I believe the evidence for this theory
is that:
The orbits surrounding Jupiter are
highly elliptical which are off the plane of the ecliptic, and many of these moons
are retrograde. This is very unlikely for moons or satellites which are formed during
the planetary accretion. Hence comes the theory.
You know that when the displacement is equal to the amplitude (A), the velocity is zero, which implies that the kinetic energy (KE) is zeero, so the total mechanical energy (ME) is the potential energy (PE).
And you know that the potential energy, PE, is [ 1/2 ] k (x^2)
Then, use x = A, to calculate the PE in the point where ME = PE.
ME = PE = [1/2] k (A)^2.
At half of the amplitude, x = A/2 => PE = [ 1/2] k (A/2)^2
=> PE = [1/4] { [1/2]k(A)^2 } = .[1/4] ME
So, if PE is 1/4 of ME, KE is 3/4 of ME.
And the answer is 3/4
Answer:
g=GM/R^2
Universal Gravutation Constant:
f=GM×m/R^2
Force can be also expressed as
f=m×g
so,
mg=GMxm/R^2
The m gets cancelled so
g=GM/R^2
The applicable equation:
P = F/A
P = pressure
F = Force or weight
A = surface area
Pressure on each cylinder = (W/n)/A
Where n = number of cylinders. Additionally, pressure in the reservoir is equivalent to the pressure in each cylinder.
Net pressure = 75 - 14.7 = 60.3 psi
Therefore,
60.3 = (W/n)/A = (450/n)/(πD^2/4) = (450/n)/(π*1.5^2/4) = (450/n)/(1.7671)
60.3*1.7671 = 450/n
106.03 = 450/n
n = 450/106.3 = 4.244 ≈ 5
The number of cylinders is 5.
