Please solve step by step. Using Lagrange's equations prove that in a closed system the conservation of energy theorem is: T+U= E= H = contant
Answers
We can demonstrate using Lagrange's equations that the conservation of energy theorem, where T is the kinetic energy, U is the potential energy, E is the total energy, and H is the Hamiltonian, is given by T + U = E = H = constant in a closed system.
A set of equations known as Lagrange's equations are used in classical mechanics to explain a system's motion using the concept of least action. The Lagrangian, which is the difference between the system's kinetic energy (T) and potential energy (U), is where the equations come from.
Lagrangian (L) equals T - U
The kinetic and potential energy are added to form the system's Hamiltonian (H):
H = T + U
We must demonstrate that the Hamiltonian's time derivative is zero in order to demonstrate the conservation of energy.
d(T + U)/dt = dH/dt
By utilising Lagrange's equations, we arrive at:
dH/dt is equal to (L/q)*dq/dt + (L/(dq/dt)) d(dq/dt)/dt *
By rearranging the terms and applying the chain rule, we arrive at:
L/q * dq/dt + L/(dq/dt) * d2q/dt2 = dH/dt
Since (L/q) = d(L/(dq/dt))/dt according to Lagrange's equations, we can reformat the equation as follows:
D/dt[L/(dq/dt)] = dH/dt * L/(dq/dt) + dq/dt * d²q/dt²
Even more simply put, we have:
(d/dt[L/(dq/dt)]) * dq/dt + (L/(dq/dt)) * d2q/dt2 = dH/dt
Euler-Lagrange equation is used to determine that d/dt[L/(dq/dt)] - (L/q) = 0. When we add this to the equation, we get:
dH/dt = 0
We have demonstrated that the conservation of energy theorem is given by T + U = E = H = constant in a closed system using Lagrange's equations. The Hamiltonian (H), which represents the total of kinetic and potential energy, is constant over time, proving that all energy is conserved. This outcome emphasises the essential idea that energy is conserved in closed systems and that the total amount of kinetic and potential energy is constant. Lagrange's equations offer a potent tool for deciphering system dynamics and establishing crucial classical mechanics concepts like the conservation laws.
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Related Questions
What does NOT experience gravity?
Answers
Answer:
Astronauts who are orbiting the Earth often experience sensations of weightlessness. These sensations experienced by orbiting astronauts are the same sensations experienced by anyone who has been temporarily suspended above the seat on an amusement park ride. Not only are the sensations the same (for astronauts and roller coaster riders), but the causes of those sensations of weightlessness are also the same. Unfortunately however, many people have difficulty understanding the causes of weightlessness.
How high up is a cliff with 45 kg boulder if the boulder has a potential energy of 90,000 j
Answers
The height of the cliff is 200 meter where potential energy of the boulder is measured.
What is potential energy?Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.
The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are examples of common types of potential energy.
The height of the cliff is = 90,000 ÷ (45 ×10) meter = 200 meter.
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Which of the technologies could mostly like be found in a wearhouse
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define watt and write how much watt is equal to one horse power
Answers
Answer:
A watt (W) is a joule (J) of energy used or produced per second. In 2010, the average US power use was 3.3 terawatts, or 3,300,000,000,000 watts. A horsepower is a unit of power. 1 horsepower (hp) is 745.7 watts.
extra info
How many watts does it take to make 1 horsepower?
746 watts !
One electric horsepower is equal to exactly 746 watts.
can someone help me with my qustions :(
A sonar signal of frequency 1 x 10^6 Hz has a wavelength of 1.5 mm in * 30 points
water. a) What is the speed of the signal in water? b) What is its period in
water? c) What is its period in air?
Answers
a) To find the speed of the signal in water, we can use the equation:
Speed = Wavelength x Frequency
Where Wavelength is given as 1.5 mm and Frequency is given as 1 x 10^6 Hz.
