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KatRina [158]
3 years ago
9

Define the difference between the Newtonian mechanics and a Lagrangian mechanics

Physics
1 answer:
Snowcat [4.5K]3 years ago
3 0

Answer:

The difference between Newtonian and Lagrangian mechanics is summarized below:

In Newtonian mechanics the fundamental thing of conceren is force that acts on a object. According to newton's laws of motion when a force acts on a body it produces acceleration and the acceleration is then related to velocity and position of the object. The basic equation of Newtonian mechanics are

\sum (\overrightarrow{F})=mass\times \overrightarrow{a}

where

'F' is the vector sum of all the forces that act on the object.

'a' is the acceleration that is produced in the body as a result of the forces.

The acceleration is related to the position of the body as

\frac{d\overrightarrow{r(t)}}{dt}=\overrightarrow{a}\\\\\overrightarrow{r}(t)=\int \overrightarrow{a}(t)dt

Thus we can know the position of any object if we know the acceleration of the object and the boundary condition of the object.

However in Lagrangian mechanics the basic parameter upon which the motion of the object is defined is the  a mathematical definition of position and change in position, thus an object can take an arbitrary path while travelling between 2 positions but only that path is physically possible in which the change in potential energy is minimum or takes least amount of work to be done this is known as principle of least work.

Mathematically

S=\int L(t)dt

and we try to minimize the work that needs to be done thus giving us the path taken by the particle.

The equations of motions can be derived from this basic premise of Lagrangian mechanics.

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: 1 khối khi lý tưởng nhận được nhiệt lượng 200J, khi đó khí nở ra đẩy pittong bằng 1 công 80J.
Ratling [72]

Answer:

DU = 120 Joules

Explanation:

Given the following data;

Quantity of energy = 200 J

Work = 80 J

To find the change in internal energy;

Mathematically, the change in internal energy of a system is given by the formula;

DU = Q - W

Where;

DU is the change in internal energy.

Q is the quantity of energy.

W is the work done.

Substituting into the formula, we have;

DU = 200 - 80

DU = 120 Joules

3 0
3 years ago
A vertical cylindrical tank 10 ft in diameter, has an inflow line of 0.3 ft inside diameter and an outflow line of 0.4 ft inside
neonofarm [45]

Answer:

\frac{dh}{dt} = 1.3 \times 10^{-3} \frac{ft}{s}, level is rising.

Explanation:

Since liquid water is a incompresible fluid, density can be eliminated of the equation of Mass Conservation, which is simplified as follows:

\dot V_{in} - \dot V_{out} = \frac{dV_{tank}}{dt}

\frac{\pi}{4}\cdot D_{in}^2 \cdot v_{in}-\frac{\pi}{4}\cdot D_{out}^2 \cdot v_{out}= \frac{\pi}{4}\cdot D_{tank}^{2} \cdot \frac{dh}{dt} \\D_{in}^2 \cdot v_{in} - D_{out}^2 \cdot v_{out} = D_{tank}^{2} \cdot \frac{dh}{dt} \\\frac{dh}{dt}  = \frac{D_{in}^2 \cdot v_{in} - D_{out}^2 \cdot v_{out}}{D_{tank}^{2}}

By replacing all known variables:

\frac{dh}{dt} = \frac{(0.3 ft)^{2}\cdot (5 \frac{ft}{s} ) - (0.4 ft)^{2} \cdot (2 \frac{ft}{s} )}{(10 ft)^{2}}\\\frac{dh}{dt} = 1.3 \times 10^{-3} \frac{ft}{s}

The positive sign of the rate of change of the tank level indicates a rising behaviour.

6 0
3 years ago
g An airplane is flying through a thundercloud at a height of 1500 m. (This is a very dangerous thing to do because of updrafts,
Stolb23 [73]

Answer:

523269.9\ \text{N/m}

Explanation:

q = Charge

r = Distance

q_1=25\ \text{C}

r_1=3000\ \text{m}

q_2=40\ \text{C}

r_2=850\ \text{m}

The electric field is given by

E=E_1+E_1\\\Rightarrow E=k(\dfrac{q_1}{r_1^2}+\dfrac{q_2}{r_2^2})\\\Rightarrow E=9\times 10^9\times (\dfrac{25}{3000^2}+\dfrac{40}{850^2})\\\Rightarrow E=523269.9\ \text{N/m}

The electric field at the aircraft is 523269.9\ \text{N/m}

4 0
3 years ago
Activity that uses 150 calories of energy per day, or 1,000 calories per week, describes ___________.
serious [3.7K]
Moderate physical activity
8 0
4 years ago
The speed at which an object falls and the acceleration at which it falls are
allochka39001 [22]

No, the speed at which an object falls is not equal to the acceleration at which it falls.

Answer:

Option B

Explanation:

Speed is defined as how fast an object can cover a specific distance and in what time it covers. So it is measured as the ratio of distance covered to the time taken to cover that distance. While acceleration is the rate of change of velocity. Moreover, speed is a scalar quantity and acceleration is a vector quantity. So most of the times, the direction will play an important role in the varying values of speed and acceleration. Also, acceleration of an object will depend upon the force and mass of the object. Thus, speed and acceleration will not attain same value always.

6 0
3 years ago
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