Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
Answer: Jupiter's mass
Explanation:
From Kepler's third law:
where T is the orbital period of a satellite, a is the average distance of the satellite from the Planet, M is the mass of the planet, G is the gravitational constant.
If the average distance of one of Jupiter's moons to Jupiter and its orbital period around Jupiter is given then mass of the Jupiter can be found:
The ideal gas constant is a proportionality constant that is added to the ideal gas law to account for pressure (P), volume (V), moles of gas (n), and temperature (T) (R). R, the global gas constant, is 8.314 J/K-1 mol-1.
According to the Ideal Gas Law, a gas's pressure, volume, and temperature may all be compared based on its density or mole value.
The Ideal Gas Law has two fundamental formulas.
PV = nRT, PM = dRT.
P = Atmospheric Pressure
V = Liters of Volume
n = Present Gas Mole Number
R = 0.0821atmLmoL K, the Ideal Gas Law Constant.
T = Kelvin-degree temperature
M stands for Molar Mass of the Gas in grams Mol d for Gas Density in gL.
Learn more about Ideal gas law here-
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Hi There!
Biotic factors are all the living things in an ecosystem, and abiotic factors are all of the non-living things in an ecosystem. So, they differ because they both mean opposite things.
Hope This Helps :)
