J- shaped tube is a device used to observe the relationship between volume and number of moles at constant pressure and temperature.
This is based on Boyle's law: A gas law known as Boyle's law asserts that a gas's pressure is inversely proportional to its volume when it is held at a fixed temperature and of a given mass.
To put it another way, as long as the temperature and volume of the gas remain constant, the pressure and volume of the gas are inversely proportional to one another. The Anglo-Irish chemist Robert Boyle proposed Boyle's law in the year 1662.
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the fact that the ratio of helium to hydrogen in the universe is so large (25%:75%) is evidence that group of answer choices the age of the universe is roughly 14 billion years the expansion of the universe is accelerating the whole universe was once as hot as the interior of a star nuclear fusion rates in stars were much higher in the past
hydrogen, accounts for 74% of the mass while helium contributes 25%. Heavier elements comprise less than 1% of the total.This universe was 13.7 billion years old, adding or subtracting approximately 130,000 years, as determined by NASA's WMAP probe.
Why do hydrogen and helium make up the majority of the universe's mass?The vast quantities of helium and hydrogen that were created during the Big Bang account for the majority of the chemical elements' abundance in the cosmos.Only 2% of the universe's mass is made up of remaining elements, which were primarily created by supernovae and some red giant stars.
Why is hydrogen most prevalent in the universe but has a low percentage on Earth?As the only element in the cosmos without a neutron, hydrogen is the most basic in the universe, that explains why it is also the most plentiful, according to Nyman. Hydrogen has just one proton one and electron.
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a single loop of wire with an area of 0.0940 m2 is in a uniform magnetic field that has an initial value of 3.80 t, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 t/s . for related problem-solving tips and strategies, you may want to view a video tutor solution of emf and current induced in a loop.
The EMF induced in a single wire loop with an area of 0.0940 m² is in a uniform magnetic field which has an initial value of 3.80 T, is perpendicular to the plane of the loop, and decreases at a constant rate of 0.190 T = 0.34 V. And the current induced in the loop = 0.57 A.
The EMF inducedInduced electromotive force or induced emf is the potential difference at the ends of the coil which will produce an induced electric current.
An induced electric current appears as long as there is a change in magnetic flux.
The equation is:
ε = d∅/dt
We have,
The area of the loop = 0.0940m²
The change in magnetic field with time = (3.80 T - 0.190 T) = 3.61 T
So, the EMF induced:
ε = d∅/dt
= {(0.0940m²) (3.61)} / 1
= 0.34 V
And the current induced in the loop =
I = ε/R
= 0.34 V / 0.600 Ω
= 0.57 A
The question is incomplete, it should be:
A single loop of wire with an area of 0.0900m2 is in a uniform magnetic field that has an initial value of 3.8 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s.
(a) What emf is induced in this loop?
(b) If the loop has a resistance of 0.600O, find the current induced in the loop.
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4.00 mol of the helium is confined to a 4.00-L container at a pressure of 14.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10?27 kg.
Calculate vrms. (Express your answer to three significant figures.)
Since 1 u = 1.661 10 kg, what is the atomic mass of helium, which is 4.00 u, in u? 27 kg equals 1031.46 m/s.
Vrms = [tex]\sqrt{3RT/m}[/tex]
PV = nRT
RT = PV/n
RT = 14 × 101325 × 4 × [tex]10^{-3}[/tex]/4
RT = 1418.55
Vrms = √1418.55 × 3/4 × [tex]10^{-3}[/tex]
Vrms = 1031.46m/s
The atomic mass ma of an isotope is divided by the atomic mass constant mu to produce a dimensionless value, which is the relative isotopic mass (see section below). As a result, while a carbon-12 atom's relative isotopic mass is simply 12, its atomic mass is defined as 12 Da. The total of all the atoms' respective isotopic masses makes up the relative molecular mass.
A unique isotope of an element is indicated by its relative isotopic mass and atomic mass. It is practical to use the elemental atomic mass, which is the average (mean) atomic mass of an element, weighted by the abundance of the isotopes, because most things are not isotopically pure.
