a) \(v = \frac{2 R_s^2 (\rho_silica - \rho_water)g}{9 \eta}\)

b) t = s/v = 5.1*10^4 s

c) I don't see how this could be done without centrifuging the cylinder. Perhaps that's what they're aiming at?

 

I think it involves changing the water with an additive to change its p. This is predicted by the equation.

 

Other than additives you could:

increase g (centrifuge)
increase size of particles
reduce temperature

 

You're probably right, BillO, but why would changing the size of the particles speed their velocity?

 

I think it involves changing the water with an additive to change its p. This is predicted by the equation.

The point of the additive is to reduce the viscoscity of the water, (the denominator in the equation) which will have a more dramatic effect than attempting to change the density.

So add some Fairy Liquid.

As Bill says the biggest effect is to increase particle size since the mass increase as the cube of the radius, whereas the surface and therefore the friction as the square.

But I am not sure this is a legitimate answer any more than replacing the silica with lead shot of the same size would be. I expect you are meant to make the existing sample sediment faster, not change it for a different one.

 

The point of the additive is to reduce the viscoscity of the water, (the denominator in the equation) which will have a more dramatic effect than attempting to change the density.

So add some Fairy Liquid.

That was my point and it's predicted by the given equation, scroll up.

As Bill says the biggest effect is to increase particle size since the mass increase as the cube of the radius, whereas the surface and therefore the friction as the square.

I was taught in physics that you can drop a steel ball bearing and a steel bowling ball at the same time from a two story window and they hit the surface at the same time. Surface area was not a thing. So is it that in a fluid it is more of a thing to think about? Mind you I was not arguing, just asking.

But I am not sure this is a legitimate answer any more than replacing the silica with lead shot of the same size would be. I expect you are meant to make the existing sample sediment faster, not change it for a different one.

No, I think you can't replace the silica, that's cheating.

 

I was taught in physics that you can drop a steel ball bearing and a steel bowling ball at the same time from a two story window and they hit the surface at the same time. Surface area was not a thing. So is it that in a fluid it is more of a thing to think about? Mind you I was not arguing, just asking.

In this situation the force due to the weight of either ball dwarfs the frictional resistance of the air.

Sedimentation is about when the frictional forces opposing settlement under gravity are of comparable magnitude to the gravitational forces due to the weight of the particles. This would also happen if one of your balls had a parachute!

Small point: η is the viscosity, - not ρ which is the density in Boks equation.

 

Thanks, Studiot. For some reason I never ran into Boks equation while at school. What you said makes good sense.