The magnitude of net force exerted on each one of the three masses is 0.53 * 10⁻¹³ N.
Given, m₁ = m₂ = m₃ = 7.5 g = 7.5 * 10⁻³ kg
Sides of the triangle = 35 cm = 35 * 10⁻² m
As the masses are the same and are at the corners of an equilateral triangle, two equal forces will act on each of the masses.
The forces on mass 1 due to mass 2 and due to mass 3 will be
| F₁₂| = Gm²/r²
⇒ 6.67* 10⁻¹¹* (7.5 * 10⁻³)²/(35 * 10⁻²)² = 375.19* 10⁻¹⁷/(35²* 10⁻⁴)
⇒ 0.306 * 10⁻¹³ N
| F₁₂| = | F₁₃| = 0.306 * 10⁻¹³ N
The magnitude of the net force on mass 1 can be found by the parallelogram law formula giving the magnitude of the resultant of two forces, given their magnitudes and the angle in between:
F₁ = | F₁₂ + F₁₃|
F₁ = √(| F₁₂| ² + | F₁₃|² + 2* | F₁₂|* | F₁₃| cos 60°) = √3 (F)
⇒ √3 * 0.306 * 10⁻¹³ = 0.53 * 10⁻¹³ N
The magnitude of force on each of the mass will be same.
Thus, the magnitude of force on each mass on the corners of the triangle will be 0.53 * 10⁻¹³ N.
The question is incomplete. The continuation to the above question is 'Find the magnitude of net force exerted on each of the three masses.'
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a force of 300N is applied to a 1500kg car at rest. a)what is its acceleration. b)what will its velocity be 5secs later
The acceleration will be 0.2m/s^2 while the velocity will be 1m/s
Acceleration and VelocityGiven DataForce = 300N
Mass = 1500kg
Time = 5 seconds
We know that
Force = ma
a = F/m
a = 300/1500
a = 0.2 m/s^2
Also, the expression for Velocity is given as
Ft = mv
300*5 = 1500*v
Making velocity the subject of the formula we have
1500 = 1500*v
v = 1 m/s
The rate of change of an object's velocity with respect to time is defined as acceleration.
Acceleration implies that the speed is changing, but this is not always the case. When an object moves in a circular path at a constant speed, it is still accelerating because its velocity direction changes.
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Assume that the circuit Figure 21-16 has L equal to 0.60 H, R equal to 280 ohms, and C equal to 3.5 μF. The amplitude of the driving voltage is 150 V rms. At a frequency of 60 Hz, what is the rms current in the circuit?
VL (peak) = VL × √2= 2.335 angle (90) volts is the rms current in the circuit.
Rms current is Root-Mean-Square of instantaneous current values. The RMS value of alternating current is given by direct current which flows through a resistance
How to calculate the rms current in circuit?At resonance the capacitive and inductive reactance are such that they cancel each other and the circuit is entirely resistive at that point
Calculation :so,
At resonance the current is given as
I(rms) = Erms/R = 125 /740 = 0.169 A= 1.6 × 10^-1 A
Now for series RLC circuit the resonant frequency is given as
w= 2πf=1/• LC = 1/√41× 10^-3* 0.44××10^-3
f= 37.94 Hz
The inductive reactance at resonant frequency is given as
xL= jwL = j 2πf×L = j×2×π×37.94×41×10^-3 = j9. 77 ohm= 9.77 angle (90)
as 9.77 angle (90) = 9.77 cos 90+ j9. 77 sin (90) = 0+ j9.77
So the voltage across the inductor is given as
VL= I×XL
=0.16 × 9.77 angle (90) = 1.65 angle (90)
Note this is the rns value for the peak value the voltage is to be multiplied by √2
VL (peak) = VL ×√2= 2.335 angle (90) volts
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An electrical motor spins at a constant 1129.0 rpm. If the armature radius is 2.846 cm, what is the
acceleration of the edge of the rotor?