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a girl pushes herself up a steep ramp in her wheelchair. She gains a vertical distance of 25.8m when she reaches the top of the ramp. She turns around and coasts back down the ramp. If the combined mass of the girl and her wheelchair is 64.6kg, what would be her coasting speed at the bottom of the ramp?
Answer:
Below
Explanation:
Her POTENTIAL energy , mgh , is converted to KINETIC energy , 1/2 mv^2
mgh = 1/2 mv^2 You can divide through by 'm' to get:
gh = 1/2 v^2 solve for 'v'
v = sqrt (2gh)
= sqrt ( 2 * 9.81 * 25.8) = 22.5 m/s
( NOTE that her mass, 64.6 kg , is irrelevant)
electronic watches keep accurate time using crystal oscillators. inside the watch, there is a tiny block of quartz which vibrates. two opposite faces of the block move alternately toward each other and away from each other. this is a caused by a standing wave in the block. the two opposite faces are at antinodes, and the plane halfway between these two faces is at a node. if the two faces are 7.79 mm apart and the speed of sound in quartz is 3.72 km/s, find the frequency of the vibration.
The frequency of the variation is 324.04 KHz.
Frequency is the wide variety of occurrences of a repeating event in step with unit time. For clarity, additionally called temporal frequency, which isn't like angular frequency. Frequency is measured in hertz (Hz) and corresponds to one occasion in keeping with 2nd. duration is the reciprocal of frequency, because duration is the time c program languageperiod between activities.
Frequency is an critical parameter utilized in technology and engineering to explain the speed of vibrations and vibrational phenomena inclusive of mechanical vibrations, audio indicators (sound), radio waves, and mild.
calculation :
[tex](\frac{lambda}{4} ) + (\frac{lambda}{4}) = 5.74 mm[/tex]
[tex]lambda = 11.48 m = 11.48*10^{-3} m[/tex]
Now,
[tex]f = \frac{v}{lambda} = \frac{3.72*10^{3} }{11.48*10^{-3} }[/tex]
[tex]= 324041.81 Hz[/tex]
[tex]= 324.04 KHz[/tex]
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we can detect a transiting planet by: we can detect a transiting planet by: an increase in the total amount of light received from the planet's star. the light that the planet emits. the doppler effect of the planet's light as it orbits. the amount of light it blocks from its star.
Transit photometry is presently the most effective and sensitive method for detecting extrasolar planets. It is a particular method for space-based observatories that can stare continuously at stars for weeks or months.
Mostly of the exoplanets have been discovered using the transit method. It occurs when a planet passes between a star and its observer.
Transits in our solar system can be observed from Earth when Venus or Mercury travel in between us and the Sun in our solar system.
Transits tell an exoplanet not because we directly see it from many light-years away, but because the planet passing in head of its star ever so slightly dims its light.
This darken can be seen in light curves graphs showing light received over a period of time. When the exoplanet passes in head of the star, the light curve will show a dip in brightness.
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An object is thrown with a horizontal velocity of 20 m/s from a vertical cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is most nearly...
5 seconds
An object is thrown with a horizontal velocity of 20 m/s from a vertical cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is nearly Five (5) seconds.
The horizontal velocity is the speed at which an object is traveling in a straight line. It can vary from object to object and can be affected by a number of factors. One of these factors is air resistance. Air resistance is a force that acts in the opposite direction to the motion of an object. It is a result of the air molecules pushing back against the object as it moves through it. The amount of air resistance acting on an object depends on its shape and size, as well as the speed at which it moves.
This means that as an object's horizontal velocity increases, the amount of air resistance acting on it also increases. This can slow down the object's velocity, or even cause it to come to a stop.
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In an experiment with a simple pendulum, measurements of the period T of the pendulum are made for different values of its length L. When plotted on a graph, which of the following should result in a straight-line fit of the data? A) Root T versus L B) T versus L C) T versus^ L2 D) T^2 versus L E) T^2 versus L^2
DataT2 vs L in a straight-line fit of the data have been plotted in an experiment .
