A steel ball of radius $r$ and mass $m$ moves straight down through oil at terminal speed $v$. The viscous drag force $D$ on the ball is given by $D = 6\pi \eta r v$, where $\eta$ is a property of the oil called its viscosity. The oil in (b) has a density of $920\,\text{kg m}^{-3}$ and a viscosity of $4.7$ in SI units. The steel ball has a mass of $2.4 \times 10^{-3}\,\text{kg}$ and a radius of $4.2 \times 10^{-3}\,\text{m}$.
(a(i))[1]
Define pressure.
(a(ii))[2]
Explain how hydrostatic pressure gives rise to an upthrust force on a solid object immersed in a liquid.
(b(i))[3]
On Fig. 2.1, draw labelled arrows from the ball to indicate the directions of the three forces acting on the ball as it falls.
(b(ii))[2]
Determine the SI base units for $\eta$.
(c(i))[1]
Show that the upthrust force on the ball is $2.8 \times 10^{-3}\,\text{N}$.
(c(ii))[3]
Determine the terminal speed of the ball.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “(normal) force divided by cross-sectional area” …