Answer:
2f
Explanation:
The formula for the object - image relationship of thin lens is given as;
1/s + 1/s' = 1/f
Where;
s is object distance from lens
s' is the image distance from the lens
f is the focal length of the lens
Total distance of the object and image from the lens is given as;
d = s + s'
We earlier said that; 1/s + 1/s' = 1/f
Making s' the subject, we have;
s' = sf/(s - f)
Since d = s + s'
Thus;
d = s + (sf/(s - f))
Expanding this, we have;
d = s²/(s - f)
The derivative of this with respect to d gives;
d(d(s))/ds = (2s/(s - f)) - s²/(s - f)²
Equating to zero, we have;
(2s/(s - f)) - s²/(s - f)² = 0
(2s/(s - f)) = s²/(s - f)²
Thus;
2s = s²/(s - f)
s² = 2s(s - f)
s² = 2s² - 2sf
2s² - s² = 2sf
s² = 2sf
s = 2f
Explanation:
The principle of an electric motor is based on the current carrying conductor which produces magnetic field around it. A current carrying conductor is placed perpendicular to the magnetic field so that it experiences a force.
The largest electric motors are used for ship propulsion, pipeline compression and pumped-storage applications with ratings reaching 100 megawatts. Electric motors are found in industrial fans, blowers and pumps, machine tools, household appliances, power tools and disk drives.
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Answer:
Tidal heating
Explanation:
Tidal force is the ability of a massive body to produce tides on another body. The tidal force depends on the mass of the body that produces the tides and the distance between the two bodies.
Tidal forces can cause the destruction of a satellite that orbits a planet or a comet that is too close to the Sun or a planet. When the orbiting body crosses the "Roche boundary", the tidal forces along the body are more intense than the cohesion forces that hold the body together.
Tidal friction is the force between the Earth's oceans and ocean floors caused by the gravitational attraction of the Moon. The Earth tries to transport the waters of the oceans with it, while the Moon tries to keep them under it and on the opposite side of the Earth. In the long term, tidal friction causes the Earth's rotation speed to decrease, thus shortening the day. In turn, the Moon increases its angular momentum and gradually spirals away from Earth. Finally, when the day equals the orbital period of the Moon (which will be about 40 times the length of the current day), the process will cease. Subsequently, a new process will begin when the power to raise tides from the Sun takes angular momentum from the Earth-Moon system. The Moon will then spiral towards Earth until it is destroyed when it enters the "Roche boundary."
<u>Tidal heating
</u>
It is the warming caused by the tidal action on a planet or satellite. The most important example of tidal heating in the Solar System is the effect of Jupiter on its Io satellite, in which the tidal effects produce such high temperatures that the interior of the satellite melts, producing volcanism.