What is pendulum used for?Pendulum: a body that is hung from a fixed location and moves back and forth as a result of gravity. Pendulums are employed to control clock movement because the period—the amount of time between each full oscillation—is constant.
What is pendulum energy?A pendulum is a straightforward illustration of energy transfer since it repeatedly transforms potential energy into kinetic energy until it comes to a halt due to the minimal amount of power lost to heat or air resistance.
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Which of the following is called the windpipe?
a. cilia.
b. veins.
C. arteries.
d. trachea.
the potential difference across the terminals of a battery is 8.20 v when there is a current of 1.55 a in the battery from the negative to the positive terminal. when the current is 3.52 a in the reverse direction, the potential difference becomes 10.40 v.
potential difference across the terminals of a battery is 8.2
V when there is a current of 1.54A in the battery from the negative to the positive terminal. When the current is 3.49A in the reverse direction, the potential difference becomes 9.2V
A-What is the internal resistance of the battery?
B-What is the emf of the battery?
The internal resistance of the battery is 0.1988 ohms and the emf of the battery is 8015 v
Given
V1=8.2 V
I1 =1.54 A
and
V2=9.2 V
I2=-3.49 A (since it is in reverse direction)
a)
since
E= V1+I1r
E=V2+I2r
V1+I1r =V2+I2r
8.2+1.54r =9.2-3.49r
5.03r =1
Resistance r=0.1988 ohms
b)
E=V1+I1r =8.2+1.54*0.1988
E=8.51 V
The effort required to transfer a unit of positive electric charge from one location to another is known as potential difference.
Due to the potential difference between the two ends of the battery, if you connect the two ends of the same wire to the opposite ends of the same battery, electricity will flow through it.
Work is done by the component when electrons travel through it. The component receives a portion of the electrons' energy
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you a generally safe inside an automobile during a lighting storm because: question 7 multiple choice options the car's radio antenna will act as a lightning rod the rubber tires insulate you from the ground metal cars do not become electrically charged the metal car body will carry the lightning current around the passengers inside
You a generally safe inside an automobile during a lighting storm because the metal car body will carry the lightning current around the passengers inside.
Storm, violent atmospheric disturbance, characterised by low barometric pressure, cloud cowl, precipitation, sturdy winds, and probable lightning and thunder.
Current the flow of electrical charge vendors, typically electrons or electron-deficient atoms. The not unusual image for present day is the uppercase letter I. the same old unit is the ampere, symbolized with the aid of A
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Find the total resistance
the answer might be 50 or 80
The total resistance will ne 80. The amount that a resistor adds to the circuit's overall resistance depends on how it is connected.
What is total resistance?When connecting electrical components, there are two options. Parallel circuits connect components along parallel branches, whereas series circuits connect components one after the other.
Ohm's Law, which states that voltage equals current times resistance, if you don't know the specific values of each resistance.
In a series circuit, the current is constant throughout the whole circuit. The supply voltage is the same as the total voltage (the battery). It differs from the voltage across a single component.
Therefore, The total resistance will ne 80. The amount that a resistor adds to the circuit's overall resistance depends on how it is connected.
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Find the phase difference between these two rays at point B, ignoring any phase shift due to reflection.
Express your answer in terms of ?.
Image result for Find the phase difference between these two rays at point B, ignoring any phase shift due to reflection.
Two sound waves of the same frequency that are perfectly aligned have a phase difference of 0 and are said to be “in phase.” Two waves that are in phase add to produce a sound wave with an amplitude equal to the sum of the amplitudes of the two waves. This process is called “constructive interference.
Phase difference = 2πλx path difference.
When the phase difference between the waves is an even multiple of (180°), constructive interference happens, but destructive interference happens when the difference is an odd multiple of.
The location of neighboring medium particles vibrating in phase is known as the wavefront. Because of this, there is no phase difference between any two places on a wavefront.
