Physics 9702 · AS & A Level · Momentum and Newton's laws of motion
Momentum and Newton's laws of motion — practice question
A sphere with radius $2.1\,\text{mm}$ descends through a liquid at terminal (constant) velocity, as illustrated in Fig. 1.1. Three forces act on the sphere while it is moving. Its weight is $7.2 \times 10^{-4}\,\text{N}$ and the upthrust on it is $4.8 \times 10^{-4}\,\text{N}$. The viscous force $F_v$ on the sphere obeys $F_v = krv$ where $r$ is the sphere’s radius, $v$ is its velocity and $k$ is a constant. The SI value of $k$ is $17$.
(a)[2]
Find the SI base units of $k$.
(b)[3]
Use the upthrust on the sphere to calculate the liquid’s density $\rho$.
(c(i))[1]
On Fig. 1.1, add three arrows to show the directions of the weight $W$, the upthrust $U$ and the viscous force $F_v$. Label the arrows $W$, $U$ and $F_v$ respectively.
(c(ii))[2]
Calculate the magnitude of the sphere’s terminal (constant) velocity.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $Fv$ together with units $\mathrm{kg\,m\,s^{-2}}$.” …