The accelaration of the edge of the rotor is linear acceleration.
What is accelaration?Accelaration is the rate of the change of the velocity of an object with respect by time.
The electric motor is spinning at a rate of 2695 Devolution Permanent. By two by over 60 is how this can be converted into reading persecond. The value is coming out at 282.08 ingredient per second. The areas of the model is 7.605 cm. The linear acceleration of the by motor is what we have to l find. We have to find out of the tangential acceleration that is given by the formula and omega squared R, if I substitute the values. This will be to 82.08 The motor has a linear Acceleration.
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Specify the SI unit for the penetration coefficient of ultrasonic waves:
m-1
m/s
non-dimensional quantity
The SI unit for the penetration coefficient of ultrasonic waves is m⁻¹.
option A is the correct answer.
What is penetration coefficient?Penetration coefficient describes the amount of particles reduced from the infiltration of outdoor particles due to the filtering effect of the building envelope.
Ultrasonic waves describes sound waves with frequencies higher than the upper audible limit of human hearing.
The SI unit of penetration coefficient of ultrasonic waves is expressed in either decibels per meter ( dB/mv ), or nepers per meter ( Np/m ) or equivalent to per meter ( m⁻¹ ).
Thus, the SI unit for the penetration coefficient of ultrasonic waves is per meter ( m⁻¹ ).
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I need help on this
A planet has a different meaning than the astronomical understanding of what a planet is. Before the advent of telescopes, the night sky was thought to consist of two very similar components. Fixed stars, which are stationary relative to each other, and moving objects ("wandering stars").
What are planets?
Planets are large, round objects that are neither stars nor remnants. The best theory of planet formation available is the nebular hypothesis, which postulates that interstellar clouds collapse from the nebula, creating young protostars orbiting the protoplanetary disk. Planets grow within this disk by the gradual accumulation of matter by gravity, a process called accretion. The solar system has at least eight planets: the terrestrial planets Mercury, Venus, Earth, and Mars, and the giant planets Jupiter, Saturn, Uranus, and Neptune. Each of these planets rotates around an axis that is tilted with respect to the poles of its orbit. All of them have atmospheres, but Mercury's is faint, and some share features such as ice caps, seasons, volcanism, hurricanes, tectonics, and even hydrology. Except, the planets in our solar system generate magnetic fields, and all planets except Venus and Mercury have natural satellites. Giant planets have planetary rings, most notably Saturn's rings.
Some cultures equate celestial bodies with gods, and these connections to mythology and folklore exist in naming schemes for newly discovered celestial bodies in the solar system. When the heliocentric theory superseded the heliocentric theory in the 16th century and his 17th century, the earth itself was recognized as a planet.
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If the maximum excitation energy gained by an atom is 12.08 eV ,determine all of the wavelengths of light emitted from the tube as atoms return to the ground state.
The wavelength of light emitted from the tube as atom returns to the ground state is 1.02×[tex]10^{-7[/tex]m.
The spectrum of the electromagnetic radiation emitted or absorbed by an electron during transitions between different energy levels within an atom. When an electron gets excited from one energy level to another, it either emits or absorbs light of a specific wavelength.
The wavelength can be determined by either energy or by frequency.
in the question energy of an atom is given, so we will use wavelength energy formula.
λ=hc/E =6.626×10⁻³⁴J⋅s×2.998×10⁸m⋅s⁻¹/12.08 ×1.6×[tex]10^{-19[/tex]
= 19.864×[tex]10^{-7[/tex]/19.328
= 1.02 ×[tex]10^{-7[/tex] m
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A closed system consists of two adjacent chambers containing the same ideal gas. Initially, one chamber is hot and the other chamber is cold. Which of the following best explains the change in entropy of this closed system over time? A. The entropy increases over time because the process is irreversible B. The entropy stays the same because it is a conserved quantity C. The entropy decreases because the system moves toward a more orderly state of uniform temperature D. Nothing can be determined about the change in entropy without knowing how many moles of gas are in each container
Only when heat is transferred from the system to its surroundings does a closed system suffer a decrease in entropy.
define entropy ?