By operating in the X-Y mode, the CRO can measure the phase difference. The pattern that CRO predicts is a diagonal straight line making 45° with the X-axis at a phase shift of = 0° or 360°. The pattern that CRO predicts at a phase shift of = 90° is a clockwise spinning circle.
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A rectangular-shaped swimming pool has dimensions of 15m by 30m and is 3.5m deep. When the pool is filled with freshwater, the average force on the short side of the pool due to the water is?
Doppler shift or Doppler impact is described because the alternate in frequency of sound wave because of a reflector shifting in the direction of or farfar from an object.
This is which withinside the case of ultrasound is the transducerλ is one wave period, then the quantity of wave lengths N which are found in a two-manner communique direction among the Radar and goal might be same to 2R/λ.
We realize that one wave period λ corresponds to an angular tour of 2π radians.The Doppler shift may be decided after appearing the variety Fourier transform (variety FFT) first. For a goal of interest, we are able to repeat the variety FFT till we've sufficient information to carry out the second one degree of FFT.
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a solar-mass star will evolve off the main sequence when a solar-mass star will evolve off the main sequence when it loses all its neutrinos, so fusion must cease. it builds up a core of inert helium. it completely runs out of hydrogen. it expels a planetary nebula to cool off and release radiation. it explodes as a violent nova.
When a solar-mass star will evolve off the main sequence when it loses all its neutrinos, so fusion must cease it builds up a core of inert helium.
The right order of evolutionary levels for a solar mass big name is: principal sequence, horizontal department, asymptotic branch, white dwarf. The electricity that fuels the sun is generated: best in its core.
Sooner or later, a chief series megastar burns through the hydrogen in its core, attaining the quit of its existence cycle. At this factor, it leaves the main sequence.
Stars smaller than 1 / 4 the mass of the solar collapse directly into white dwarfs. White dwarfs now not burn fusion at their center, however they still radiate warmness.
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A person throws a 2.5 lb stone into the air with an initial upward speed of 15 ft/s. Make a free-body diagram for this stone (a) after it is free from the person's hand and is traveling upward, (b) at its highest point, (c) when it is traveling downward, and (d) while it is being thrown upward, but is still in contact with the person's hand
Answer: In cases a, b, and c, the only force acting on the stone is the force of gravity, mg, straight downward. In case d, the force of gravity also acts straight downward, however, there is an applied force with greater magnitude acting upward.
Note that this explanation assumes that drag (air resistance) is negligible.
a_____n increase in the volume of water produced by thermal expansion creates a corresponding rise in .
Increase in the volume of water produced by thermal expansion creates a corresponding rise in sea level
What is thermal expansion?
Solids, liquids, and gases all exhibit the phenomena known as thermal expansion. This process involves the expansion of an object or body when heat is applied (temperature). Thermal expansion is the tendency of an object to change its dimensions as a result of heat, including length, density, area, or volume. The substance has more kinetic energy when it is heated.
Three forms of thermal expansion exist:
Linear expansionArea expansionVolume expansionAccording to the question:
Sea level rise is brought on by a larger volume of ocean water as a result of thermal expansion. The amount of water in the oceans is also rising as a result of melting ice and snow on land brought on by rising temperatures. Sea level will only rise as a result of land-based ice and snow melting.
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Two balls of clay known masses hang from the ceiling on masslessstrings of equal length. They barely touch when both hang atrest. One ball is pulled back until its string is45o, the released. It swings down, collides withthe second ball, and they stick together. To determine theangle to which the balls wing to the opposite side, you need toinvoke:
A. Conservation of momentum
B. Conservation of mechanicalenergy
C. Both conservation of momentum andconservation of mechanical energy
D. Either, but not both.
E. These principles alone are not sufficientto find the angle
The combination of momentum conservation and mechanical energy conservation yields the letter C.
You need:
1.Conservation of energy to calculate the velocity of the firstball of clay by the time it descends:
mgh=1/2mu2
[calculate h by using h=L(1-cos45)]
2.Conservation of momentum to find out the final velocity of theballs of clay using:
m1u1+m2u2=(m1+m2)v ---note:u2=0
3.Conservation of energy to calculate the max height the balls ofclay will go by using:
1/2(m1+m2)v2=mgh
Once you have h,
h=L(1-cosθ), solve for θ
In Newtonian physics, an object's mass and velocity are combined to form momentum, more precisely linear momentum or translational momentum. It has both a magnitude and a direction, making it a vector quantity. If an item has mass (m) and velocity (v), both of which are vector quantities, then it has momentum (p).
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String is wrapped around a solid wood cylinder and a hollow metal cylinder, both of
which have mass 4.0 kg and radius 0.30 m. Both start from rest at a distance 6.0 m above the ground and unwind the string while rotating without slipping under the influence of gravity. What are the final linear velocities (v) of the two cylinders just before they hit the ground?
The final linear velocity of the solid wood cylinder just before it hits the ground is 8.85 m/s.
The final linear velocity of the hollow metal cylinder just before it hits the ground is 7.7 m/s.
What is the final velocity of the two cylinders?
The final linear velocities of the two cylinders just before they hit the ground is calculated by applying the principle of conservation of energy.
translational kinetic energy + rotational kinetic energy = gravitational potential energy
¹/₂mv² + ¹/₂Iω² = mgh
where;
v is the linear velocityω is the angular velocity = v / rI is the moment of inertiaThe moment of inertia of solid cylinder, I = ¹/₂mr²
¹/₂mv² + ¹/₂Iω² = mgh
¹/₂mv² + ¹/₂(¹/₂mr²)(v/r)² = mgh
¹/₂mv² + ¹/₄(mr²)(v²/r²) = mgh
¹/₂mv² + ¹/₄(mv²) = mgh
¹/₂v² + ¹/₄v² = gh
2v² + v² = 4gh
3v² = 4gh
v² = 4gh/3
v = √ (4gh / 3)
v = √ (4 x 9.8 x 6 / 3)
v = 8.85 m/s
The moment of inertia of hollow cylinder, I = mr²
¹/₂mv² + ¹/₂Iω² = mgh
¹/₂mv² + ¹/₂(mr²)(v/r)² = mgh
¹/₂mv² + ¹/₂(mr²)(v²/r²) = mgh
¹/₂mv² + ¹/₂(mv²) = mgh
¹/₂v² + ¹/₂v² = gh
2v² = 2gh
v² = 2gh / 2
v² = gh
v = √ (gh)
v = √ (9.8 x 6)
v = 7.7 m/s
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A charged particle of mass \displaystyle {m}m is traveling horizontally with speed \displaystyle {v}_{{0}}v 0
when it enters the region between two horizontal, oppositely charged parallel plates. The particle follows the path indicated in the figure, hitting the bottom plate. Which of the following factors determine the time the particle takes to reach the bottom plate? Select two answers.
The horizontal length of the plates
The magnitude of the charge on each plate
The mass of the particle
The initial speed \displaystyle {v}_{{0}}v 0
of the particle
The particle follows the path indicated in the figure, hitting the bottom plate. The mass of the particle and the magnitude of the charge on each plate factors determine the time the particle takes to reach the bottom plate.
What occurs when an electrically charged particle moves?
Magnetic force fields are produced by charged particles in motion. Charged particles that are accelerated create shifting electric and magnetic force fields that travel as EM waves. Polarized electromagnetic radiation (EMR) has all electric and magnetic field variations along the same plane.
A charged particle moves because of what?
Charged particles may move in spiral or elliptical patterns as a result of magnetic fields. Protons are kept on circular courses by particle accelerators using magnetic force. When cosmic rays come into contact with an astronomical object or planet's magnetic field, they will travel in spiral patterns.
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The particle follows the path indicated in the figure, hitting the bottom plate. The mass of the particle and the magnitude of the charge on each plate factors determine the time the particle takes to reach the bottom plate.
