4.5 * 10⁷ J energy, in joules, is needed to make it oscillate with an amplitude of 0.095 m.
What is it Electrical amplitude?The highest payout of a current or voltage is its amplitude. Either of the diffraction signals of the sine wave can be used to symbolize it. The peak voltage is another name for this voltage level, which might be positive or negative. Positive and negative only describe the flow of current in one direction.
Briefing:From the periodic motion we know that the energy of the system :
E = 1/2 kA²
E is the system's energy reserve.
The spring's amplitude is denoted by A.
The spring constant is k.
A = 0.95 m
k = 1.1 × 10⁸
Putting in known data to obtain
E = 1/2 k A²
E = 1/ 2 * 100 * 10⁸ * 0.95²
E = 4.5 * 10⁷ J
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Self-perception only shapes physical appearance.
OA. True
OB. False
Answer:
TRUE
Explanation:
What would be the final speed of a 40g car released from an initial height of 25cm?
What would be the final speed of a 600g car released from an initial height of 115cm?
Answer:
Below
Explanation:
Potential Energy of the cars is turned into Kinetic Energy (ignoring friction)
mgh = 1/2 mv^2 divide both sides by 'm'
gh = 1/2 v^2 solve for v
v = sqrt (2gh) Note that the mass of the cars is irrelevent
For the first car : 25 cm = .25 m
v = sqrt (2 * 9.81* .25) = 2.2 m/s
Similarly , for car 2 v = 4.8 m/s (115 cm = 1.15 m)
select all options that can correctly complete the following statement. if the temperature of a gas in a sealed container increases, we can determine... (note: it is possible for the volume of the gas to change.) the sign of the work done on the gas (e.g., positive, negative, or zero). the sign of the change in thermal energy of the gas (e.g., positive, negative, or zero). the sign of the heat exchange with the gas (e.g., positive, negative, or zero).
The sign of heat exchange is positive.
Work Done on the gas is zero.
The sign of change in thermal energy is also positive.
Since the chamber container is closed, So, Volume of the container is fixed.
dV = 0
Since Work Done by the system is dW = PdV = 0
Work Done by the gas and Work done by the gas is zero.
We use First Law of Thermodynamics, we have :
dQ = dU +dW
dQ = dU + PdV
dQ = dU = [tex]C_{v} dT[/tex]
Also thermal energy ∝ T
In the given situation, The temperature is rising, dT > 0
So, we can conclude that dQ > 0, dU > 0 and [tex]dE_{thermal} > 0[/tex]
The sign of heat exchange is positive.
Work Done on the gas is zero.
The sign of change in thermal energy is also positive.
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what fraction of the mass needed to halt expansion is known to exist in the form of visible mass in the universe?
The fraction of the mass needed to halt expansion is known to exist in the form of visible mass in the universe is 1 percent
What is meant by visible mass in the universe ?
Baryons, a general term for subatomic particles including protons, neutrons, and electrons, make up visible matter, also known as baryonic matter. What dark matter is constituted of is a topic of conjecture among scientists.
A mysterious, invisible substance called dark matter (25%) and a force that defies gravity called dark energy appear to make up the rest of the universe.
It is estimated that dark energy is responsible for 73% of the universe's total mass and energy. Dark matter makes up another 23% of the universe, leaving only 4% of it to be made up of ordinary matter like stars, planets, and people.
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certain stars, like betelgeuse, have a lower surface temperature than the sun and yet are more luminous. how do these stars produce so much more energy than the sun?
Some stars, like Betelgeuse, are more bright and produce a lot more energy than the Sun despite having a lower surface temperature. This is as a result of their expansion into massive stars. Because of their considerably larger size (each portion of the star's surface is cool, but there are so many bits that, collectively, the stars send out more energy), they generate more total energy.
The mass of a star is always drawn toward its core by gravity. There is a mechanism that can prevent a star from collapsing due to gravity, and there is a "balance" between them at different times in a star's life.
When a star is in equilibrium, the gamma rays produced by fusion in the center of the star fight against the inward gravitational collapse. In general, balances are reached when a "fuel" (element) hot enough to fuse is present in the core, as is the case during the main-sequence stage when hydrogen fusion takes place and during helium core fusion following the helium flash
Astronomers who desire to study the evolution of stars can benefit greatly from stellar clusters. It is plausible to believe that each star in a cluster emerged from the same cloud of gas and dust at roughly the same time. The only first distinction between the stars is hence their mass (and not their composition or the time that they began). Additionally, by monitoring where a cluster of stars' stars are now departing the main sequence, we can infer the age of the cluster because high-mass stars evolve considerably more swiftly than low-mass stars do.
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In comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?.
Yes. If the smaller force is farther from the fulcrum than the larger mass.
What is rigid body?A body that does not deform or alter shape is idealized as a hard body. Formally, it is described as a group of particles with the feature that their distance from one another does not change as the body moves.
What is torque?When an engine exerts itself, torque, which is a twisting force, speaks to the rotational force of the engine and quantifies how much of that twisting force is accessible. Everyday activities like turning a doorknob, opening a drink bottle, using a wrench, or peddling a bicycle all involve torque.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
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at what temperature is the reading on a fahrenheit scale twice the reading on a celsius scale? express your answers, separated by a comma, to three significant figures.
The reading on the Fahrenheit scale is twice the temperature on the Celsius scale at 160 degrees Celsius.
Relationship between Fahrenheit scale and Celsius scale
F=9C/5+32
Applying the given condition
2C=F (given)
Replace F in the first formula with 2C from the second,
Then 2C = 9C/5+32
Subtract 9/5C from both sides,
2C-9C/5=32
1C/5=32
C= 160 degrees
Therefore 160 degrees Celsius scale is twice as long as the Fahrenheit scale
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if the distance between two charges is doubled, what will happen to the force between the charges? (4 points)
The force between them is reduced to 1/4 when the distance between the two charges is doubled. The force between them is inversely proportional to the distance.
What is coulomb's law?
Charged bodies experience a force of attraction or repulsion on approach.
From Coulomb's Law, it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.
From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:
[tex]F=k\frac{Qq}{d^{2}}[/tex]
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).
Q and q are the values of the two-point charges. They are measured in Coulombs (C).
d is the value of the distance that separates them. It is measured in meters (m).
K is a constant of proportionality called Coulomb's law constant. It depends on the medium in which the charges are located.
Thus, force is reduced to 1/4.
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during an isothermal compression of an ideal gas, 200 j of heat must be removed from the gas to maintain constant temperature. how much work is done by the gas during the process?
The overall work done for isothermal compression is 200 Joules.
Theory :
Thermal and ISO stand for temperature and constant, respectively. The processes in which the temperature is constant are known as isothermal processes. When a system's volume is reduced or its pressure is raised, this is referred to as compression. The compression process known as isothermal compression occurs at a constant temperature. A closed system is where the thermodynamic process takes place. Thermal equilibrium is maintained by the process.Integration of dW, where dW is the displacement work or PdV, constitutes the work produced by an isothermal process.Boyle's law, which applies to an ideal gas in this process, governs the behavior of the gas and the work it does.The system's molar heat capacity in this process is infinite because there is no temperature difference.Mathematics & Calculations:
[tex]dQ=dU + w\\\\\\dq=heat \\dU=energy\\\\dU=nCdT=0 \\\\dQ=w\\\\dQ =200J\\\\Work=w=200J[/tex]
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unpolarized sunlight with intensity 1000 w m2 is incident on two polarizers, whose transmission axes make an angle of 30◦ . calculate the intensity of the transmitted light from the second polarizer. select one of
The intensity of the transmitted light from the second polarizer is 375 W/m².
Let the two polarized sunlight be P₁ and P₂
Given,
Angle between P₁ and P₂ = 30⁰
Intensity of the unpolarized sunlight = 1000 W/m²
Now,
Angle between P₁ and P₂ = 90⁰ - 30⁰ = 60⁰
The intensity of light transmitted by P₁ is
I₁ = I₀/2 = 1000/2 = 500 W/m²
According to Malus law the intensity of light transmitted by P₂ is
I₂ = I₁ cos²30⁰ = 500[(√3)/2]² = 375 W/m²
Therefore, The intensity of the transmitted light from the second polarizer is 375 W/m².
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a ceiling fan at rest is turned on and reaches a speed of 12.5 rad/sec in 2.4 sec. how many revolutions does it rotate during this time?
5.20rad/sec revolutions does it rotate during this time.
What is average velocity?Average velocity is a sign of a vector. Average velocity is defined as the difference between a change in position or displacement (x) and the intervals of time (t) during which it occurs. The average velocity may be positive or negative depending on how the displacement is dispersed.
According to the equation v = s/t, velocity (v) is a vector quantity that measures displacement (or change in position, s), over change in time (t).
velocity = number of revolutions / time
12.5 rad/sec = number of revolutions/time
number of revolutions = 12.5/ 2.4
number of revolutions = 5.20rad/sec.
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An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz.
Find:
(a) the period
(b) the angular frequency
(c) the mass of this object.
An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz: =0.0845 kg.
(a) Time period, T = 1/f = 1/6.0 = 0.167 s
(b) Angular frequency, ω = 2πf = 6.28x6 =37.7 rad/s
(c) For the mass, use the formula. ω2 =k/m
So, mass, m =k/ ω2
= 120/37.68x37.68
=0.0845 kg.
In physics, a force is a power that may change the movement of an object. A force can purpose an object with mass to trade its velocity, i.e., to accelerate. pressure can also be defined intuitively as a push or a pull. A force has both significance and path, making it a vector amount.
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If the sun mysteriously gets twice as massive as it is right now, what effect will it have on its pull on mars?.
Answer:
well, it would start burning it slowly. but it wouldn't just melt it immediately. then, if it got any bigger it would definitely melt it
Explanation:
the heating coil of a water heater has a resistance of 20 ohms and operates at 210 v. how long does it take to raise the temperature of 200 kg of water from 15oc to 80oc? ( cwater
The heating coil of a water heater has a resistance of 20 ω and operates at 210 v. It takes 5 hrs to raise the it take to raise the temperature of 200 kg of water from 15oc to 80oc.
What is resistance?
Obstruction is a proportion of the resistance to flow stream in an electrical circuit. Opposition is estimated in ohms, represented by the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who concentrated on the connection between voltage, current and opposition. In any case, obstruction and conductance are broad as opposed to mass properties, implying that they additionally rely upon the size and state of an item. Channels permit the free progression of power. Yet, in materials, for example, semiconductors and covers, the power encounters a specific power that goes against the free progression of electrons.
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Who has a greater weight to mass ratio, a person weighing 400 n or a person weighing 600 n?.
A greater weight to mass ratio, a person weighing 400 N or a person weighing 600 N is never possible .
What is gravity?
The force of attraction felt by a person which is directed at the center of a planet or Earth is called as the gravity.
The force of attraction is directly proportional to the product of masses of the object and inversely proportional to the square of distance between them.
Weight = Mass x Acceleration due to gravity (g)
W₁/m₁ =g = W₂/m₂
400 N/m₁ = 600N/m₂ = 9.81 m/s²
So, weight to mass ratio for a person weighing 400 N and person weighing 600 N will be same.
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In a study conducted by a University of Illinois researcher, the football team at Unity High School in Tolono, IL was equipped for an entire season with helmets containing accelerometers. Information about every impact in practice and in games was sent to a computer present on the sidelines. The study found that the average force on a top of the head impact was 1770 N. If the initial velocity of the head was 2.09 m/s and the collision brings the head to a stop, and assuming the head has a mass of 4.12 kg, determine the duration of the impact.
(Note: we are treating the head as a free body which is a bit of an approximation).
The duration of the impact, given that the head has a mass of 4.12 Kg is 0.005 s
How do I determine the duration (i.e time)?We'll begin by obtaing the impulse. This can be obtained as follow:
Initial velocity = 2.09 m/sMass (m) = 4.12 KgFinal velocity = 0 m/sImpulse =?Impulse = m(v + u)
Impulse = 4.12 × (0 + 2.09)
Impulse = 4.12 × 2.09
Impulse = 8.61 Ns
Finally, we can obtain the duration of the impact. This can be obtained as follow:
Force (F) = 1770 NImpulse = 8.61 NsDuration (t) =?Impulse = force × time
8.61 = 1770 × t
Divide both sides by 1770
t = 8.61 / 1770
t = 0.005 s
Thus, we can conclude that the duration is 0.005 s
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a child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25°. what is the maximum speed of the child as she swings?
A child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25° the maximum speed of the child as she swings is approximately 0.829 m/s.
To find the maximum speed of the child as she swings, we can use the formula for the velocity of an object in simple harmonic motion:
v = Aωcos(ωt)
where A is the amplitude of the motion, ω is the angular frequency (ω = 2π/T, where T is the period of the motion), and t is the time.
Given:
- T = 3.3 s (period of the motion)
- A = 25° (amplitude of the motion)
To use the formula, we need to convert the amplitude from degrees to radians:
- A = 25° * (π/180)
= 0.4363 radians
Now we can calculate the angular frequency:
- ω = 2π/T
= 2π/3.3
= 1.90 rad/s
At the maximum displacement (when the child is at the bottom of the swing), the velocity is at its maximum.
At this point, cos(ωt) = 1, so we can simplify the formula to:
v = Aω
Substituting the values, we get:
- v = 0.4363 radians * 1.90 rad/s = 0.829 m/s
Thus, the maximum speed of the child as she swings is approximately 0.829 m/s.
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(1) the electrons in a certain material have a full band of possible energies separated from a completely empty energy and by energy gap of 2.8 ev. this material is a
When the electrons in a certain material have a full band of possible energies, the material is a semiconductor.
What is a semiconductor?A semiconductor is a material with specific electrical properties that allow it to be used as the foundation for computers and other electronic devices. It is typically a solid chemical element or compound that conducts electricity only under certain conditions.
If the valence band is completely full and the conduction band is completely empty, electrons cannot move within the solid because there are no available states, and no current generation occurs because there is no net charge carrier mobility. The semiconducting material is represented by an energy gap of 1.1 eV.
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2. A place-kicker strikes a football with a horizontal velocity of 22 meters per second and vertical velocity of 10 meters per second. The ball reaches its maximum height within 1. 02 seconds. What is the total time that the ball with spend in the air?
The total time that the ball with spend in the air is 2.04 Seconds.
As per the data given in the above question.
It is given that the initial velocity of football is 22 meters per second.
And vertical velocity is 10 meters per second.
Also the ball reaches its maximum height within 1. 02 seconds.
We have to find the Time of flight.
As we know that the time of flight i.e ball travel in air is just double the maximum-height time.
Total time of ball in air is equal to double the maximum-height time.
[tex]=2 \times 1.02\\=2.04 \:Seconds[/tex]
The ball will be in the air for a total of 2.04 seconds.
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a particle of charge q and mass m is moving with a velocity v along the x-axis in a magnetic field b which is along the z-axis. how much time will it take for the particle to return to its original location
The time required for the particle to return to its original location is (2πm/Bq) s.
We have to see the direction of magnetic force works on a particle. Using right-hand rule
Point your pointer finger according to the direction particle is moving. To the x-axis.Point your middle finger in the direction of the magnetic field. To the z-axisYour thumb points to the direction of the magnetic force pushing on the particle. To -y-axis.The magnetic force will deflect the direction of the particles so that the particles will move in a circle. The magnetic force becomes the centripetal force because it always points to the center of the circle.
Fc = Fm
[tex]m \frac{v^2}{R} \:=\: Bqv[/tex]
mv² = BqvR
mv = BqR
[tex]R \:=\: \frac{mv}{Bq}[/tex]
R = mv ÷ Bq
If the particle return to its original location, it means the particle travel one full circle. According to uniform motion
t = d ÷ v
t = perimeter of the circle ÷ v
t = 2πR ÷ v
t = (2πmv ÷ Bq) ÷ v
t = (2πm ÷ Bq) s
t = [tex]\frac{2 \pi m}{Bq}[/tex]
t = (2πm/Bq) s
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the cosmic microwave background tells us a lot about our universe, including what shape it is, geometrically! what shape do we believe the universe is, and based on which property of the cmb?
We believe that the shape of the universe is geometrically flat based on critical density of the CMB.
New measurements of the cosmic microwave background by the Atacama Cosmology Telescope find that the universe is flat, with a density matching the critical density. There is no evidence of deviation from flatness. According to ACT scientists, the interpretation that the deviation seen by Planck is a statistical fluctuation.”
The CMB is useful to scientists because it helps us learn how the early universe was formed. It is at a uniform temperature with only small fluctuations visible with precise telescopes. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large-scale structures of galaxies and they can measure the basic parameters of the Big Bang theory.
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assuming that the wave’s frequency ω remains constant, create a plot of the wavelength λ as a function of the current speed u. as u increases, what do you expect to happen to i) the wave’s length? ii) the wave’s amplitude? iii) the wave’s steepness? (5p)
A wave is a propagating dynamic disturbance of one or more quantities. Waves can be periodic, in which these quantities repeatedly oscillate around their equilibrium values at specific frequencies.
Whether vibrations or waves, they can all be characterized by four characteristics: Amplitude, Wavelength, Frequency, Velocity.
u = ωλ
Where, u = velocity of the wave
ω = frequency of wave
λ = wavelength of wave
For the first case:
If the wave’s frequency ω remains constant, then the velocity of wave will be proportional to wavelength:
u ∝ λ
So, if the velocity increases then there will be an increase in wavelength.
For the second case:
The amplitude of the wave is completely independent of the speed of propagation u and depends only on the amount of energy in the wave.
So, there will be no change of amplitude.
For the third case:
Wave steepness is the ratio of wave height(H) to wave length(λ).
Wave steepness = H/λ
This indicates that wave steepness is inversely proportional to wavelength.
Wave steepness ∝ 1/λ
But we know,
u ∝ λ
Then,
Wave steepness ∝ 1/λ ∝ 1/u
So, according to above application wave steepness in inversely proportional to velocity. This means that steepness will decrease with increasing velocity.
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the interaction between two waves that meet is called a. reflection. b. refraction. c. diffraction. d. interference. please select the best answer from the choices provided a b c d
The interaction between two waves that meet is called interference.
Interference is a phenomenon of wave interactions. When two waves meet at a point, they cancel each other out.
There are two types of interference, constructive and destructive.When the crests or troughs of two interfering waves meet, their amplitudes add up. This principle is known as constructive interference. When the opposite happens and it's called destructive interference. When the crest and trough of two interfering waves meet, one amplitude is subtracted from the other.Wave interference is a phenomenon that occurs when two waves meet while traveling through the same medium.Interference of waves causes the medium to take on a shape that results from the net effect of two individual waves on the particles of the medium.Answer d. interference is the correct answer
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what potential difference, acting over a distance of 2.0 cm, would be needed to balance the downward force of gravity so that an electron would remain stationary? assume that the electric field is uniform.
An object is put through work (energy) when it is lifted off the ground. You might think of it as the force operating on an object to try to get it back to its lowest potential energy (the "ground state") when you do so.
The object obtains potential energy equal to the force needed to raise it (roughly) when you do so. Water towers and dams are frequent examples of structures that humans have used to harvest gravitational potential energy.
Every facet of modern life, including using your phone or turning on your hose, depends on your ability to harness potential energy (we do it more with fuels rather than gravity nowaday though if you think about it, gravity is why we have oil inthefirstplace).
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a battery is several electrochemical cells stacked together. please select the best answer from the choices provided t f
True; A battery is several electrochemical cells stacked together.
A source of electricity made up of one or more electrochemical cells with connections on the outside that can be used to run electrical appliances is known as an electric battery.
The cathode and anode of a battery are represented by their positive and negative terminals, respectively, when it is supplying electricity.
Electrons will come from the terminal labeled "negative" and travel to the terminal labeled "positive" via an external electric circuit. When a battery is connected to an external electrical load, a redox reaction changes high-energy reactants into lower-energy products, and the free-energy difference is sent to the external circuit as electrical energy. Historically, a "battery" was a device made up of numerous cells; however, the phrase has come to be used to describe a single cell as well.
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. the latent heat for the water/steam transition is 2256 kj/kg, i.e., to convert 1 kg of water into steam requires 2256 kj. what is the latent heat per molecule of h2o? express your answer in joules and in ev.
Latent heat per molecule of H2O expressed in joules is 124976.7 J/mol.
Latent heat is the amount of heat energy required to change the state of a substance without changing its temperature. To calculate the latent heat per molecule of H2O, we need to use the following equation:
Latent heat per molecule = (Latent heat / Mass of 1 molecule of H2O)
The mass of one molecule of H2O is approximately 18 x 10-3 kg.
Therefore, the latent heat per molecule of H2O is:
Latent heat per molecule = (2256 kJ / 18 x 10-3 kg) = 125333.33 kJ/mol
This is equivalent to 125333.33 kJ/mol = 124976.7 J/mol
In terms of electron volts, this is equivalent to 124976.7 J/mol = 7.2 x 1020 eV.
