tex]$$\begin{gathered}T-m_1 g=m_1 a, \\T-m_2 g=-m_2 a .\end{gathered}$$[/tex]
Eliminating [tex]$T$[/tex], we get:
[tex]$$\begin{gathered}\left(m_2-m_1\right) g=\left(m_1+m_2\right) a, \\a=\frac{\left(m_2-m_1\right) g}{m_1+m_2}, \\a=\frac{(12 \mathrm{~kg}-4 \mathrm{~kg}) \cdot 9.8 \frac{\mathrm{m}}{\mathrm{s}^2}}{4 \mathrm{~kg}+12 \mathrm{~kg}}=4.9 \frac{\mathrm{m}}{\mathrm{s}^2} .\end{gathered}$$[/tex]
(b) By adding "a" to the first equation, we can get the cord's tension:
[tex]$$T=m_1(a+g)=4 \mathrm{~kg} \cdot\left(4.9 \frac{\mathrm{m}}{\mathrm{s}^2}+9.8 \frac{\mathrm{m}}{\mathrm{s}^2}\right)=58.8 \mathrm{~N}$$[/tex]
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A rock is suspended by a light string. When the rock is in air, the tension in the string is 55.9 N. When the rock is totally immersed in water, the tension is 37.6 N. When the rock is totally immersed in an unknown liquid, the tension is 20.4 N. What is the Density of the unknown liquid. -When I looked at this problem, I though we needed to know the volume of the rock. Can someone show me how to do it without the volume of this rock?
Volume of water is 17.2N,
The rock displace volume of water whose weight is 37.6 - 20.4 = 17.2N
The mass of this water is 17.2/9.80 =1.755 kg and its volume equal to the rock volume is 1.755/1000 = 1.755 × [tex]10^{-3}[/tex]
The form of the container where the water is contained affects the amount of water inside. You must know the vessel's length, width, and depth in order to calculate the volume of a square or rectangular vessel. The volume equation is V=L W D, where L stands for length, W for width, and D for depth. The formula for the rectangular tank's filled volume is provided as V(fill) = l b f, where "l" denotes the tank's length, "b" denotes its width, "f" denotes its level of water fill, and "V(fill)" is the filled volume of the tank.
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if the raidus of the track is increased the centipital forcenecessery to keep the object revolving at the same speed
If the radius of the track is increased, the centripetal force necessary to keep the object revolving at the same speed decreases.
We know the formula for centripetal force as,
F = mv²/r
where, F is centripetal force
v is tangential velocity
r is radius
m is mass
From the above relation, it is clear that centripetal force is inversely proportional to radius. If radius increases, force should decrease and if radius decreases force should increase, in order to keep the object revolving at the same speed.
Suppose, the radius increases two times, then the force will be halved. This can be calculated by substituting 2r in place of r in the above formula.
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1. Determine the moment of inertia (tensor) of a flat square of mass M, and side length A with respect to its center of mass.
The moment of inertia of the square also known as the MOI of the square is (1/6) MA².
Moment of inertia of the square formula = I = (1/6) MA²
In this mathematical equation, "A" refers to the sides of the square. However, this equation applies to the solid of a square where its center of gravity is along the x-axis.
To determine the moment of inertia of a square plate, we need to consider several things.
First, we will assume that the plate has mass (M) and sides of length (L). Surface area A = L X L = L²
We now define mass per unit area as;
Surface density, ρ = M / A = M / L²
Use of integration;
I = ∫ dI = ∫ (dIcom + dIparallel axis)
I = x=-L/2∫x=L/2 (1/12) ρ L³dx + ρ Lx2dx
I = ρ (L³ / 12) [x |-L/2L/2 + ρ L [ ⅓ x3 |-L/2L/2
I = ρ (L³ / 12) [ L / 2 – (-L / 2)] + ρ L [(⅓ L³ / 8) – (- ⅓ L³ / 8)]
I = ρ (L³ / 12) (L) + ρ L (⅔ L³ / 8)
I = (ρ / 12) L⁴ + (ρ / 12) L⁴
I = (1 / 6) ρ L⁴
I = (1/6) (M/L2) L⁴
I = (1/6) M L²
Moment of inertia of the square is (1/6) M L².
