Physics 9702 · AS & A Level · Elastic and plastic behaviour
Elastic and plastic behaviour — practice question
A steel ball with radius $r$ and mass $m$ descends vertically at terminal speed $v$ through oil. The viscous drag force $D$ on the ball is defined by $D = 6\pi\eta rv$, where $\eta$ is the oil’s viscosity. In part (b), the oil has density $920\,\text{kg m}^{-3}$ and viscosity $4.7$ in SI units. The steel ball’s mass is $2.4 \times 10^{-3}\,\text{kg}$ and its radius is $4.2 \times 10^{-3}\,\text{m}$.
(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, add 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 of $\eta$.
(c(i))[1]
Show that the upthrust force acting on the ball is $2.8 \times 10^{-3}\,\text{N}$.
(c(ii))[3]
Determine the terminal speed $v$ 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 per unit cross-sectional area” …