Speed = 1.5 x 10^-3 m x 10^6 Hz = 1.5 x 10^3 m/s
So the speed of the signal in water is 1.5 x 10^3 m/s
b) To find the period in water, we can use the equation:
Period = 1 / Frequency
Where Frequency is given as 1 x 10^6 Hz
Period = 1 / (1 x 10^6) s = 1 x 10^-6 s = 1 microsecond
So the period of the signal in water is 1 microsecond
c) The speed of sound in air is approximately 343 m/s. Since the frequency of the signal remains constant and the speed of sound in air is different than the speed of sound in water, the wavelength of the signal will also be different. However, since the period is inversely proportional to the frequency and is independent of the medium, the period of the signal in air will be the same as in water, which is 1 microsecond.
what does it mean for a plate to subduct?
Answers
Answer:
what does it mean for a plate to subduct?
Explanation:
Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, the heavier plate dives beneath the second plate and sinks into the mantle.
Which of the following statements is true of the strong nuclear force?
A. It repels neutral charges
B. It holds protons and neutrons together
C. It acts over very great distances
D. It is much weaker than gravitational forces
Answers
Explanation:
it holds protons and neutrons together
Strong nuclear force holds protons and neutrons together.
What is protons?Proton is a subatomic particle with a positive electric charge.
What is neutrons?Neutrons is a subatomic particle of about the same mass as a proton but without an electric charge.
What is nuclear force?The nuclear force is a force that acts between the protons and neutrons of atoms.
What is strong nuclear force?The strong nuclear force is created between nucleons by the exchange of particles called mesons. It is stronger than the force of gravity as it binds the fundamental particles to form large particle.
Strong nuclear force is strongest force in nature. So, it is much stronger than gravitational forces. It binds the neutral charges i.e. neutron instead of repelling them. It is a short range force so it can not act over very large distances.
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on which law is the given diagram based? state the law.
Answers
Answer:
Explanation:
law of flotation
or
pascal's law
what happens to the temperature of the gas during an isobaric expansion?
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With an increase in gas volume, the gas's temperature must also rise. Temperature and volume changes result in work and an internal energy shift.
An illustration of an isobaric processBoiling water into steam or freezing water into ice are two examples of isobaric processes. A gas either expands or contracts during the process to maintain constant pressure, and as a result, the net work done by the system or on the system is determined.
What does "isobaric vs. adiabatic" mean?An adiabatic process where no heat is added to or removed from the system. an isobaric process, in which there is no change in the pressure of the system. the system's volume remains constant throughout an isochoric process.
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Name the way by which energy is transferred in the following processes a) A battery is used to light a lamp b) A ball is thrown upwards
Answers
Answer:
a)light energy
b) kinetic energy
A twenty-acre park was created to give residents a place to hike, bike, and enjoy other recreational activities. Kathy was hired to design a map that would show residents how they could easily access different areas of the park. Sean was hired to monitor the number of visitors they have per month and analyze the park’s popularity for funding possibilities. Joan was hired to offer assistance and teach residents about the plants and animals they may encounter while at the park.
Which best describes the tasks Kathy, Sean, and Joan perform?
Kathy and Joan perform tasks common to the Engineering and Technology pathway and Sean performs tasks common to the Science and Math pathway.
Kathy performs tasks common to the Engineering and Technology pathway and Sean and Joan perform tasks common to the Science and Math pathway.
Sean performs tasks common to the Engineering and Technology pathway and Kathy and Joan perform tasks common to the Science and Math pathway.
Sean and Joan perform tasks common to the Engineering and Technology pathway and Kathy performs tasks common to the Science and Math pathway.
Answers
Answer:
Answer
Kathy-Leadership
Sean-Entrepreneurial skill
Joan-Communication skills
Explanation:
Kathy practices leadership skills because she is responsible for communing up with a new thing in the area through designing the map for the park and informing residents about it
Sean applies entrepreneurial skills through gathering information from the park and making the funds available as well.
Joan as guide of people around the park practices strong communication skills to practice the personable and outgoing tasks.
Determine the moment at point b using method of section if w=40.3lb/ft Answer:
Answers
Method of section is a significant method of determining forces in members of a structure.
The basic concept of the method of section is to find out the forces acting on the sections by separating them from the rest of the structure.
In this problem, the moment at point b has to be determined using the method of section.
The given weight of the beam is
w = 40.3 lb/ft.
Let's draw the free-body diagram for the given beam:
Free-Body Diagram:
As we can see from the above diagram, the section has been drawn which passes through point b.
