Help with circular motion of zero gravity

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Homework Help Overview

The problem involves determining the duration of a day required for a person at the Earth's equator to experience a reading of zero on a bathroom scale, indicating a state of weightlessness. The context is circular motion in a gravitational field.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to set up force equations related to centripetal force and gravitational force but encounters difficulty in determining the necessary variables. Some participants clarify the relationship between centripetal force and weight, suggesting that mass cancels out in the equations. Others seek further clarification on the proportionality of mass in the equations.

Discussion Status

The discussion is active, with participants providing insights into the relationship between centripetal force and gravitational force. Clarifications about the cancellation of mass in the equations have been offered, and there is an ongoing exploration of the mathematical relationships involved.

Contextual Notes

Participants are working with the assumption that the centripetal force must equal the gravitational force for the person to feel weightless. There is a focus on the radius of the Earth and the gravitational acceleration as key parameters in the discussion.

koopa347
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Homework Statement


How long would the day have to be in order that for a person standing at the equator of the Earth would see a bathroom scale that she is standing on read zero?
This is all the info that is given.

Homework Equations


Fc=m(v^2)/r


The Attempt at a Solution


I setup my force equations so the sum of f=Fc=Fn-Fg. I then found out the radius of the earth, and this is where i got stuck , i know that the radius of the Earth is 6377.34km, but how do i figure out v and m; if v has to be greater than Earth's current centripetal force?
 
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You're spinning so fast that gravity is just barely providing enough force to keep you in your circular "orbit." In other words, the centripetal force required for this orbit is equal to your weight (which is why you feel no normal force, which as you've correctly stated, is the difference between the two).

If the centripetal force is equal to the weight, and both are proportional to m, then m cancels from both sides of the equation (the mass of the object in the orbit doesn't matter). Hence you're finding the speed at which the centripetal acceleration equals g. You know r. You know g. You just have to solve for v.
 
What do you mean by both are proportional to m? Could you type out an equation that shows this step? Do you just mean
(m)(9.8)=mv^2/r
so those m's cancel, so we know now that we're left with 9.8=v^2/r?
 
koopa347 said:
What do you mean by both are proportional to m? Could you type out an equation that shows this step? Do you just mean
(m)(9.8)=mv^2/r
so those m's cancel, so we know now that we're left with 9.8=v^2/r?

Yes, that's exactly what I meant. To be proportional to "x" means to be equal to "x" multiplied by some factor.
 

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