Easy -1.3 This is a straightforward application of the centre of mass formula for particles at given coordinates. Students simply substitute the given masses and coordinates into the standard formulas x̄ = Σ(mx)/Σm and ȳ = Σ(my)/Σm. It requires only arithmetic calculation with no problem-solving, making it significantly easier than average.
2 The diagram shows four particles, \(A , B , C\) and \(D\), which are fixed in a horizontal plane which contains the \(x\) - and \(y\)-axes, as shown.
Particle \(A\) has mass 2 kg and is attached at the point ( 9,6 ).
Particle \(B\) has mass 3 kg and is attached at the point ( 2,4 ).
Particle \(C\) has mass 8 kg and is attached at the point \(( 3,8 )\).
Particle \(D\) has mass 7 kg and is attached at the point \(( 6,11 )\).
\includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-2_748_774_1402_625}
Find the coordinates of the centre of mass of the four particles.
2 The diagram shows four particles, $A , B , C$ and $D$, which are fixed in a horizontal plane which contains the $x$ - and $y$-axes, as shown.
Particle $A$ has mass 2 kg and is attached at the point ( 9,6 ).\\
Particle $B$ has mass 3 kg and is attached at the point ( 2,4 ).\\
Particle $C$ has mass 8 kg and is attached at the point $( 3,8 )$.\\
Particle $D$ has mass 7 kg and is attached at the point $( 6,11 )$.\\
\includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-2_748_774_1402_625}
Find the coordinates of the centre of mass of the four particles.
\hfill \mbox{\textit{AQA M2 2011 Q2 [5]}}