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A bucket of water is accelerated upward at 1.8 $\mathrm{g} .$ What isthe buoyant force on a 3.0 -kg granite rock $(\mathrm{SG}=2.7)$submerged in the water? Will the rock float? Why or why not?

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30.5$N$The rock will sink

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Cornell University

University of Michigan - Ann Arbor

McMaster University

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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So here we need to investigate whether the rock will sink or not. We know that the force, the buoyant force, will be equal to be rather the buoyant force minus the mass of the water Times G equals the mass of the water times the acceleration, eh? We know that. Then the brilliant force is going to be equal to the mass of the water times G plus A. Or we can say that this is gonna be equal to the volume of the rock times the density of the water times G plus A. So the brilliant force would then be equal to the mass of the rock times the density of the water times a plus, g, uh, divided by the density of the rock. Uh, and so this is going to be equal to the mass of the rock divided by the specific gravity of the rock times G plus 1.8 G. And so the buoyant force is gonna be equal to 3.0 kilograms divided by ah 2.7 um, multiplied by 2.8 times 9.8 meters per second squared and the 1,000,000,000 forces, then 30.5 Nunes. So keep that in mind for the for the rock to not sink the upward Brilliant force on the rock minus the weight of the rock must be equal to net force on the block. So we can say that the brilliant force equaling FB would be equal. Rather brilliant force would be, uh, apologies going force minus the mass of the rock. Times G should be equal to the mass of the rock. Time's a, um and so basically, the buoyant force would be equal to the mass of the Rock Times G plus A. And so the buoyant force would be equal to the mass of the rock. Three kilograms times 2.8 times 9.8 meters per second squared. This is equaling 82 Newton's now because, um, this 82 Newton's is gonna be greater than what we've just found. 30.5 Newtons. Ah, that means that f b The buoyant force does not support the weight of the rock. The rock will sink. That is the end of the solution. Thank you for watching

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