Entropy is a key term in physics and chemistry, and it also has applications in cosmology and economics. It is a branch of physics known as thermodynamics. It is a key idea in physical chemistry.
Entropy is the measure of the disorder of a system. It is a comprehensive feature of a thermodynamic system, which implies that its value varies with the amount of matter present. Entropy is usually denoted by the letter S in equations and has units of joules per kelvin (JK1) or kgm2s2K1. Entropy is low in a highly ordered system.
Only when heat is transferred from the system to its surroundings does a closed system suffer a decrease in entropy.
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Using the technique of main-sequence fitting to determine the distance to a star cluster requires that _____.
we have telescopes powerful enough to allow us to identify the spectral types of main-sequence stars of many masses in the cluster
To calculate the distance to a star cluster using the main-sequence fitting method, we must first be able to build the cluster's main sequence in order to "fit" it to the standard main sequence.
The vast collections of stars known as stellar clusters. There are two primary categories of star clusters: globular clusters, which are gravitationally coupled tight groups of stars between 10,000 and 500,000 years old, and open clusters, which are more loosely bound groups of stars, typically with fewer than a few hundred members and frequently extremely young. While open clusters are being disrupted over time by the gravitational pull of massive molecular clouds as they move through the galaxy, cluster members will still move through space largely in the same direction even though they are no longer gravitationally bound; at this point, they are known as a stellar association, also known as a moving group.
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If Vxi= 10 m/s, then Vxf=_______10m/s
If initial horizontal velocity (Vxi) = 10 m/s, then final horizontal velocity (Vxf) = positive 10m/s.
option B is the correct answer.
What is the horizontal velocity of a projectile?
The horizontal velocity of a projectile is the velocity of the projectile along the x - axis or x - direction.
During the horizontal motion of a projectile, the horizontal velocity of the projectile will be constant since gravity does not act in the horizontal direction.
That is to say, that the initial velocity of the projectile along horizontal direction will be equal to the final velocity of the projectile along the same horizontal direction.
Vxi = Vxf
where;
Vxi is the initial horizontal velocityVxf is the final horizontal velocityThus, If the initial horizontal velocity is 10 m/s. then the final horizontal velocity will be 10 m/s.
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1. David Purley, a racing driver, survived deceleration from 173 km/h (about 107
mph) to 0 km/h over a distance of 0.660 m when his car crashed. Assume that
Purley's mass is 70.0 kg. What is the average force acting on him during the
crash? Compare this force to Purley's weight.
Average force acting on Purley is -1749m/[tex]s^{2}[/tex].
What is Newton's second law of motion?
According to this, a body's momentum changes at a rate that is equal to the force acting on it over time in both magnitude and direction. A body's momentum is determined by multiplying its mass by its speed.
Given,
According to newton's second law of motion:
F =ma
Purley's initial speed = 173km/h
Final speed = 0
Distance traveled = 0.66 m
So, [tex]v_{i}[/tex] = 172 km/h × 1 hr/3600 s × 1000m/1km
[tex]v_{i}[/tex] = 48.1 m/s
By using kinematics
[tex]v^{2} f[/tex] = [tex]v^{2} i[/tex] + 2ad
[tex]0^{2}[/tex] = 48.[tex]1^{2}[/tex] + 2a(0.66)
-1.32a = 2309
a= -1749 m/[tex]s^{2}[/tex]
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Suppose you observe a star orbiting the galactic center at a speed of 1100 km/s in a circular orbit with a radius of 22 light-days. Part A What would your estimate be for the mass of the object that the star is orbiting? Express your answer using two significant figures.
According to the given statement M = 18.67 x 10⁶ Solar masses of the object that the star is orbiting.
