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- Homework Statement
- An object floats in liquid. The depth of the object below the surface is d and its height above the water is h. The density of the ball is p_b and the density of the liquid is p_liq. What is the pressure at the bottom of the object? The pressure above the water is P_atm.

- Relevant Equations
- hydrostatic equation: dP/dz = -pg

Let's say there's an object floating in liquid. The depth of the object below the surface is π and its height above the water is β. The density of the ball is ππ and the density of the liquid is ππΏ. The pressure above the water is πππ‘π.

I understand this situation when only the density of the ball matters; you integrate to get P(z) = ππππ§ + C, and given the initial condition P(d) = πππ‘π. (pressure at water-air interface is atmospheric), C = πππ‘π - ππππ , so P(z) = ππππ§ + πππ‘π - ππππ

What I am confused about is how to find the pressure given the influence of the density of the liquid. I don't really understand why or how the density of the liquid affects the equation for pressure at all, besides that in order for the object to be floating, ππ< ππΏ. It seems like since you're only interested in the ball, so the only distance that matters is the distance of the ball under the water, and the only density relevant there

I understand this situation when only the density of the ball matters; you integrate to get P(z) = ππππ§ + C, and given the initial condition P(d) = πππ‘π. (pressure at water-air interface is atmospheric), C = πππ‘π - ππππ , so P(z) = ππππ§ + πππ‘π - ππππ

What I am confused about is how to find the pressure given the influence of the density of the liquid. I don't really understand why or how the density of the liquid affects the equation for pressure at all, besides that in order for the object to be floating, ππ< ππΏ. It seems like since you're only interested in the ball, so the only distance that matters is the distance of the ball under the water, and the only density relevant there

*would*be the one of the ball. Or do you take the ratio of the densities? Is it their difference? Why does the liquid matter at all?
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