NextStep Physics Chapter 5 Fluids

[kim3]

Hello,
My question is referring to the passage based question at the end of chapter 5 on fluids. Question 3 is asking for the relationship b/t buoyant force and weight of a bulb that is suspended in the middle of the surrounding fluid of Galileo's thermometer. I'm very confused why this answer is B and not C? I understand since it is suspended the net force in the vertical direction is equal to zero. But how can the buoyant force be less than the weight and still have the bulb suspended and not sinking directly to the bottom?? How can the net force be equal but the forces be different at the same time?

Any help would be much appreciated

[NS_Tutor_Andrew]

Hi kim3,

Thanks for the excellent question! Your point makes a lot of sense. The trick here is that we have to account for the fact that the passage tells you that there is a slight pressure differential between the top and bottom of the bulb that can be formulated as ΔP = ρgh. In most setups where we analyze buoyancy, we would neglect this factor, but since the passage explicitly tells us that it's relevant, we have to account for it.

We have two forces pushing down: the weight and the pressure on the top of the bulb from the surrounding water. We also have two forces pushing up: the buoyant force and the pressure on the bottom of the bulb from the surrounding water. We know that the sum of upward forces and the sum of downward forces have to cancel out. We also know that the magnitude of the pressure on the top of the bulb from the surrounding water is going to be less than the corresponding force from the water on the bottom of the bulb, because the term h, referring to the depth of submersion or the height of the fluid on top of the object, will be lower on the top than on the bottom. Combining this information w/ the fact that the weight is not going to change, we can conclude that the buoyant force has to be slightly smaller in magnitude than the weight for everything to balance out.

This is a little confusing to follow verbally, so I've attached a picture to help clarify things. In the picture I've drawn the discrepancy in the forces as relatively large to make things visually clearer, but keep in mind that in reality, the pressure differential would be quite small in absolute terms.

imageedit_2_5231430482.png

(35.72 KiB) Not downloaded yet

Hope this helps to clarify things!