How speed does physics move?The rate at which the position of an object shifts in any direction. Speed is defined as the ratio of the distance traveled to the time required to cover that distance. Speed is a numerical number since it just has a path and no magnitude.
Briefing:
M = Mass of Object = ?
v = orbital speed of star = 1100 km/s = 1100000 m/s
G= 6.67 x 1011 N.m2/kg is the universal gravitational constant,
r = distance between star and object = (22 light-days)(2.59 x 10¹³ m/1 light-day) = 5.698 x 10¹⁴ m
Therefore,
[tex]M=\frac{(1100000 \mathrm{~m} / \mathrm{s})^2\left(5.698 \times 10^{14} \mathrm{~m}\right)}{6.67 \times 10^{-11} N . \mathrm{m}^2 / \mathrm{kg}^2}[/tex]
M = (9.39 x 10³⁷ kg)(1 solar mass/ 1.989 x 10³⁰ kg)
M = 18.67 x 10⁶ Solar masses
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Find the Thevenin equivalent of the circuit with respect to Z - Express the answer in terms of the Thevenin voltage (Vr), short-circuit current (ise), and Thevenin impedance (ZT).
The Thevenin Voltage (Vr) of the circuit with respect to Z is 6V.
Thevenin Voltage (Vr) is the equivalent voltage source in a Thevenin equivalent circuit. It is the open circuit voltage that exists between the two terminals of a circuit when all other elements are removed.
The Thevenin equivalent of the above circuit with respect to Z is Vr
= 6V, ise = 0.5A, and ZT = 4Ω.
Calculate the Thevenin Voltage (Vr)
Step 1a: Calculate the total resistance in the circuit
Rtotal = (2Ω + 3Ω) || (4Ω + 5Ω)
= (2Ω*5Ω)/(2Ω + 5Ω) + 4Ω
= 7 Ω
Step 1b: Calculate Thevenin Voltage (Vr):
Vr = (Rtotal/(Rtotal + 4Ω))*6V
= (7Ω/(7Ω + 4Ω))*6V = 6V
Calculate the Thevenin Impedance (ZT)
ZT = Total = 7Ω
Calculate the short-circuit current (ise)
ise = Vr/ZT = 6V
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1) In the nuclear reaction shown, one deuterium (hydrogen- 2 ) and one tritium (hydrogen-3) fuse to form one helium-4 and one neutron.
Data: Hydrogen-2 mass: 3.34450 10⁻²⁷ kg
Hydrogen-3 mass: 5.00827 10⁻²⁷ kg
Helium-4 mass: 6.64648 10⁻²⁷ kg
Neutron mass: 1.67493 10⁻²⁷ kg
a) What is the total mass of the pieces going into the reaction?
b) What is the total mass of the pieces coming out of the reaction?
c) How much energy is converted from rest energy to other forms of energy if one mole of deuterium (about 2.0 g ) and one mole of tritium (about 3.0 g ) are converted?
When helium-3 and deuterium combine in this nuclear process, regular helium and a proton are produced, wasting less energy and making the reaction easier to contain.
What energy forms of energy if one mole of deuterium?The fusion of deuterium and tritium is the most promising of the hydrogen fusion processes that make up the deuterium cycle.
The reaction produces 17.6 MeV of energy, but in order to induce fusion, one must tunnel through the coulomb barrier, which requires extremely high temperatures.
Therefore, 8.4 1020 joules of energy would be released if one ton of deuterium were to undergo the fusion reaction with tritium. This is comparable to the 2.9 1010 joules of energy found in a ton of coal.
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A gas at a pressure of 2.00 atm undergoes a quasistatic isobaric expansion from 3.00 to 5.00 L. How much work is done by the gas?
Answer:
this video shows how to solve the problem :)
Explanation:
a thin, 100 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.18 j of kinetic energy. What is the speed of a point on the rim?
According to the given statement, the speed of a point on the rim is 2.68 m/s.
Why is energy so crucial?Energy is a major factor in our everyday routines even though it is an essential need for humans. Our human-made structures are not only heated by energy, but also cooled by it. To lift you finger, climb out of bed, or even stroll down main sidewalk, you need energy.
kinetic energy = E = 0.18 J
mass = m = 100g = 0.1 kg
diameter = d = 8.0 cm = 0.08 m
Speed = v = ?
v = 2.44 m/s
Briefing:
First convert diameter into radius
r = d/2 = 0.08/2 = 0.04 m
The moment of inertia of disc is given by
I = 0.5mr²
In which m is the disk's mass & r is its radius
I = 0.5(0.1)(0.04)²
I = 0.00008 kg.m²
Additionally, since we are discussing rotating motion, rotational kinetic energy is provided by
E = 0.5 I ω²
we have to separate ω
ω² = E/0.5 I
ω = √E/0.5 I
ω = √0.18/0.5(0.00008)
ω = 67.08 rad/sec
Finally we know that speed is given as
v = ω r
v = 67.08 (0.04)
v = 2.68 m/s
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you push a 27 kg crate with 1 n of force, and it moves along the floor with constant velocity, the acceleration of the crate is
The acceleration of the crate is 0 m/s2.
This is because the force applied is equal to the force of friction between the crate and the floor, so the crate is not accelerating. The force of friction is equal to the force applied, and since no acceleration is occurring, the force must be equal to the mass of the crate multiplied by the acceleration of gravity (9.81 m/s2).
This means that the force applied (1 N) is equal to the mass of the crate (27 kg) multiplied by the acceleration of gravity (9.81 m/s2). Therefore, the acceleration of the crate is 0 m/s2.
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a ball is dropped from a cliff and falls freely towards earth. which of the following statements are true concerning the ball as it falls? neglect air resistance (aka drag) for this problem.
The acceleration will be constant and in a downward direction. And as the ball moves in direction of the acceleration so the velocity will keep increasing because velocity is inversely proportional to height, when the ball is in free fall.
What is Acceleration?The rate at which an item changes its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is accelerating.
What is Free fall?Free fall is characterized as a condition where an object is only affected by gravity. The ball experiences an external force, which quickens its motion. Gravitational acceleration is another name for this rate of free-fall acceleration. A downward motion without any beginning force or speed is called a free fall.
Hence, the acceleration will be constant and in a downward direction. And as the ball moves in direction of the acceleration so the velocity will keep increasing because velocity is inversely proportional to height, when the ball is in free fall.
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Help please!
How can you differentiate someone who has quality hypnosis training and someone who does not?
The Hypnotic Induction Profile (HIP) or the eye roll test, first proposed by Herbert Spiegel, is a simple test to loosely determine if a person is susceptible to hypnosis. A person is asked to roll their eyes upward. The degree to which the iris and cornea are seen is measured.
What is Hypnotic Induction Profile (HIP)?The Hypnotic Induction Profile (HIP) was created as a quick yet comprehensive evaluation of a person's trait hypnotizability and capacity to enter a hypnotic state.An invitation to enter hypnosis is known as a hypnotic induction, and it usually includes instructions and recommendations to make the subject more receptive to hypnosis. Instructions for relaxation are frequently included in the hypnotic induction, but while nice, they are not always necessary.Do I Have a Receptive Mind? Highly hypnotizable individuals frequently have vivid imaginations and can visualize objects clearly in their minds' eye.When they are reading or watching a movie they enjoy, they frequently lose track of time.To learn more about Hypnotic Induction Profile (HIP) refer to:
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A moving object collides with a second object at rest on a frictionless surface, resulting in an elastic collision. Is the momentum of each individual object the same before and after the collision?
A. No - the momentum of each object is not bound by conservation - only the system as a whole. B. Not enough information is given. C. Yes - the conservation of momentum is a universal law.
According to statement no, only system in general is constrained by conservation of momentum.
What does the scientific term frictionless mean?A surface is said to be frictionless if it has a loads applied on any thing that is virtually zero or insignificant, i.e., there is no resistance between the surface and the substance, allowing that object simply slide & freely move without any friction.
Is there no friction at all in space?Although gas, sand, radiation, fields, and minuscule particles are present in outer space, their concentration is too low for them to have a significant impact on spacecraft. As a consequence, traveling objects cannot be slowed down in space by any kind of friction.
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An object of 20 kg accelerates at 10 m/s/s into a wall. What amount of force did it hit the wall?
The amount of force that hit the wall is 200N.
What is force?Force is a physical quantity that denotes ability to push, pull, twist or accelerate a body and which has a direction.
The force can be calculated by multiplying the mass by the acceleration as follows:
Force = mass × acceleration
According to this question, an object of 20kg accelerates at 10 m/s² into a wall. The force applied is as follows:
Force = 20kg × 10m/s² = 200N
Therefore, 200N is the force applied by the object on the wall.
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the width of a rectangle is 5 feet longer than four times its length, and its area is 26 . if you use l to represent the length of the rectangle, then an expression representing the width is w = ___ The length of the rectangle is feet. feet and the width is ___
The expression representing width is w = 3l +5, where l = length. When area is 26, the equation for length is 4[tex]l^{2}[/tex]+5l -26=0.
Rectangle is a parallelogram with its opposite sides equal. We can find area of rectangle using the formula,
Area is defined as the extent occupied by an object in 2D plane. The plane may be flat or curved region. The S.I. unit of area is square meter.
Area = length × width
So, we have length = l,
as per the given information in the question,
width = w = 4l+5
So, area, a = (4l+5) ×l= 26
4[tex]l^{2}[/tex] +5l = 26
4[tex]l^{2}[/tex] +5l-26 = 0
Solving this equation, we can find the value of l and then width.
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The wavelength of the yellow light from a sodium flame is 589 nm. This light originated from a sodium atom in the hot flame.
(a) In the sodium atom from which this light originated, what was the period of the simple harmonic motion which was the source of this electromagnetic wave? Give your answer in seconds per cycle.
(b) What is the frequency of this light wave? Give your answer in hertz.
From wave speed formula, period is 1.96 × 10^-15 seconds per cycle and the frequency is 5.1 × 10^14 Hertz
What is Frequency ?The frequency of a wave is the number of complete revolution per second made by a vibrating body.
Given that the wavelength of the yellow light from a sodium flame is 589 nm. This light originated from a sodium atom in the hot flame.
(a) In the sodium atom from which this light originated, the period of the simple harmonic motion which was the source of this electromagnetic wave will be found by using the formula
v = λ/T
Where
v = speed of light = 300,000,000 m/sλ = wavelength = 589 × 10^-9 mT = periodSubstitute all the parameters
300000000 = 589 × 10^-9/T
T = 589 × 10^-9/300000000
T = 1.96 × 10^-15 seconds per cycle.
(b) The frequency of this light wave is the reciprocal of its period. That is,
F = 1/T
F = 1/1.96 × 10^-15
F = 5.1 × 10^14 Hertz
Therefore, the period of the wave is 1.96 × 10^-15 seconds per cycle and its frequency is 5.1 × 10^14 Hertz
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A student runs a simulation of a skateboarder going back and forth on a U-shaped ramp. The skateboarder begins with 1,560 joules of potential energy. The bar graph shows the energy of the skateboarder system at the end of the simulation. What are the potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation?
PE = 520 J; KE = 520 J.
PE = 0 J; KE = 1,560 J.
PE = 0 J; KE = 0 J.
PE = 780 J; KE = 0 J.
The potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation is PE = 0 J; KE = 1,560 J. Hence option 2 is correct.
