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: mass x height x gravitational field strength (g)
note: gravitational field strength (g) = 10 N/Kg
55 x 15 x 10 = 8250
gpe = 8250j
Explanation:
Answer:infrared radiation
Explanation:
Most remote control uses infrared radiation
The function of sleep theory supported by the illustration is sleep conserves and protects.
<h3>
Positive impact of sleep</h3>
From the first sentence, bats sleep a lot because they face little danger from predators and as such, they have a high-calorie diet of insects.
<h3>Negative impact of sleep</h3>
From the second sentence, cows sleep less, because they face more danger from predators and as such, they have a low-calorie diet of insects.
We can conclude that sleep helps to keep animal safe. Therefore, the correct option will be, "Sleep conserves and protects".
Learn more about important of sleep here: brainly.com/question/10224591
