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+--- Thread: How do you get from Fnet=Ïf-Ïo to Fg/Fb=Ïo/Ïf? (/thread-163419.html)
How do you get from Fnet=Ïf-Ïo to Fg/Fb=Ïo/Ïf? - mummy - 06-12-2014 12:07 AM
This has to do with buoyancy.
You can substitute Fnet for Fg-Fb.
Ï is not the letter p it is the symbol for density.
Ïo = density of an object
Ïf = density of the fluid
Fg = force of gravity
Fb = buoyant force
- markum - 06-12-2014 12:12 AM
Fnet = Fb - Fg since Fnet is the net force
Plugging into the first equation above, with object volume V and gravity g:
Fb - Fg = (pf - p0) * V * g
Dividing both sides by Fg = p0 * V * g
(Fb - Fg) / Fg = (pf - p0) * V * g / Fg
(Fb - Fg) / Fg = (pf - p0) * V * g / (p0 * V * g)
Fb/Fg - 1 = pf / p0 - 1
Fb/Fg = pf / p0
Done, although both sides need to be flipped