What is the ultimate source of energy that makes the Sun shine?
1 answer:
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(a) 0.448
The gravitational potential energy of a satellite in orbit is given by:
where
G is the gravitational constant
M is the Earth's mass
m is the satellite's mass
r is the distance of the satellite from the Earth's centre, which is sum of the Earth's radius (R) and the altitude of the satellite (h):
r = R + h
We can therefore write the ratio between the potentially energy of satellite B to that of satellite A as
and so, substituting:
We find
(b) 0.448
The kinetic energy of a satellite in orbit around the Earth is given by
So, the ratio between the two kinetic energies is
Which is exactly identical to the ratio of the potential energies. Therefore, this ratio is also equal to 0.448.
(c) B
The total energy of a satellite is given by the sum of the potential energy and the kinetic energy:
For satellite A, we have
For satellite B, we have
So, satellite B has the greater total energy (since the energy is negative).
(d)
The difference between the energy of the two satellites is:
The electron is accelerated through a potential difference of 
, so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B:
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B: