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goldfiish [28.3K]
3 years ago
5

Consider a civilization broadcasting a signal with a power of 1.2×104 watts. The Arecibo radio telescope, which is about 300 met

ers in diameter, could detect this signal if it is coming from as far away as 110 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.
Physics
1 answer:
Talja [164]3 years ago
6 0
The same power (1.9×10^4 watts) gets diminished by Inverse square law 
<span>(ratio of distances)² </span>
<span>= (138/70000)² </span>
<span>= 3.886506 X 10^-6 . </span>
<span>This is the diminution factor for the given sensitivity of the telescope. But at 3.8865 millionth below the sensitivity its is far below detection; it needs to be enhanced by collecting the energy over an area so many times more (by an aperture multiplied by same factor) </span>
<span>1/[3.886506 X 10^-6] = 257298.88 </span>
<span>In other words the diameter should have the ratio of square root of this </span>
<span>(70000/138). </span>
<span>This multiplied by 300m dish gives </span>
<span>300 X (70000/138) = 152173.913 m = 152.1739 km. </span>
<span>This should be the aperture of the new telescope for detecting the signal.</span>
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Because Kinetic Energy(KE) is not the same as Momentum(P)

Kinetic Energy is a scalar(has magnitude only). For a body of mass M, velocity V:

KE = 0.5MV^2

The units of KE: Joules.

Energy is the ability to do work.

Momentum is not a form of energy.

Momentum is a vector(has magnitude and direction).

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Units of momentum: kg m/s

If you have rifles of mass 2, 4, 8, 16 kg, using the same cartridge, with the same load, barrel length(remember momentum of projectile is proportional to velocity), they all have the same recoil momentum.

But the kinetic energy of recoil would be inversely proportional to the mass of the gun.

Thus the 2kg gun(possible even in large powerful calibers due to modern materials like titanium etc), would have 8 times the recoil ENERGY of the 16kg gun.

A lot of confusion exists in America because of retention of old units, namely Foot Pounds(force) for KE, and Pounds(mass) Feet Per Second for Momentum(P). Because of the more awkward momentum units, a lot of old books had a bad habit of calling the momentum units Pounds Feet, leaving out the rest. Naturally this created confusion with Foot Pounds. Multiplication being commutative and all that:).

Remember that the momentum of the rifles is the same. But the ones with the highest recoil energy hurt the most.

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If momentum killed, then consider two dinosaur killer asteroids with the same masses and velocities, striking vertically at the same time antipodal points on the Earth’s surface. Total momentum delivered would be Zero. That would not make us safe at all:)

Similarly, being shot simultaneously at close range from opposite sides with a 5 round burst from each from two M4 assault rifles(by definition must be able to fire full auto) delivered in 0.3 seconds, would deliver zero momentum. But not zero harm.

Also, the recoil momentum of any firearm is equal to the mass of projectile x velocity + mass of propellant x exit velocity of propellant. This is obviously greater, often much greater, depending on range, than the striking momentum of the projectile at the target.

The recoil kinetic energy is vastly less than the kinetic energy of the bullet/projectile. Neglecting propellant contribution:

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That’s why you want to be behind the gun, and not in front.

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