Rotation Problem: Earth lengths/Apparent Weights

[a Vortex]

Homework Statement

A friendly Brazilian has a mass of 150 kg. Being in Brazil, he rotates in a circle around the center of the Earth once per day, The radius of this circle (which is essentially the radius of the Earth) is 6.40 x 10^6 m.

I have found that the normal force is 1.4649 x 10^3.

Homework Equations

a_c = v²/r , centripetal acceleration
$\Sigma$F=ma
v = (2$\pi$r)/T , T is period of one revolution

The Attempt at a Solution

I only got to mg - F_n = ma_c
I know what the apparent weight is but I'm not sure about the normal force. If I can find this, then I can then find a_c, v, and then T to find about the length of day.

 

[ehild]

What is the question?

ehild

 

[a Vortex]

Sorry forgive me. The question is: How long would a day have to be for the Brazilian's apparent weight to be 1.46 x 10^3 N?

Btw, the answer should be about 6.16 x 10^4 sec or 17.1 hours.

 

[ehild]

The weight is equal to the force the man presses a horizontal support - scales, ground, chair ... So its is the same as the normal force.

ehild