Let's say I have a bucket filled with some liquid which is not compressible. I also have an object with the same density as this liquid. Since the liquid and object have the same density. Object would stay anywhere inside liquid. Let's assume our object is put in the center of this liquid. Now here comes the question: Would the bucket weigh more in this scenario? My reasoning says no(I will show it in free-body diagram), but I want to make sure of it.
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3$\begingroup$ What if you just added more water to the bucket, would it weigh more? $\endgroup$– RichCommented Apr 22 at 17:07
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$\begingroup$ It would weigh more but would there be buoyant force on that added water? $\endgroup$– f3rhd_Commented Apr 22 at 18:28
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$\begingroup$ What would happen if first you closed that water you added in a plastic bag? That could be your object with the same density as the water you put it in. It would be buoyant. $\endgroup$– RichCommented Apr 22 at 21:14
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2 Answers
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The bucket weighs more.
The red free-body diagram you draw is representative of the forces directly acting on the neutrally buoyant object, not on all of the forces internal/external to the bucket.
Consider where "$F_b$" comes from: the water is pushing up on the object due to the weight of water that is displaced by the object. The water as a whole has to support the weight of the ball, in the same way that if you were to hold a book above your head, the weight of the book is supported by the internal forces in the bones of your body. That force then has to travel into the floor so that the both of you don't start sinking!
If it is easier, consider it as a black box: when the ball is in the water the mass of the system is higher, which means regardless of internal forces the total weight of the system must be higher.
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$\begingroup$ Would the scenario be the same if it was some kind of gas not liquid? $\endgroup$– f3rhd_Commented Apr 22 at 18:11
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$\begingroup$ You mentioned the water has to support the weight of the ball. Doesn't buoyant force cancel out the mg? $\endgroup$– f3rhd_Commented Apr 22 at 18:25
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$\begingroup$ If you put a lid on the container and pumped in a gas to a high pressure, it would weigh more (as long as the container is rigid). You are adding more "stuff" to the container, and it doesn't particularly matter what that stuff is. The buoyant force cancels the weight of the ball specifically in the case of the ball. There has to be an equal and opposite force to allow for the buoyant force in the first place, and that force is put onto the walls of the container, and eventually onto whatever the container is sitting on. $\endgroup$– MatteoCommented Apr 22 at 19:17
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If the liquid/bucket exerts a buoyancy force on the object equal to its weight then by Newton's Third Law the object must exert an equal and opposite force on the liquid/bucket.
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$\begingroup$ I was thinking that the reaction force causes water to displace $\endgroup$– f3rhd_Commented Apr 22 at 18:19