fluidistic
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And to solve a physics problem, it feels like a plug and chug with not the right formulae, making a stupid assumption and giving a result that, humanly intuitively I hope, isn't right at the first glance.
fluidistic said:Please solve the following physics problem "How many times faster would have the Earth to spin for someone based in NYC feel weightless?"
chatGPT said:In order for someone based in NYC to feel weightless, the gravitational force between that person and the Earth must be balanced by a centrifugal force. This can be achieved if the Earth's rotation speed is increased.
The formula for centrifugal force is:
F = m * r * w^2
where F is the centrifugal force, m is the mass of the object, r is the distance from the axis of rotation, and w is the angular velocity (in radians per second).
For a person standing on the surface of the Earth, r is equal to the radius of the Earth, which is approximately 6,371 km.
The formula for gravitational force is:
F = G * m1 * m2 / r^2
where F is the gravitational force, G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the person, and r is the distance between the person and the center of the Earth.
For a person standing on the surface of the Earth, r is approximately equal to the radius of the Earth plus the person's height, which we'll assume to be 1.8 meters.
In order for the person to feel weightless, the centrifugal force must be equal in magnitude to the gravitational force. Therefore:
m * r * w^2 = G * m1 * m2 / r^2
Simplifying this equation, we get:
w^2 = G * m1 / r^3
Substituting in the values for G, m1, and r, we get:
w^2 = 3.986 * 10^14 m^3/s^2 / (6,371,000 + 1.8)^3 m^3
Solving for w, we get:
w = 7.905 * 10^-5 radians per second
The current angular velocity of the Earth is approximately 7.292 * 10^-5 radians per second, so the Earth would need to spin approximately 1.08 times faster for someone based in NYC to feel weightless.