We have to determine the moment at point b using this section.
Now, we will write the equation for the moment of the section passing through point b as:
- 12(6) - 4(8) - (20)(12) - (32)(20) - (40.3)(12/2) = 0Mb = 1126.05 lb-ft
the moment at point b is 1126.05 lb-ft.
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Is science based off observations? Explain how observations are important to your experiment.
Answers
Answer:
Observation is essential in science. Scientists use observation to collect and record data, which enables them to construct and then test hypotheses and theories. Scientists observe in many ways – with their own senses or with tools such as microscopes, scanners or transmitters to extend their vision or hearing. These tools allow for more precise and accurate observations. Scientists also use equipment to measure things like radiation or pH – phenomena not directly observable.
Explanation:
What is the electric potential, i.e. the voltage, 0.30 m from a point charge of 6.4 x 10-C?
Answers
Answer:
V = 192 kV
Explanation:
Given that,
Charge, \(q=6.4\times 10^{-6}\ C\)
Distance, r = 0.3 m
We need to find the electric potential at a distance of 0.3 m from a point charge. The formula for electric potential is given by :
\(V=\dfrac{kq}{r}\\\\V=\dfrac{9\times 10^9\times 6.4\times 10^{-6}}{0.3}\\\\V=192000\ V\\\\V=192\ kV\)
So, the required electric potential is 192 kV.
Q/C S Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as the rate of change in velocity over distance. He chose the former, so let's use the name "vroomosity" for the rate of change of velocity over distance. For motion of a particle on a straight line with constant acceleration, the equation v= vi + at gives its velocity v as a function of time. Similarly, for a particle's linear motion with constant vroomosity k, the equation v=vi + kx gives the velocity as a function of the position x if the particle's speed is vi at x=0 .(b) Describe an example of such a motion or explain why it is unrealistic. Consider
Answers
The acceleration of the car is 75 km/h^2.
Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as the rate of change in velocity over distance. He chose the former, so let's use the name "vroomosity" for the rate of change of velocity over distance.
For motion of a particle on a straight line with constant acceleration, the equation v= vi + at gives its velocity v as a function of time. Similarly, for a particle's linear motion with constant vroomosity k, the equation v=vi + kx gives the velocity as a function of the position x if the particle's speed is vi at x=0.
Suppose that a car travels at a steady speed of 150 km/h. After 2 hours, it reaches its destination. Its initial speed is 0 km/h, and it travels for a total of 300 kilometers.
To compute the car's acceleration, divide its final velocity by the amount of time it took to get there. 150 km/h is the car's final velocity, and 2 hours is the time it took to get there. 150 km/h / 2 h = 75 km/h^2
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How do we represent Earth’s face?
Answers
Answer:
Human-driven changes in arrive utilize and arrive cover such as deforestation, urbanization, and shifts in vegetation designs moreover change the climate, coming about in changes to the reflectivity of the Soil surface (albedo), emanations from burning timberlands, urban warm island impacts and changes within the normal water cycle.
You throw an orange out a widow at a height of 12 meters upwards at an angle of 32 to the horizontal with an initial velocity of 3.5m/s.How long will the orange be in flight before it hits the ground? Round the answer to the nearest tenth.__ Seconds
Answers
Answer:
3 meters
Explanation:
add up dum boi
A current of 6.5 A flows through a battery for 3 minutes. How much charge passes through the battery in that time?
Answers
The amount of charge that passes through the battery in 3 minutes is 1170 coulombs.
When a current flows through a circuit, it carries electric charge with it. The unit of electric charge is the coulomb (C), which is defined as the amount of charge transported by a constant current of one ampere in one second.
Therefore, the amount of charge that passes through a battery in a certain time can be calculated by multiplying the current by the time, using the formula:
Q = I × t
where Q is the electric charge in coulombs, I is the current in amperes, and t is the time in seconds.
In this case, the current is 6.5 A and the time is 3 minutes, or 180 seconds. To convert minutes to seconds, we can multiply by 60. Therefore:
t = 3 min × 60 s/min = 180 s
Substituting into the formula, we get:
Q = 6.5 A × 180 s = 1170 C
This calculation is useful for understanding how much energy is consumed by the battery, as well as for calculating other properties of the circuit, such as the voltage or resistance.
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Communication satellites are often put in a geo-synchronous orbit, meaning they have an orbital period of 24 hours and stay over the same spot above the equator at all times. Given that the Earth has a mass of 5.97 x 1024 kg and a radius of 6.37 x 106 meters, determine the following: a. What is the orbital height of the satellite relative to the surface of the Earth
Answers
Answer:
h = 35857 km
Explanation:
A geosynchronous orbit can be defined as circular orbit which lies on the Earth's equatorial plane and follows the direction of the Earth's rotation in a period that's equal to the Earth's rotational period and thereby appearing motionless, at a fixed position in the sky relative to the ground observers.
We are given;
Radius of earth(R) = 6.37 x 10^(6) m
Mass of earth (Me) = 5.97 x 10^(24) kg
Gravitational constant = 6.67 × 10^(-11) m³/kg.s²
The earth has a rotational period of 24 hours per day. This gives in seconds
T = 24 × 60 × 60
T = 86400 s
Let's make the height of the orbit from Earth's surface to be h
Also, let ω be the uniform angular velocity in rad/s with which the satellite rotates in the geosynchronous orbit
Now, equating the centripetal force with the gravitational force gives us;
mω²(R + h) = G•Me•m/(R + h)²
m will cancel out. Also ω can be written as 2π/T
Thus,we now have;
(R + h) = ∛(G•Me•T²/(4π²))
Plugging in the relevant values, we have;
(R + h) = ∛(6.67 × 10^(-11) × 5.97 x 10^(24) × 86400²/(4π²))
(R + h) = 42227 Km
Since R = 6.37 x 10^(6)m = 6370 km
Thus;. h = 42227 - 6370 = 35857 km
How did the heavy elements originate and what did they create?
Answers
Heavy elements, such as gold, silver, and mercury, as well as the elements that make up the earth's core, such as iron and nickel, originated in the hearts of stars. They were created through the process of nuclear fusion, which occurs when the temperatures and pressures inside a star are high enough to overcome the electrostatic repulsion between the positively charged nuclei of atoms.
What are heavy element?When fusion occurs, the nuclei of the atoms merge, creating a new, heavier element. This process is called nucleosynthesis. The fusion of lighter elements, such as hydrogen and helium, produces heavier elements, such as carbon, oxygen, and neon.
Therefore, most heavy elements, such as gold and platinum, are created in supernovae, massive explosions that occur when the fuel in a star runs out, and the star collapses under its own gravity. The intense pressure and temperatures that are created during the collapse cause the nuclei of atoms to fuse together, creating elements with atomic numbers higher than iron.
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What type of meter is connected in
parallel with a resistor in a circuit, and why?
• A. An ammeter, to measure potential difference
• B. A voltmeter, to measure potential difference
• C. A voltmeter, to measure current
O. D. An ammeter, to measure current
Answers
Answer / Explanation:
B
Potential difference is measured using a device called a voltmeter . Just like ammeters, some types have a pointer on a dial, but most have a digital display. However, unlike an ammeter, you must connect the voltmeter in parallel to measure the potential difference across a component in a circuit.
Calculate the acceleration if you push with a 6 N horizontal force on a 8 kg block on a
horizontal friction free air table.
Answers
What is the the y value of the line y=3x +4 when x=2? *
Answers
Evidence:
X=2, so 3x would be 3 times 2
3 times 2 is 6
Now it’s Y= 6 + 4 which equals 10
Y = 10
A 400 n force accelerates an object at a rate of 3.6 m/s what is the mass
Answers
Answer:
F = 2.8 =16N
Explanation:
what was the history of a trebuchet
Answers
Answer:
The trebuchet was invented in France and was first reported to be used in 1124AD in the siege of Tyre (in present-day Lebanon) during the Crusades. As it was much more powerful than a catapult, a trebuchet became the siege weapon of choice.
Explanation:
Most people think that the trebuchet is a medieval weapon, but actually, it has its origins in ancient China. The ancient Chinese trebuchet could throw huge boulders up to 250 pounds, a distance of 200 feet. In addition, it was lightweight and mobile which was crucial as it could be moved around the battlefield with ease. The thing I love about the chinese trebuchet is that it pushes the boundaries of ancient engineering to create a ballistics revolution - a flexible, portable, killing machine.
