- #1
MPat
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Homework Statement
Earth is a spherical object, which completes a full rotation every 24 hours. How long should the day on Earth be so that an object at the equator is able to float freely above the ground?
Homework Equations
v=2πr/T
Fr=mv^2/r
v=velocity
r= radius
T = time for comleting 1 revolution in seconds
Fr= centripetal force/force in a radial direction
The Attempt at a Solution
1 revolution in 24 hours so T = 24x3600sec = 86400
Fr=mv^2/r
Fr at the Earth is equal to mg
mg=mv^2/r
mass cancels out
g=v^2/r Eq. 1
v=2πr/T
vT/2π = r Eq. 2
Sub Eq. 2 into 1
g=v^2/(vT/2π)
re arrange the equation to
v=gT/2π
v= 9.8*86400/2π
v=134 760m/s
Thats where I'm at so far...I'm just not sure if that's correct...and if so where to go from there.