Question

Question #3394d

Answer 1

`F_B = rho_WgV= (rho_W/rho_Bg)m_B`

Explanation:

Let's denote
`F_B larr` the buoyancy force
`Vlarr` the submerged volume,
`rho_W, rho_Blarr` density of water, density of the body
`m_W, m_B larr` mass of water, mass of the submerged part of the body (note, not the mass of the body it self)

Buoyancy is the weight of the volume of water being displaced by
partially immersed body; hence, it's directly related to the (total) mass of body. However, the mass of the submerged part of the body is related to the submerged volume by density. So we can reformulate the buoyancy force as the followings:

The buoyancy is expressed as:

`F_B = m_Wg = rho_WVg` ...............................................(1)

From the mass of the submerged part of the body:

`m_B= rho_BV rArr V=m_B/rho_B`..................................(2)

`F_B = rho_W(m_B/rho_B)g = (rho_W/rho_Bg)m_B`

However, buoyancy defined this way in not very practical because `m_B` is not as easily determined as it's submerged volume.w

The more practical form of buoyancy is Eq.(1)