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
Answer: An jack makes changing a tire easier because it lifts up the car to get the tire off of the ground.
Explanation:
Answer:
C) Burmese pythons lack natural predators and can utilize a wide variety of food sources in the Everglades.
Explanation:
Due to it being an invasive specie (naturally found in South Asia), and also one of the five largest species of snakes in the world, the Burmese pythons lack natural predators in this new territories.
The Burmese viper is also an opportunistic hunter and would eat anything it can overpower, it easily made a wide range of food varieties in these swamps.
SI will always be in metric, so the answer is D. Meter.