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What is the minimum diameter at section (1) in the pipe below to avoid cavitation at that location? Take D2= 15 cm. Neglect friction head loss in the pipe. (3) Water 5 m (1) (2)
The minimum diameter at section (1) in the pipe below to avoid cavitation at the location is 16.6 cm.
Look at the picture
In section (1) according to Torricelli's law the speed of waterAccording to Bernoulli's equation in sections (1) and (2)
p₁ + 0.5 ρv₁² = p₂ + 0.5 ρv₂²
1.5 × 10⁵ + (0.5 × 1,000 × 14²) = 1.01 × 10⁵ + (0.5 × 1,000 × v₂²)
1.5 × 10⁵ - 1.01 × 10⁵ + 98,000 = 500 × v₂²
49,000 + 98,000 = 500 × v₂²
147,000 = 500 × v₂²
v₂² = 147,000 ÷ 500
v₂² = 294
[tex]v_2 = \sqrt{294}[/tex]
v₂ = 17.15 m/s
According to the continuity equation for fluids
A₁ v₁ = A₂ v₂
[tex]\frac{1}{4} D_1^2 v_1 = \frac{1}{4} D_2^2 v_2[/tex]
D₁² v₁ = D₂² v₂
D₁² × 14 = 15² × 17.15
D₁² = 3,858.75 ÷ 14
D₁² = 275.625
[tex]D_1 = \sqrt{275.625}[/tex]
D₁ = 16.6 cm
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what happens to the gravitational force between two objects if the distance between them triples? (1 point)
Gravitational force between two objects if the distance between them triples reduces by 9.
What is gravitational force ?
The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation. The force constantly tries to pull different masses towards each rather than pushing them apart from each other we tend to refer to this force of attraction as gravity.
Gravitational force [tex]F[/tex] = [tex]G\frac{m_{1} m_{2} }{r^{2} }[/tex]
where m1 = mass of object 1
m2 = mass of object 2
G gravitational constant
r = distance between the two object
If the distance between the two object is triples i.e. r = 3r
Then Gravitational force [tex]F^{'} = \frac{F}{(3r)^{2} }[/tex] =
[tex]F^{'} = \frac{F}{9r}[/tex]
Thus gravitational force between the object will reduce by a factor of 9.
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Three identical train cars, coupled together, are rolling east at speed . A fourth car traveling east at catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?
There are two collisions occurring in this question, finally after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity, by the conservation of momentum principle.
What is Conservation of Momentum?
According to the Principle of Conservation of Momentum, when two objects meet, their total momentum is the same before and after the collision (provided that no external forces - for example, friction - act on the system). This is incredibly helpful since it means you can predict what will happen following a collision before it occurs.
What are the Calculations?
First collision (between three-car trains and a fourth car moving with 2[tex]V_{0}[/tex] in the same direction)
We will apply conservation of momentum to calculate the velocity of the train after the first collision
M1V1 + M2V2 = (M1 + M2)V 3M([tex]V_{0}[/tex]) + M2[tex]V_{o}[/tex] = (3 M + M)V .(5M)V. V (4M.V) V = [tex]\frac{5}{4} Vo[/tex]
Now the mass of the four-car train is 4M and is moving with a velocity of [tex]\frac{5}{4} Vo[/tex]
Second collision (between four-car trains and fifth car at rest)
Again we will apply conservation of momentum to calculate the velocity of the train after the second collision
M1V1 + M2V2 = (M1 + M2)V (4M × [tex]\frac{5}{4} V_{o}[/tex]) + (M × 0) = (4 M + M)V (5M)[tex]V_{o}[/tex] = (5M)V. V = [tex]V_{o}[/tex]
Finally, after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity.
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an optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is 1.37 m from the slits. if the slits are illuminated with 633 nm light, how far apart should the slits be?
In this case the angle made by fringes is 0.5291
Explain in detail.
Tan θ = 15.7 x 10-3 / 1.7
= 0.5291
The condition of Interference is
d sin θ 0.5291 = (1) 633NM
d = (1)633nm / sin 0.5291
= 68.54 x 10-6 m
= 69.54 um
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