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For both containers it is true that:

$p_{bottom}=p_{atm}+\rho gh$ and $F_{bottom}=a*p_{bottom} \iff F_{bottom}=a*p_{atm} + a\rho gh$

I do not know how a scale functions, but I guess that the only force it can count is the force by the liquid on the bottom of each container (the only surface that is in touch with the scale is the bottom of the container). Thus, if we measured the mass of these two masses of water (lets assume that the mass of the containers is negligible) it would appear to be the same in each case. Am I right?

Rontogiannis Aristofanis
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1 Answers1

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No, you're not right. The container with more mass on the right will weight more on the scale. Pressure always acts normal to a surface, and the pressure forces acting on the slanted walls of the container will have downward components, which exert net downward forces on the container. You must include these downward forces in the force balance on the container, and not just include the forces acting on the base of the container. When you do that, the total downward force of the liquid on the container will be just equal to the weight of the liquid.

Chet Miller
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