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 $\mathrm{kg\,m\,s^{-2}}$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI