Answer:
Explanation:
Hi!
In order to obtain the Lagrangian of the system we must first write the Kinetic and Potential Energies. Lets orient our axes such that the axis of the cone coincide with the z axis. In cilindrical coordinates we have
- (1)
But, since the particle is constrained to move on the surface of the cilinder, we have the following relation between r and z:
or:
- (2)
and:
replacing (2) in (1) we obtain:
- (3)
Now the kinetic energy is given as:
- (4)
And the potential energy is given by:
So the Langrangian is given by:
And the equations of motion are:
For θ
For r
Obtained from the Euler-Langrange equations
Here the conserved quantity is given by the first equation of motion, namely:
Which is the magnitude of the angular momentum
B 10,000 - 30,000 K Blue-white stars
A 7,500 - 10,000 K White stars
F 6,000 - 7,500 K Yellow-white stars
G 5,000 - 6,000 K Yellow stars (like the Sun)
The lowest temperature stars are red while the hottest stars are blue. Astronomers are able to measure the temperatures of the surfaces of stars by comparing their spectra to the spectrum of a black body.
There is a limited amount of energy in the universe since it cannot be destroyed or created only transferred. This being said, eventually the universe will have expanded to vastly that all of its energy will be spread too thin for any form of life to be possible.
Answer: screen
A mixture of sand, salt and iron can be separated using magnet, filter paper and water. Iron being a magnetic material, can be separated using magnet. The rest of the mixture, salt and sand can be mixed in water. The salt would dissolve in water but sand would not because sand is insoluble in water. This mixture can be filtered using a filter paper. The filter has very minute openings through which sand would not pass through and get separated. Then, salty water can be heated. The water would evaporate leaving behind salt.
In this whole process, screen would not be useful because it would depend on the size of the sand particles and available screen.