Upthrust
I'm stuck with some physics homework. The question is based around the fermentation of wine, and asks which three forces act on a particle falling downwards within the wine. Are the forces upthrust, viscous drag, and gravity?
It also asks to explain how the given expression for upthrust is derived of U = 4/3Nr^3pg where p is the density of the wine and r is the radius of the falling particle. I don't understand what the question is asking me. Any help?
It also asks to explain how the given expression for upthrust is derived of U = 4/3Nr^3pg where p is the density of the wine and r is the radius of the falling particle. I don't understand what the question is asking me. Any help?
Help?
The forces acting on the particle are indeed its weight, viscous drag and upthrust. 
For the second part, use Archimedes' principle, which states that for a body floating or submerged in a fluid, the upthrust acting on the body is equal to the weight of fluid that the body has displaced by being in the fluid.
Since the particle is completely in the fluid, the upthrust acting on it is equal to the weight of wine with the same volume as the particle. Using the formula for the volume of a sphere and that W = mg, you should be able to see how the expression given was derived.
For the second part, use Archimedes' principle, which states that for a body floating or submerged in a fluid, the upthrust acting on the body is equal to the weight of fluid that the body has displaced by being in the fluid.
Since the particle is completely in the fluid, the upthrust acting on it is equal to the weight of wine with the same volume as the particle. Using the formula for the volume of a sphere and that W = mg, you should be able to see how the expression given was derived.
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The forces acting on the particle are indeed its weight, viscous drag and upthrust.
For the second part, use Archimedes' principle, which states that for a body floating or submerged in a fluid, the upthrust acting on the body is equal to the weight of fluid that the body has displaced by being in the fluid.
Since the particle is completely in the fluid, the upthrust acting on it is equal to the weight of wine with the same volume as the particle. Using the formula for the volume of a sphere and that W = mg, you should be able to see how the expression given was derived.
For the second part, use Archimedes' principle, which states that for a body floating or submerged in a fluid, the upthrust acting on the body is equal to the weight of fluid that the body has displaced by being in the fluid.
Since the particle is completely in the fluid, the upthrust acting on it is equal to the weight of wine with the same volume as the particle. Using the formula for the volume of a sphere and that W = mg, you should be able to see how the expression given was derived.
Thank you. Could you help explain why the terminal velocity velocity formula comes to 2r^2g(p1-p2) over ( 9 times visocity).
The first part is the weight isnt it?
When the particle is at terminal velocity, there is no resultant force acting on it. So its weight is equal to the sum of the upthrust and viscous drag that opposes its motion. Write this as an equation and solve it, using the definition of Stokes' viscous drag, the formula for the upthrust you just worked out and the weight of the particle as the product of its density, volume and the gravitational field strength.
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