What occurs when an electrically charged particle moves?Magnetic force fields are produced by charged particles in motion. Charged particles that are accelerated create shifting electric and magnetic force fields that travel as EM waves. Polarized electromagnetic radiation (EMR) has all electric and magnetic field variations along the same plane.
A charged particle moves because of what?Charged particles may move in spiral or elliptical patterns as a result of magnetic fields. Protons are kept on circular courses by particle accelerators using magnetic force. When cosmic rays come into contact with an astronomical object or planet's magnetic field, they will travel in spiral patterns.
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A truck moving with an initial speed v collides with a car that is one-third as massive as the incident truck and is initially at rest. After the collision, the truck moves off in the same direction as before the collision with a speed v/2. Determine the following.
(a) the final speed of the car in terms of the initial speed v of the truck
The final speed of the car in terms of the initial speed v of the truck is 3v/2.
What is the final speed of the car?
The final speed of the car in terms of the initial speed v of the truck is calculated as follows;
Apply the principle of conservation of linear momentum as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of the truck u₁ is the initial speed of the truckm₂ is the mass of the caru₂ is the initial speed of the carv₁ is the final speed of the truckv₂ is the final speed of the carlet the mass of the truck = m
then, mass of the car = m/3
let the final speed of the truck, v₁ = v/2
The final speed of the car is calculated as follows
m(v) + (m/3)(0) = (m)(v/2) + (m/3)(v₂)
mv = (mv)/2 + (mv₂)/3
6mv = 3mv + 2mv₂
6mv - 3mv = 2mv₂
3mv = 2mv₂
v₂ = 3mv / 2m
v₂ = 3v / 2
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) explain the concept of radiative forcing. (b) (4 points) some parts of the earth system are likely to respond rather slowly to rising greenhouse gases. describe at least two of these, mention roughly what time scales are involved, and explain what makes their response slow. (c) (3 points) explain why low clouds tend to have a net cooling effect on climate. (d) (3 points). depending on the efforts taken to mitigate greenhouse gas emissions, the trajectory of climate change can take very different paths in the future. which of the following is most likely to be true regardless of mitigation efforts in year 2
When the quantity of energy entering and leaving the Earth's atmosphere is not the same, radioactive forcing results.
What is a good illustration of radioactive forcing?A radioactive forcing is an energy imbalance that the climate system is subjected to, either externally or as a result of human activity ( changes in solar energy output, volcanic anthropogenic emissions of greenhouse gases, aerosols, and their precursors; intentional land change.
The significance of radioactive forcing?In other words, if you want to know how to tell if something is good or bad, you need to know how to tell if it's good or bad.
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A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in place a distance dd above the first plate. Assume that dd is much smaller than r. The two plates are attached by wires to a battery that supplies voltage V.1) What is the tension in the cable? Neglect the weight of the plate.Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.F=2) The upper plate is slowly raised to a new height 2d. Determine the work done by the cable by integrating ∫d to 2d F(z)dz, where F(z) is the cable tension when the plates are separated by a distance z.Express your answer in terms of the variables d, r, V, and constants ϵ0,pi.W=3) Compute the energy stored in the electric field before the top plate was raised.Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.U=4) Compute the energy stored in the electric field after the top plate was raised.Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.U=5) is the work done by the cable equal to the change in the stored electrical energy? If not, why not?The work done in separating the plates is equal to energy change in the plates.The work done in separating the plates is equal to the magnitude of the energy change in the plates. This does not mean that the work done is equal to the change in the energy stored in the plates. The work done on the plates is positive but the plates lose energy. The plates are connected to the battery, so the potential difference across them remains constant as they are separated. Therefore charge is forced off of the plates through the battery, which does work on the battery.
An electrical charge and electrical energy are stored in a capacitor. Typically, capacitors have two electrical conductors that are spaced apart.
(Note that although these electrical conductors are frequently called "electrodes," they are actually "capacitor plates.") A capacitor is referred to as a "vacuum capacitor" if the distance between capacitors is merely a vacuum. However, a dielectric, an insulating substance, is typically used to fill the void. (In the sections on dielectrics later in this chapter, you will learn more about dielectrics.) You will learn more about the capacitance property of capacitors a little bit later in this section. Capacitance is what determines how much storage a capacitor can hold.
