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A microwave has a 3cm wavelength. How many complete microwaves could you fit into a long wave radio wavelength of 1000m
A rock dropped into a well is heard to splash 2.30 seconds later. How deep is the well to the water's surface?
Assume that dwarf spherical galaxy has the so-called Plummer sphere potential Φ(r) = − (r0v02)/(sqr(r2+r02)), with constants v0 = 125 km/s, and r0 = 2.5 kpc (core radius). [This is the force per unit mass of the test particle, a.k.a. specific potential. The same way we talk about the specific force, which is simply force/mass or acceleration!] The objective is to fully characterize the system based on the potential. This is always easy in spherically symmetric systems. Find the specific force field created by specific potential Φ(r). Find asymptotic behavior of F and Φ with r at r <<r0 and at r → ∞. Note: by *behavior* we mean not only the value, but also functional form, in this case a certain power law. For example, 1/(1+x3 ) behaves like ≈ 1−x3/3 for x <<1 (first 2 terms of Taylor expansion; we can give only one leading term, but here it was so easy..), and like ∼ x −3 at large radii; the function goes to zero as the 3rd power of radius.
A sun-like star is torn apart by the tidal force (differential attraction) of a black hole of mass 1 million solar masses. It forms an accretion disk around a black hole which quickly flows into a black hole releasing 1/4 of its rest mass in the form of radiation during a time equal to one orbital period at the radius of the black hole horizon (Schwarzschild radius). What power in watts and in units of solar luminosity is emitted and for how long? Would a less massive black hole produce a smaller or larger luminosity? Is the released energy larger or smaller than the energy obtainable from the star via hydrogen fusion?
Galaxy NGC2300 has an flat disk dominating the visible light image. Surface brightness is given by
the exponential law
I(R) = I0 exp(−R/Rd)
where I0 is the central surface brightness, R distance from the center, and Rd = 4 kpc the exponential
radial scale of the disk (e-folding distance). The total luminosity of the galaxy equals L = (2.5·10^10)L(sun) .
Considering that the total luminosity is surface brightness I(R) integrated over the area of the
whole disk from R = 0 to R = ∞ (not over the radial distance, a mistake some people make!), compute
I0 (in units of L(sun) /pc^2)
I learned Kepler's second law which was about equal areas and we PROVED that law of areas mathematically and also in his third law we PROVED, mathematically, that the period squared is equal to semi-major axis cubed, but in his first law which is:"All planets move about the Sun in elliptical orbits, having the Sun as one of the foci" we did not PROVE this law. My instructor just said that "as L is constant, which implies that the orbit lies in a plane!" It just says that the orbit lies in a plane, not that it is elliptical which is actually the law. Should not we be proving that the orbit is elliptical with Sun as on of the foci? Or am I missing something?
An astronomical object has its mass 4 times the mass of earth and radius half of the radius of
earth. If acceleration due to gravity at earth is g, find its value at the surface of the astronomical
object.
an acceleration force of 500N changes an object from 40m/sec to 60m/sec in a distance of 100m. the mass is 25 kg. determine the force of friction acting opposite this force
what formula should I use to answer a question such as the one below when my normal formula doesn't fit:
'The radius of the Earth is 6400km, the height of a geostationary satellite is 35000km above the earth's surface. What is the speed of the geostationary satellite?'
If the temperature of the background radiation today is 3 K, at what time after the
birth of the universe was the temperature 10^15 K. Take the age of the universe as
15 × 10^9 years.