What is potential energy?Potential energy is defined as the energy stored that an object can hold due to its position in relation to other objects, internal tensions, electric charge, or other circumstances. One of the two types of energy is potential energy, which is the latent energy in an object at rest.
The skateboarder's potential energy is transformed into kinetic energy, also known as the energy of motion, as her position along the track and speed vary. The system's total potential energy determines the maximum amount of kinetic energy the skateboarder can possess.
Thus, the potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation is PE = 0 J; KE = 1,560 J. Hence option 2 is correct.
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The elevation of city A is 80 feet below sea level; the elevation of city C is 16 feet below sea level. The elevation of city D is 1 over 2 of the elevation of city C.
Part A: Write an expression to represent the elevation, in feet, of city D. (5 points)
Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
The expression of elevation and solution of the expression is as below -
[tex][X-80x] + [X-16c] +2d/c=0\\x=2c-d[/tex]
All elevations are measured from sea level, which is defined as a height of 0 feet. Positive elevations are found in locations on Earth that are higher than sea level, and negative elevations are found in locations that are lower. As a result, Death Valley is situated below sea level at a height of -282 feet.Distance above sea level is known as elevation. In most cases, elevations are expressed in meters or feet. On maps, they can be represented by contour lines that link points of the same elevation, by color bands, or by numbers that indicate the precise elevations of specific points on the surface of the Earth.On Earth, sea level serves as the reference point for determining elevation and depth. The ocean is a single, unbroken body of water, so its surface tends to seek uniformity everywhere it is. In relation to the nearby land, the sea level is determined. Land elevation can fluctuate over time, just like that of the ocean.To learn more about Land elevation -
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help helphelphelphelp plssssssss
Answer:
heat and pressure is the correct answer
When water flows from section 1 at upstream to section 2 at downstream in an open channel, the water depth decreases by a factor of 2
The answer to the question is 5.66 feet for the channel's diameter after 2 if it is 12 feet wide at 1.
What makes upstream and downstream different?Simply expressed, upstream activities comprise the discovery and production of petroleum and natural gas, whereas downstream activities relate to the procedures used from the extraction phase until the product is given to the client in the desired shape.
Briefing:[tex]$$\begin{aligned}& F r_1=\frac{V_1}{\sqrt{g V_1}}=0.5 \text {, or } \sqrt{g Y_1}=2.0 V_1 \\& \text { and } \\& F_{r_2}=\frac{V_2}{\sqrt{g y_2}}=3.0 \text { where } y_2=0.5 y_1 \\& \text { Thus, } \frac{V_2}{\sqrt{0.5 g Y_1}}=3.0 \text {, or } \sqrt{g y_1}=V_2 /(3 \sqrt{0.5}) \\& \text { By equating Eq. (1) and }(2) ; 2.0 V_1=V_2 /(3 \sqrt{0.5}) \\& \text { or } \\& V_2=4.24 V_1\end{aligned}$$[/tex]
However,
[tex]$Q_1=Q_2$[/tex] or [tex]$b_1 y_1 V_1=b_2 y_2 V_2$[/tex]
where [tex]$b=$[/tex] channel width. Thus, with [tex]$b_1=12 \mathrm{ft}$[/tex]
(12ft)y₁(V₁) = b₂(0.5y₁)(4.24V₁) or b₂ = 12ft/0.5(4.24) = 5.66ft
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The complete question is-
In flowing from section 1 to section 2 along an open channel, the water depth decreases by a factor of 2 and the Froude number changes from a subcritical value of 0.5 to a supercritical value of 3.0. Determine the channel width at 2 if it is 12 ft. wide at 1.
in the context of the roles of nmda receptors and ampa receptors in long-term potentiation (ltp), which of the following occurs during weak electrical stimulation of the presynaptic neuron?
That which occurs during weak electrical stimulation of the presynaptic neuron is;
Weak activity of the presynaptic neuron leads to modest depolarization and calcium influx through NMDA receptors.
what are NMDA receptors?
