Tangential velocity of the earth

AI Thread Summary
To determine the speed required for a person at the equator to weigh 3/4 of their normal weight, the discussion focuses on the relationship between tangential velocity and gravitational force. The initial equation used is based on centripetal acceleration, where the forces acting on the person are balanced. The attempt to solve the problem reveals a sign error leading to an incorrect final equation. Clarifications are sought on the correct interpretation of normal force and the equations needed to find the final tangential velocity. The conversation emphasizes the importance of accurately applying physics principles to solve the problem.
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Homework Statement


Determine the speed with which the Earth would have to turn to rotate on its axis so that a person on the equator would weigh 3/4 as much


Homework Equations


VT=r*ω ; Vi=469 m/s is tangential velocity of earth

ƩF=M*ac=m*Vt^2/r



The Attempt at a Solution



The positive direction is toward the center of the earth.

From ƩF=m*ac

Initial: m*g-Ni=m*Vi^2/r

Final: 3/4m*g-Nf=m*Vf^2/r

Since m*g is the same for initial and final state I assume that Ni=Nf

Therefore:3/4m*g-[mg-m*Vi^2/r]=m*Vf^2/r or

Vf=Sqrt(Vi^2-r*g/4)

I have a sign error. I end up taking the square root of a negative number but the physics looks OK. Suggestions?
 
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Nf is to be 3/4 of what? And what equation tells you what it will actually be? (Your 'Final' equation is completely wrong.)
 
OK, Final:m*g-3/4*N=m*Vf^2/r
 
Looks right, if N is what you wrote as Ni previously,
 

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