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the figure(figure 1) shows a particle of mass m at distance x along the axis of a very thin ring of mass m and radius r. calculate the gravitational potential energy of these two masses. use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on m when it is at position x>0 .
The magnitude of the gravitational force on mass m at distance x along the axis of a very thin ring when it is at position x>0 is 4GMm/4x^2-L^2.
Every body in the universe attracts every other body with a gravitational force that decreases with distance as 1/r2. if two bodies of different masses have the same acceleration they must be feeling forces in the same ratio as their masses (so a body twice as massive feels twice the gravitational force), that is, the gravitational force of attraction a body feels must be proportional to its mass.
The gravitational field at any point P in space is defined as the gravitational force felt by a tiny unit mass placed at P.
This relation can be find out by using the formula of gravitational potential = GMm/r and further integrating on small dx length at x from the origin of the rod, we get,
U = GMm/L㏑2x-2/2x+2.
now differentiating with respect to dx, we get
F = 4GMm/4x^2-L^2.
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a. A mass, m2, is initially at rest. A mass, m1, traveling with velocity, v1, collides with m2 in an elastic collision. After the collision, the two objects move with final velocities, v1f and v2f respectively. Using the laws of conservation of energy and momentum, show that the ratio of the final velocities in terms of m1 and m2 is given by: (v2f/v1f) = (2m1/m1 −m2) b. Linearize the expression in Exercise 1 by making the following substitutions: y≡m2/m1 andx≡v1f/v2f If y is plotted as a function of x, what values do you expect for the slope and intercept? c. Based on your result from Exercise2, what ratio of masses, m2/m1,results in final velocities, v1f andv2f that are equal in magnitude and opposite in direction?
The collision energy is used for the proving of the equation and the ratio of masses is 1:3.
By conservation of momentum,
m1v1 + 0 = m1v1f + m2v2f
=) v1 = v1f + (m2/m1)v2f -------------- 1
By conservation of kinetic energy
(1/2)m1v1^2 + 0 = (1/2)m1v1f1^2 + (1/2)m2v2f2^2
m1v1^2 + 0 = m1v1f1^2 + m2v2f2^2 ------------- 2
m1[v1f + (m2/m1)v2f]^2 = m1v1f^2 + m2v2f^2
m1v1f^2 + (m2^2/m1)v2f^2 + 2m2.v1f.v2f = m1v1f^2 + m2v2f^2
(m2^2/m1)v2f^2 + 2m2.v1f.v2f = m2v2f^2
(m2^2/m1)v2f^2 + 2m2.v1f = m2v2f
v2f[1-m2/m1] = 2v1f
v2f/v1f = (2m1/m2 - m2) ----------- 3
Hence proved.
B
v1f/v2f = 1/2 - (1/2)(m2-m1)
Now y = 2 / m1 and = v1f/v2f
x = 1/2 - 1/2y
2x = 1-y
y = 2x + 1 -------------- 4
C
Comparing y = mc + x
slope is m = -2
intercept c = 1
Putting v1f = - v2f means x = -1
from eq 4,
m2/m1 = y = -2 * -1 * +1 = 3
m2/m1 = 3.
Therefore, the collision energy is used for the proving of the equation and the ratio of masses is 1:3.
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Two identical thin rods_ each of mass m and length L_ are joined at right angles to form an L-shaped object; This object is balanced on top of . sharp edge (Figure 1) If the object is displaced slightly; it oscillates: Part A Assume that the magnitude of the acceleration due to gravity iS g- Find W, the angular frequency of oscillation of the object Your answer for the angular frequency may contain the given variables mn and L as well as g- Figure 1 of 1 View Available Hint(s) AZd XOn Submit Previous Answers
The angular frequency of oscillation of the object, ω is calculated to be= √3g / 2√ 2 L.
What is angular frequency of oscillation?Number of oscillations per second of a particle executing simple harmonic motion is called angular frequency.
