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
The acceleration of this item will remain constant if I double the force and double the mass.
<h3>What does acceleration mean ?</h3><h3 />
The rate at which a moving object's speed and direction change over time. When something moves faster or slower, it is considered to be accelerating. Motion on a circle accelerates even while the speed is constant because the direction is always changing.
- If an object is accelerating and moving in the appropriate direction, it has positive acceleration. The speeding automobile in the first scenario showed positive acceleration. The car is moving forward and accelerating in the same direction as the acceleration.
Learn more about Acceleration here:
brainly.com/question/605631
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energy never disappears, for example, if you give some kinetic energy to a ball and it stops few seconds later, friction steals this energy to ground which ball was going on. "Law of Conservation of Energy" tell us that energy can't disappear
Answer: D
Explanation: :) Just took the quizz
