# Reaction force for buoyancy?

According to Newton's 3rd law each force (action) has a counter-force (reaction).

What is the reaction (counter-force) of buoyancy?

We call buoyancy a force, but really, what is it ? It's only gravity. This is only a difference in the gravity force applied to the water and the gravity force applied to your object. So buoyancy is not a force applied by the water to the object. It's gravity applied differently to the water and the object by the earth. Here, the real force is gravity.

I'll attempt to explain the nature of buoyant force with an example. Consider a cube with side $l$ and density $500kg/m^3$, is submerged completely in water. Let the mass of this cube be $m_{cube}=1kg$ We know that density of water, $\rho_{water}=1000kg/m^3$

Now,

1. Water above the cube exerts a force equivalent to its weight. The cube exerts an equal and opp. force on water above.

$$V_{water}=l^{2}h$$ $$\rho_{water}=1000kg/m^3$$ $$mass_{water}=\rho V=1000l^{2}h$$ $$\therefore F=Weight_{water}=1000l^{2}hg$$ $$~~~~~~~~~~~~~~~~~=9800l^{2}h$$

1. Upward force from beneath the cube : Volume of water at $h+l$ (in the figure) exerts a force on water beneath $h+l$. As a result, water below $h+l$ exerts an equal and opposite force on water at $h+l$ and on the cube too, upwards.

$$\text{Upwards force} = \rho ghl^{2}$$ $$~~~~~~~~~~~~~~~=(1000h+1000l)(gl^{2})$$ $$~~~~~~~~~~~~~~~=9800hl^{2}+9800l^{3}$$

Now, by calculating net force on the block, we can obtain the buoyant force. $$Buoyant force = (9800hl^{2}+9800l^{3})-9800hl^{2}~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=9800l^{3}=\text{Weight of the fluid(water) displaced.}$$ $$\text{Volume of the cube}=\frac{m}{\rho} = \frac{1}{500} = l^{3}$$ $$\text{Buoyant force on the cube}=9800l^{3}=\frac{9800}{500}=19.6\text{N}$$

CONCLUSION

Therefore, as Pierre said, buoyant force is the result of Gravity only. If you need help in visualising buoyancy, PhET's Buoyancy Simulation can come in handy.

The weight of a mass m is m*g, this weight acting in the downward direction will cause a pressure on the fluid below the body. So the fluid must give a reaction force on the body according to Newton's third law. So the reaction force is the buoyant force.

## protected by Qmechanic♦Mar 12 '16 at 20:13

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