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coherent light from a sodium-vapor lamp is passed through a filter that blocks everything except for light of a single wavelength. it then falls on two slits separated by 0.470 mm . in the resulting interference pattern on a screen 2.24 m away, adjacent bright fringes are separated by 2.86 mm .What is the wavelength of the light that falls on the slits?
Im lost I don't know where to start.
The light that hits the slits has a wavelength of [tex]5.692 *10^{-4} m[/tex]
Fringe separation = 2.90 mm = 0.0029 m
Slit separation = 0.420 mm = 0.00042 m
Screen distance from slits =2.14 mm = 0.00214 mm
Wavelength is given by the following relation;
Wavelength = Fringe Separation * Slit Separation / Distance from the slit to Screen
Thus,
Putting all the given values in the above formula,
We evaluate the wavelength in the following way, we get
Wavelength = [tex]\frac{0.0029 *0.00042}{0.00241}[/tex] = [tex]5.692 *10^{-4}[/tex] m
The light's wavelength when it hits the slits is [tex]5.692 *10^{-4}[/tex] m
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TRUE/FALSE. for a power system modeled by its positive squence network both bus addmittance matrix and bus impedance matrix are symmetric
Yes, it is true that for a power system modeled by its positive sequence network both the bus admittance matrix and bus impedance matrix are symmetric.
Admittance: In a power system, Bus Admittance Matrix represents the nodal admittances of the various buses. With the help of the transmission line, each bus is connected to another other bus.
It is used to analyze the data that is needed in the load or a power flow study of the buses. It justifies the admittance and the topology of the network.
The primitive network matrices are the most basic and depend purely on the impedance or admittance of the individual elements. However, they do not contain any information about the behavior of the interconnected network variables.
So, it is necessary to transform the primitive matrices into more meaningful matrices which can relate to variables of the interconnected network.
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A neutron of mass 1.7 × 10-27 kg, travelling at
2.2 km/s, hits a stationary helium nucleus of mass
6.6 x 10-27 kg. After the collision, the velocity
of the helium nucleus is 0.53 km/s at 52° to the
original direction of motion of the neutron.
Determine the final velocity of the neutron
Answer: The final velocity of the neutron is 1.31 km/s.
Explanation:
To determine the final velocity of the neutron, we need to use the law of conservation of momentum. According to this law, the total momentum of a closed system (in this case, the neutron and the helium nucleus) is conserved. In other words, the total momentum before the collision must be equal to the total momentum after the collision.
We can use the following formula to calculate the momentum of an object:
p = mv
where p is the momentum, m is the mass of the object, and v is the velocity of the object.
The initial momentum of the neutron is:
p = 1.7 × 10-27 kg * 2.2 km/s = 3.74 × 10-26 kg*km/s
The initial momentum of the helium nucleus is zero, since it was stationary before the collision.
The final momentum of the helium nucleus is:
p = 6.6 x 10-27 kg * 0.53 km/s = 3.518 × 10-26 kg*km/s
Since the total momentum is conserved, the final momentum of the neutron must be equal to the initial momentum of the neutron minus the final momentum of the helium nucleus:
3.74 × 10-26 kgkm/s - 3.518 × 10-26 kgkm/s = p
p = 0.222 × 10-26 kg*km/s
To find the final velocity of the neutron, we can divide the momentum by the mass:
v = p / m
v = (0.222 × 10-26 kg*km/s) / (1.7 × 10-27 kg)
v = 1.31 km/s
So the final velocity of the neutron is 1.31 km/s.
an air-track glider attached to a spring oscillates between the 3.00 cmcm mark and the 59.0 cmcm mark on the track. the glider completes 10.0 oscillations in 37.0 ss . you may want to review
The time period and frequency of the glider are found to be 3.7 second and 0.27 Hz respectively.
The air glider is oscillating between the 3.00 cm marl and 59.0 cm mark.
It is given that the air glider completes 10 oscillations in 37.0 seconds.
So, in order to find the time period of the oscillation, we can write,
Time taken by glider to complete 10 oscillations = 37 seconds.
Time taken by glider to complete 1 oscillation = 37/10 seconds.
Time taken by glider to complete 1 oscillation = 3.7 seconds.
So, the time period of oscillation of the glider is 3.7 seconds.
Now, the frequency of the air glider will be,
f = 1/T
Where,
T is the time period,
So, putting values,
f = 1/3.7 Hertz
f = 0.27 Hz.
So, the frequency of the air glider is 0.27 Hz.
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Complete question - an air-track glider attached to a spring oscillates between the 3.00 cm mark and the 59.0 cm mark on the track. the glider completes 10.0 oscillations in 37.0 s. Find the a. Time period b. Frequency.
8.8 moles of an ideal monatomic gas expand adiabatically, performing 9000 jj of work in the process.
Part A
What is the change in temperature of the gas during this expansion?
Express your answer to two significant figures and include the appropriate units.
82 K is the change in temperature of the gas during this expansion.
What is ideal mono atomic gas?Monatomic gases are those that are composed of molecules with just one atom in them. Monatomic gases include gases like helium or sodium vapor. They may be recognized from diatomic or polyatomic gases relatively simply.
A single atom makes up a monoatomic gas. Examples include the gases helium and neon. Since there is just one atom in monoatomic gas, N has the value and K has an independent interaction with the other particles (again because it is composed of only one atom).
Given that,
no. of moles (n) = 8.8 moles
work (W) = 9000 J
For adiabatic process, Q = 0
=> ΔU = - W
For ideal mono-atomic gas, ΔU = 3nRΔT/2
So, ΔT = -2W/3nR
or, ΔT = - (2 × 9000) / (3 × 8.8 × 8.314)
or, ΔT = - 82 K
So, 82 K is the change in temperature of the gas during this expansion.
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when a loop repeats until a variable has a specific value, that value is referred to as the value.
When a loop repeats until a variable has a specific value, that value is often referred to as the "terminating condition" or the "loop condition."
It is the value that determines when the loop will stop executing and control will be passed to the next line of code. In programming languages, loops are used to execute a block of code repeatedly until a certain condition is met. There are different types of loops, such as for loops, while loops, and do-while loops, that can be used to accomplish this.
In a for loop, the loop condition is typically specified as part of the loop header, along with the initialization and increment/decrement of the loop variable. For example:
for (int i = 0; i < 10; i++) {
// code to be executed
}
In this example, the loop will repeat until the value of the variable "i" is equal to 10. At that point, the loop will terminate and control will be passed to the next line of code.
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reflection around a point is equivalent to reflection in a plane with simultaneous rotation about an axis perpendicular to that plane. t/f
The statement saying that reflection around a point is equivalent to reflection in a plane with simultaneous rotation about Axis perpendicular to the plane is true.
Light follows the law of reflection, that says that the light coming at a particular angle of incidence will reflect by a surface by the same angle, the angle that is made by the light after reflection is called the angle of reflection.
When light falls on a surface we generally defined the angle of reflection and the angle of incidence with respect to a normal that he made to the plane.
On one particular point the incident ray the reflected ray and the normal coincides.
Around a point is equivalent to reflection in a plane with simultaneous rotation about an axis perpendicular to the plane.
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for floating objects, the buoyant force equals the weight of the objects. since each object has the same weight, they must have the same buoyant force to counteract that weight and make them float
Yes, for floating objects, the buoyant force equals the weight of the objects. since each object has the same weight, they must have the same buoyant force to counteract that weight and make them float.
What occurs to an item when its weight and buoyant force are the same?The object can stay suspended at its current depth if the buoyant force is equal to its weight. Regardless of whether an item floating, descends, or is immersed in a liquid, the buoyant force is constantly at work. Any item in any fluid will experience an upward push called the buoyant force.
What connection exists between an object's weight and the buoyant force acting on it?The total upward force acting on any item in any fluid is known as buoyant force. The object will ascend to the surface as well as float if the buoyant force is higher than its weight. The object will sink if the buoyant force is lower than its weight.
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A 3.45-g bullet embeds itself in a 1.37-kg block, which is attached to a spring of force constant 785 N/m. Part A: If the maximum compression of the spring is 5.88 cm, find the initial speed of the bullet. Part B: Find the time for the bullet-block system to come to rest.
Refer to the photo attached. Let me know if it works out for you :)
Answer: 787 m/s & 0.0589s