Answer:12.8 ft/s
Explanation:
Given
Speed of hoop 
height of top 
Initial energy at bottom is
Where m=mass of hoop
I=moment of inertia of hoop
=angular velocity
for pure rolling 
Energy required to reach at top
Thus 512.2 m is converted energy is spent to raise the potential energy of hoop and remaining is in the form of kinetic and rotational energy
Therefore
Answer:
F = GMmx/[√(a² + x²)]³
Explanation:
The force dF on the mass element dm of the ring due to the sphere of mass, m at a distance L from the mass element is
dF = GmdM/L²
Since the ring is symmetrical, the vertical components of this force cancel out leaving the horizontal components to add.
So, the horizontal components add from two symmetrically opposite mass elements dM,
Thus, the horizontal component of the force is
dF' = dFcosФ where Ф is the angle between L and the x axis
dF' = GmdMcosФ/L²
L² = a² + x² where a = radius of ring and x = distance of axis of ring from sphere.
L = √(a² + x²)
cosФ = x/L
dF' = GmdMcosФ/L²
dF' = GmdMx/L³
dF' = GmdMx/[√(a² + x²)]³
Integrating both sides we have
∫dF' = ∫GmdMx/[√(a² + x²)]³
∫dF' = Gm∫dMx/[√(a² + x²)]³ ∫dM = M
F = GmMx/[√(a² + x²)]³
F = GMmx/[√(a² + x²)]³
So, the force due to the sphere of mass m is
F = GMmx/[√(a² + x²)]³
B.)a car that rounds a curve at a constant speed
A big part of the reason that mirrors are seldom if ever used to generate
electricity is the simple fact that there is no way to generate electricity using
mirrors. They are as useless for the purpose as smoke is, although there are
those who have used both items simultaneously to create the impression that
they have succeeded in that attempt.
