Moderate -0.8 This is a straightforward application of the centre of mass formula for a system of particles. Students need to use the formula with given masses and coordinates, requiring only careful arithmetic with no conceptual challenges or problem-solving insight—significantly easier than average A-level questions.
Four tools are attached to a board.
The board is to be modelled as a uniform lamina and the four tools as four particles.
The diagram shows the lamina, the four particles \(A\), \(B\), \(C\) and \(D\), and the \(x\) and \(y\) axes.
\includegraphics{figure_3}
The lamina has mass 5 kg and its centre of mass is at the point \((7, 6)\).
Particle \(A\) has mass 4 kg and is at the point \((11, 2)\).
Particle \(B\) has mass 3 kg and is at the point \((3, 6)\).
Particle \(C\) has mass 7 kg and is at the point \((5, 9)\).
Particle \(D\) has mass 1 kg and is at the point \((1, 4)\).
Find the coordinates of the centre of mass of the system of board and tools. [5 marks]
Four tools are attached to a board.
The board is to be modelled as a uniform lamina and the four tools as four particles.
The diagram shows the lamina, the four particles $A$, $B$, $C$ and $D$, and the $x$ and $y$ axes.
\includegraphics{figure_3}
The lamina has mass 5 kg and its centre of mass is at the point $(7, 6)$.
Particle $A$ has mass 4 kg and is at the point $(11, 2)$.
Particle $B$ has mass 3 kg and is at the point $(3, 6)$.
Particle $C$ has mass 7 kg and is at the point $(5, 9)$.
Particle $D$ has mass 1 kg and is at the point $(1, 4)$.
Find the coordinates of the centre of mass of the system of board and tools. [5 marks]
\hfill \mbox{\textit{AQA M2 2014 Q3 [5]}}