| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Variable force (position x) - find velocity |
| Difficulty | Standard +0.3 This is a standard M2 variable force question requiring application of F=ma in the form v(dv/dx), followed by straightforward integration and substitution. Part (i) is direct application of Newton's second law, part (ii) is routine integration with initial conditions, and part (iii) requires comparing two force expressions. While it involves calculus and multiple steps (7 marks total), the techniques are all standard M2 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.06a Variable force: dv/dt or v*dv/dx methods |
A small block $B$ of mass 0.25 kg is released from rest at a point $O$ on a smooth horizontal surface. After its release the velocity of $B$ is $v$ m s$^{-1}$ when its displacement is $x$ m from $O$. The force acting on $B$ has magnitude $(2 + 0.3x^2)$ N and is directed horizontally away from $O$.
\begin{enumerate}[label=(\roman*)]
\item Show that $v\frac{dv}{dx} = 1.2x^2 + 8$. [2]
\item Find the velocity of $B$ when $x = 1.5$. [3]
\end{enumerate}
An extra force acts on $B$ after $x = 1.5$. It is given that, when $x > 1.5$,
$$v\frac{dv}{dx} = 1.2x^2 + 6 - 3x.$$
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the magnitude of this extra force and state the direction in which it acts. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2016 Q3 [7]}}