Complete the sentence using word "parallel, perpendicular or sixty"
degrees.
The normal force is always_______
to the surface.
Answers
Answer:
Perpendicular
Explanation:
The normal force is always directed perpendicular to the surface.
The normal force is the support force that surfaces exerts on the objects in contact with them.
The force is needed to prevent a body from going through another.
Normal forces are projects perpendicular to the surface. This force is a very component when treating free body diagrams.Consider the circular motion of a positively charged particle in the plane of this paper, due to a constant magnetic field B~ which points out of the paper. Neglect the effect
Answers
Since the particle is spinning in a circle in a magnetic field, "When the Neglect the influence due to gravity in the direction of the particle is anti-clockwise."
What is the importance of Circular motion?
It is a positive particle, as far as we can tell that it is rotating in a magnetic field in a circle. The magnetic field's direction is clear to us. Since the magnetic force is travelling in a circle, we can then determine its direction.
When the force is directed toward the centre of the circle, that is what keeps the object moving in a circle.
We can apply the right-hand rule to determine the direction of the particle because the particle is positive and we know the direction of the magnetic field and the force.
Using the right-hand rule, the particle's thumb is pointing counterclockwise. The particle will then move counterclockwise.
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5 ohms resistors are connected in parallel, the equivalent resistance is?
Answers
The formula you use is 1/Rt= 1/R1+1/R2
A student takes notes in class.
Sound Waves
I. Created by a vibration
A. Vibration: something that causes air molecules to move
back and forth quickly and steadily
II. Move through a medium
A. Solid
B. Liquid
C. Gas
Which line of her notes contains an error?
I
I A
II B
II C
Answers
The wrong statement is that sound waves created vibration Option A.
What are sound waves?Sound is a type of waves that moves in compressions and rare factions. This implies that sound is a mechanical wave. Recall that a mechanical wave is one that requires a material medium for propagation. Now we know that if we set the medium into vibration, that is when the sound waves begins to vibrate. That brings us to the idea that it is the vibration that causes the sound waves and not the sound waves that creates the vibration.
Thus, knowing that sound is a mechanical wave which moves through solids liquids and gas and that the vibration of the source of sound is what causes the air to vibrate, we conclude that the wrong statement is that sound waves created vibration Option A.
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Answer:
a
Explanation:
Imagine that you are Robert Milliken, a physicist living in the early 1900s when Einstein first proposed the photon theory of light. Based on the wave theory of light, select the hypotheses from the list below that describe how the photoelectric effect experiment should turn out.If the light has enough intensity electrons will be ejected.If the intensity is larger, electrons will have more kinetic energy.Electrons will be emitted for low intensity light if we wait long enough.The light must have a minimum frequency for electrons to be ejected.If light has higher frequency the electrons will have more kinetic energy.Below the threshold frequency, no matter how long you wait, no electrons willbe emitted.After Milliken completed the experiment, did his findings support wave theory? Which hypotheses were supported? Justify your answer.If the light has enough intensity electrons will be ejected.If the intensity is larger, electrons will have more kinetic energy.Electrons will be emitted for low intensity light if we wait long enough.The light must have a minimum frequency for electrons to be ejected.If light has higher frequency the electrons will have more kinetic energy.Below the threshold frequency, no matter how long you wait, no electrons willbe emitted.
Answers
According to wave theory, electrons will have more kinetic energy if the intensity is higher.
(2) In order for electrons to be ejected, the light must have a minimum frequency.
(3) If the light has a higher frequency, the electrons will have more kinetic energy.
Based on Particle theory:
1- There must be a minimum amount of light .The frequency of elections will be decided.
Electrons will be ejected from a material when a light beam comes into contact with it because there is a minimum frequency in every material. The electrons will be refuted when the light reaches or exceeds this frequency. The term for this frequency is "Threshold frequency."
2. Electrons will have more Kinetic Energy if light has a higher frequency.
Yes. if the frequency of incidents. is more than the threshold recurrence, the leftover frequently will blocked out to K-E.
K. E = [4 h₀-hv]
3. No electron will escape below the threshold regardless of how long you wait.
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