Upthrust

starwars32

Hi.. Can someone explain when will upthrust change? cos i come across books saying that upthrust will not change when two objects of different density but same material are placed in the same fluid. I also come across that upthrust will not change when same objects are being transferred from liquid a of different density to liquid b of another density, the upthrust also will remain same. Can some one pls explain to me when and when will upthrust not change? Under wad conditions thanks! I thought that upthrust is dependent on density of liquid? as U= Vrollg?

arkofnoah

upthrust is calculated using the archimedes principle. the magnitude of upthrust is the same as the weight of the fluid displaced.

so of course it depends on the volume of fluid displaced (and hence the volume of the object that displaces the fluid) and density of fluid displaced. Note that the density, shape, mass or density of the object does not affect the magnitude of upthrust. Only the volume of the immersed object will affect the magnitude of upthrust. So a styrofoam cube and a metal cube of the same volume will experience the same upthrust, but of course the metal cube has a greater weight than the upthrust and the net force is downwards and it sinks. The styrofoam cube has a smaller weight and therefore it will only sink to the extent that the upthrust (= weight of the fluid displaced) = its own weight, and it will just float at this half-submerged position.

starwars32

so the positioning of the objects does not determine the magnitude of the upthrust ? cos different density?
Next qn: a lot of people say that under different fluids, the upthrust will change. But wad about for the same object, at first u put it in fresh water of density 1, and then u shift it to sea water of density 2, the upthrust will change?

arkofnoah

Yes positioning doesn't affect upthrust, as long as the submerged volume is the same. The positioning only affects the fluid resistance/drag force as the object moves through the water, which isn't relevant here.

Yes. Assuming that the volume of the displaced fluid is the same, if the density doubles, the weight of the displaced fluid also doubles and therefore the upthrust doubles as well. Upthrust is proportional to the density of the fluid.

starwars32

Ok nvm, here is the qn: a ship with uniform cross-sectional area A is floating in the sea. THe ship then unloads its cargo and rise a distance y. Given the density of sea water is Psea water, find the weight of the cargo W in terms of Pseawater, A, Y and g where g is the acceleration due to gravity.
ANs: AgyP seawater

Another identical ship carrying the same cargo is floating in fresh water. The ship then unloads its cargo and rises a distance z. Given that the density of fresh water is Pfresh water, find the weight of the cargo W in terms of Pfresh water, A, z and g.
Ans: AgzP freswater

Hence find the ratio of Pseawater/Pfreshwater in terms of y and z.
Ans : Pseawater/ Pfreshwater= z/y

Okay here is the gist of the qn: Suggest whether the upthrust in the fully laden ship will change when the ship moves from fresh water to sea water.
Ans given was no.

arkofnoah

Of course no. If a ship is floating that means the upthrust = weight of the ship such that there is no net force acting on the ship and it is in mechanical equilibrium. And since the fully laden ship has the same weight whether it is in the freshwater or seawater, the upthrust is the same.

starwars32

Hmm..so if its floating then upthrust will be same if different density of liquid but when its submerged, then upthrust will not be same if different density?

arkofnoah

Yes that's right. The ship will displace different volume of water in seawater and in freshwater. The sink will sink a bit more in freshwater than in seawater because freshwater is less dense and more water needs to be displaced to support the ship's weight, but the upthrust will end up to be the same in both cases.

If the ship is completely submerged then the volume of water displaced is the same, so now the density will affect the weight of the water displaced and therefore the magnitude of the upthrust.

starwars32

so we do apply archimedes law here and principle of floatation here?

arkofnoah

For your question? Neither. Just Newton's first law which states when an object is at rest, the net force is zero and therefore upthrust = weight.