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A beaker of water rests on an electronic balance that reads 998.0 g. A 2.6 -cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

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Balance new reading $=998.0 g+9.2 g=1007.2 g$

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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here we can draw a diagram. The forced tension, it struggle smaller. The force, tension and the brilliant force and then going straight down is of course, gravity. So we can say that we want to find the tension, the force tension. So we can say that the net force in the right direction would be equal to a forced tension plus the force, the bully and force minus and G and this is equaling zero. Because we know that this is this has translational equilibrium. So we can say that the tension force is gonna be equal to the weight minus the boy in force. We can say that this is gonna be equal to, uh whether we can say the force. Tension will be equal to 4/3 pi r Cubed density of copper times the acceleration due to gravity minus 4/3 pi r cubed the density of water times G and this is equaling 4/3 pi r cubed G Ah, the density of copper minus the density of water. And so at this point, we can solve. So the force tension would be equal to four over three times pi times the radius of 0.13 meters, cubed times 9.8 meters per second squared and then times 8900 The density of copper minus the density of water, uh, kilograms per meek per cubic meter. And so we find that the forest tension is gonna be equal 2.7125 Newtons. So this would be the answer to the first part of the question. And now, in order to balance their reading, that means that the mass of B equals the buoyant force over G. So basically, the mass of the ball must be equal to the bully and forests divided by the acceleration due to gravity, which means that the brilliant force must be equal to 4/3 pi r cubed density ofwater times G s o. The mass needs to be equal to 4/3 pi r cubed density ofwater. Given that G cancels out and so we can solve this is gonna be 4/3 pi times 0.0 13 meters cubed and then times 1000 kilograms per cubic meter and we find that the mass needs to be equal 29 0.203 times 10 to the negative third kilograms. So essentially the reading on the balance with the 998.0 grams. Now this is equaling 9.203 g, and this will be minus 9.2 g approximately. And so the balance reading would be 1000. Sorry, the balance reading would be 998 grams, plus the, uh, m sub be so 998.0 grams plus 9.2 grams. The balance reading is going to show 1007.2 grams. So this would be your answer, and that would be the balance reading for the second part of the question. That is the end of the solution. Thank you for watching.

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