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A brass ball of radius 1.2 mm (density 8500 kg/m³) falls through glycerine (density 1260 kg/m³…

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A brass ball of radius $1.2\ \text{mm}$ (density $8500\ \text{kg/m}^3$ ) falls through glycerine (density $1260\ \text{kg/m}^3$ , viscosity $0.80\ \text{Pa s}$ ). Find its terminal speed, and the drag on it at that speed. ( $g = 9.8\ \text{m/s}^2$ .)

Need a reminder? The key ideaShow

Viscosity: the force to slide a plate of area $A$ at speed $v$ over a film of thickness $d$ is $F = \eta A\dfrac{v}{d}$ . Stokes' law: a small sphere feels $6\pi\eta rv$ , so it falls at a terminal speed $v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$ .

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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