Given acceleration due to gravity is g,
=mg. L/2 {-2/√2* sinФ
When L- shaped object is slightly displaced by an angle, then
τ0 =mg. L/2 [(sin 45° - Ф) - (sin 45° + Ф)]
= 2 (mL²/3) α
= - (m*g*L Ф)/√3
α = -3g Ф/ 2√ 2 L
ω= √3g / 2√ 2 L
The angular frequency of oscillation of the object, ω= √3g / 2√ 2 L.
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determine the mass flow rate (lbs/hr) of a liquid with a density of 58.30 pound (lbs/ft3) and a volumetric flow rate of 332 gpm. (round the final answer to nearest whole number.)
The mass flow rate of the liquid is found to be 152,135 Lbs/hr.
The volume flow rate is given to be 332 gpm.
It means that 332 gallons per minute is flowing.
The density of the liquid is given to be 58 lbs/ft³.
We have to calculate the mass flow rate in lbs/hr.
The amount of liquid flowing in one hour is = 332×60 gallons per hour.
= 19920 gallons per hour.
1 gallon = 0.134 ft³
Converting,
The amount of liquid flowing in one hour is,
= 19920×0.134 ft³/h
= 2609.52 ft³/h.
Now,
Density = Mass/volume
Putting values,
58.30 = Mass/2609.52
Mass flow rate = 152,135.016 lbs/h.
Rounding off to the nearest Whole number.
So, the mass flow rate of the liquid is 152135 lbs/h.
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An object is thrown horizontally off a cliff with an initial velocity of 5.0 meters per second. The object strikes the ground 3.0 seconds later. (i) What is the vertical speed of the object as it reaches the ground? a) – 29.4 m/s b) zero. c) 15 m/s.
d) 29.4 m/s
(ii) How far from the base of the cliff will the object strike the ground? a) – 44.1 m/s b) zero. c) 15 m/s. d) 29.4 m/s
Answer:
Below
Explanation:
Vertical speed = at = 9.81 m/s * 3 = 29.4 m/s
For 3 seconds it travels 5 m/s horizontally = 15 meters (NOT m/s)
Mitch Trubisky throws a football straight up into the air where it stays for 5.18 seconds
before he catches it. If the height that he releases the ball and catches the ball is the same,
and assuming that point is the origin, what is the maximum height the ball the ball will reach?
The acceleration due to gravity is 9.8m/s/s downward. Answer to two decimal places and do
not include units.
Answer:
32.93 ( m )
Explanation:
The ball travels up for half the time 1/2 * 5.18 = 2.59 s
( the other 2.59 s is coming down time)
When it reaches max height , vf = 0
vf = vo - 9.8 (t)
0 = vo - 9.81(2.59)
so vo = 25.4079 m/s
d = max height = vo t + 1/2 a t^2
= 25.4079 ( 2.59) + 1/2 ( - 9.8) (2.59^2) = ~ 32.93 m (Pretty high!!!)
an inclined ramp is set up on your table. from the top of the ramp, you release a disk, hoop, and solid sphere at the same time. all objects are well manufactured with exactly the same mass. they are completely uniform and roll without slipping. which object reaches the bottom of the ramp first, second and third? select from the following, which are listed in order of first, second, third.
Sphere, disk, hoop due to Torque.
Torque = I α if a man and radius is same α will be more for lesser moment of theta.
Is = 2/5 MR², Iloop = MR², Id = 1/2MR²
The order is
Is < Id< Ih
Sphere, disk, hoop.
rFsin() is the definition of torque. Or, to put it another way, torque is the cross product of the distance vector (the distance between the pivot point and the point at which force is applied) and the force vector, where 'a' is the angle between r and F. The torque is a pseudovector in three dimensions and is determined for point particles by the cross product of the force vector and the position vector (also known as the distance vector). The force applied, the lever arm vector[2] connecting the torque measurement point to the force application point, and the angle between the force and lever arm vectors all play a role in determining how much torque a rigid body can generate.
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