MediumChemistryHigh School (11–12)States of MatterNumericalAP A-Level IB

A steel ball of radius 2.0 mm and density 7800 kg/m³ is dropped into a tall jar of glycerol…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A steel ball of radius $2.0\ \text{mm}$ and density $7800\ \text{kg/m}^3$ is dropped into a tall jar of glycerol. The glycerol has a density of $1260\ \text{kg/m}^3$ and a viscosity of $1.41\ \text{Pa s}$ . Find the steady speed of the ball, and check that Stokes' law applies by calculating the Reynolds number. Then find the time that the ball takes to fall $60\ \text{cm}$ at this speed, ignoring the start.

Need a reminder? The key ideaShow

Poiseuille: $Q = \dfrac{\pi\Delta Pr^4}{8\eta L}$ . Stokes: a steady speed $v = \dfrac{2r^2(\rho_s - \rho)g}{9\eta}$ , valid when $Re = \dfrac{\rho vd}{\eta}$ is below about $1$ . Ostwald viscometer: $\dfrac{\eta_1}{\eta_2} = \dfrac{\rho_1t_1}{\rho_2t_2}$ . For a liquid, $\eta = Ae^{E/RT}$ , which falls as $T$ rises.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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