Answer:
The answer is given below
Explanation:
u is the initial velocity, v is the final velocity. Given that:
a)
The final velocity of cart 1 after collision is given as:
The final velocity of cart 2 after collision is given as:
b) Using the law of conservation of energy:
The highest point<span> of the </span>pendulums<span> swing is when the potential energy is at its </span>highest<span> and the </span>kinetic energy<span> is at its lowest.</span>
The higher density allows the protogalactic clouds to cool faster and form an elliptical galaxy rather than a spiral galaxy.
In physical cosmology, a protogalaxy or protogalactic cloud , which could also be called a "primeval galaxy", is a cloud of gas which is forming into a galaxy. It is believed that the rate of star formation during this period of galactic evolution will determine whether a galaxy is a spiral or elliptical galaxy; a slower star formation tends to produce a spiral galaxy. The smaller clumps of gas in a protogalaxy form into stars.
Composition
Since there had been no previous star formation to create other elements, protogalaxies would have been made up almost entirely of hydrogen and helium. The hydrogen would bond to form H2 molecules, with some exceptions. This would change as star formation began and produced more elements through the process of nuclear fusion.
Mechanics
Once a protogalaxy begins to form, all particles bound by its gravity begin to free fall towards it. The time taken for this free-fall to conclude can be approximated using the free-fall equations. Most galaxies have completed this free-fall stage to become stable elliptical or disk galaxies, the disks taking longer to fully form. The formation of galaxy clusters takes much longer and is still in progress now.
This stage is also where galaxies acquire most of their angular momentum. A protogalaxy acquires this due to gravitational influence from neighbouring dense clumps in the early universe, and the further the gas is away from the centre, the more spin it gets.
Learn more about protogalactic clouds here : brainly.com/question/28166070
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Answer:
a♦1 E_average = n E₀ / 2
, b) E_average= infinity
Explanation:
The energy values form an arithmetic series, whose sum is
S = n (a₁ + aₙ) / 2 = n (2a₁ + (n-1) r)/ 2
Where n is the number of terms, a₁ is the first term, aₙ the last term and r is the difference between two consecutive numbers in the series
r = 2E₀ - 0 = 2E₀
Therefore the sum is
S = n (0 + n E₀) / 2
S = n² E₀ / 2
The average value is
E_average = S / n
E_average = n E₀ / 2
b) the case of harmonic oscillation
We have two possibilities.
- if we take a finite number and terms gives the same previous value
- If we take an infinite number of fears the series gives infinity and the average is also infinite
E_average= infinity
