List at least three practices that have resulted from the impact factor. Argue which of these is most problematic and explain wh
1 answer:
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Answer:
x = 2.33 R from the center of mass of the smallest sphere.
Explanation:
Due to the symmetry of the spheres, the center of mass of any of them, is located just in the center of the sphere.
If we align the centers of the spheres with the x-axis, the center of mass of any of them will have only coordinates on the x-axis, so the center of mass of the system will have coordinates on the x-axis only also.
By definition, the x-coordinate of the center of mass of a set of discrete masses m₁, m₂, m₃, can be calculated as follows:
In this case, we need to get the coordinates of the center of mass of each sphere:
If we place the spheres in such a way that the center of the first sphere has the x-coordinate equal to its radius (so it is just touching the origin), we will have:
x₁ = 2*R
For the second sphere, the center will be located at a distance equal to the diameter of the first sphere plus its own radius, as follows:
x₂ = 4*R + R = 5*R
Finally, for the third sphere, the center will be located at a distance equal to the diameter of the first sphere, plus the diameter of the second sphere, plus its own radius, as follows:
x₃ = 4*R + 2*R + 3*R = 9*R
We can calculate the mass of each sphere (assuming that all are from the same material, with a constant density), as the product of the density and the volume:
m = ρ*V
For a sphere, the volume can be calculated as follows:
So, we can calculate the masses of the spheres, as follows:
m₁ = ρ*
m₂ = ρ*
m₃ = ρ*
The total mass can be calculated as follows:
M= ρ* * (8*r³ + r³ + 27*r³) =ρ*
* 36*r³
Replacing by the values, and simplifying common terms, we can calculate the x-coordinate of the center of mass of the system as follows:
As the x-coordinate of the center fof mass of the entire system is located at 7.33*R from the origin, and the center of mass of the smallest sphere is located at 5*R from the origin, the center of mass of the system is located at a distance d:
d = 7.33*R - 5*R = 2.33 R
Answer:
Effective temperature, Doppler velocity
Explanation:
Since star behave localy as a blackbody, Wíen's displacement law can be use in order to determine its effective temperature. From the spectrum it will be take the wavelength at which is the peak of emission greater in the continuum
Then, the maximum peak of emission () will be replace in the next equation of the Wien's displacement law:
(1)
Where T is the effective temperature of the star.
Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect).
By using that shift in the spectral lines it can be determine the Doppler velocity.
(2)
Where is the wavelength shift,
is the wavelength at rest, v is the velocity of the source and c is the speed of light.