Physics 9702 · AS & A Level · Non-uniform motion

Non-uniform motion — practice question

A sphere with radius $R$ is travelling through a fluid at a steady speed $v$. A frictional force $F$ acts on the sphere, and it is given by $F = 6\pi DRv$, where $D$ is a constant that depends on the fluid.
(a(i))[3]

Show that the SI base units of $D$ are $\text{kg m}^{-1}\,\text{s}^{-1}$.

(a(ii).1)[1]

A raindrop with radius $1.5\,\text{mm}$ is falling vertically through air at a speed of $3.7\,\text{m s}^{-1}$. For air, $D = 6.6 \times 10^{-4}\,\text{kg m}^{-1}\,\text{s}^{-1}$. Water has density $1000\,\text{kg m}^{-3}$. Calculate the magnitude of the frictional force $F$.

(a(ii).2)[3]

Calculate the acceleration of the raindrop.

(b(i))[3]

The speed $v$ of the raindrop in (a) changes with time $t$ as shown in Fig. 2.1. State how the raindrop’s acceleration varies with time.

(b(ii))[2]

A second raindrop has a radius smaller than the one in (a). On Fig. 2.1, sketch how the speed varies with time for this second raindrop.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Force has the correct base units $\text{kg m s}^{-2}$, radius has $\text{m}$, and velocity has $\text{m s}^{-1}$

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