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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 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?
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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