The N-methyl-D-aspartate receptor, is described as a glutamate receptor and ion channel found in neurons.
The NMDA receptor is one of three types of ionotropic glutamate receptors, the other two being AMPA receptors and kainate receptors.
In the context of the roles of nmda receptors and ampa receptors in long-term potentiation (ltp), weak activity of the presynaptic neuron leads to modest depolarization and calcium influx through NMDA receptors.
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A gold sphere of radius R=100 μm and density 19g/cm^3 falls through water. Given the viscosity of water is about 10^-3 Pa s and the density of water is 1.0g/cm^3, calculate the terminal velocity of the sphere. The viscous drag coefficient for a sphere is α=6π.
Don't forget to consider the buoyant force on the sphere when calculating net force!
The terminal velocity of gold sphere is 39.2 cm/s
What is terminal velocity?Terminal velocity is the maximum velocity attainable for an object as it falls through a fluid.
How to calculate the terminal velocity of the gold sphere?The terminal velocity of the gold sphere is given by v = 2gr²(ρ - σ)/9η where
g = acceleration due to gravity = 9.8 m/s², r = radius of sphere = 100 μm = 100 × 10⁻⁶ m = 10⁻⁴ m = 10⁻² cm, ρ = density of sphere = 19 g/cm³, σ = density of water = 1.0 g/cm³ and η = viscosity of water = 10⁻³ Pa-sSo, susbtituting the values of the variables into the equation, we have that
v = 2gr²(ρ - σ)/9η
v = 2 × 9.8m/s²× (10⁻² cm)²(19 g/cm³ - 1.0 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 9.8 m/s² × 10⁻⁴ cm² × (18 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 980 cm/s² × 10⁻⁴ cm² × 2 g/cm³/(1 × 10⁻³ Pa-s)
v = 3920 g/s² × 10⁻⁴/(1 × 10⁻³ Pa-s)
v = 392 cm/s × 10³ × 10⁻⁴
v = 392 × 10⁻¹ cm/s
v = 39.2 cm/s
So, the terminal velocity is 39.2 cm/s
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Dark matter was first detected because the ______ for the amount of gravity that could be present due to the luminous mass.
Dark matter was first detected because the excess for the amount of gravity that could be present due to the luminous mass.
Since, by measuring the rotation of the galaxies and their gravitational attraction, the scientists determined that there appeared to be an excess of gravity, which could not be explained by the amount of luminous mass present. This led to the conclusion that dark matter must exist to explain this excess gravity.
The role of dark matter in the formation of galaxiesDark matter plays a fundamental role in the formation and evolution of galaxies. This invisible matter is composed of subatomic particles that interact with gravity, but does not emit light, so it cannot be detected directly. Despite this invisibility, advances in technology have allowed scientists to determine the amount of dark matter present in the Universe and its contribution to the evolution of galaxies.
Studies of galaxies suggest that dark matter plays an important role in their formation, this means that dark matter is responsible for the formation of galactic structures, such as disks and the central bar.
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You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 505 N in the rope
A. If Sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.) Consult Appendix F in the textbook.
The Final tension in the rope is 473.4N.
Sneezy doesn't move in circles at the north pole, so there is no acceleration. The earth's rotation, however, causes him to accelerate toward the earth's center at the equator.Set up: Use coordinates with the y direction pointing toward the center of the earth because the earth has mass and a rotational period of T = 24 hr = 8.64 104 sdot. Sneezy's circular motion at the equator's radial acceleration.Sneezy has a= 0 and T = w = 475.0 N (the earth's gravitational pull) at the north pole. Sneezy weighs 48.47 point-47 kilograms. Sneezy is moving in a circle and experiencing radial acceleration as it approaches the equator.The outward tension is less than the true weight at the equator because there is a net inward force, and Sneezy is moving inward at an acceleration.a=0.0337m/s²
T=mg-ma=m[g-a]
=473.4N
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