Standard +0.3 This is a straightforward centre of mass problem requiring knowledge of the standard result for the centroid of a circular arc (2r sin(θ)/θ from centre), then applying the composite centre of mass formula. It involves multiple steps but uses bookwork formulas with clear substitution, making it slightly easier than average.
\includegraphics{figure_2}
A bow consists of a uniform curved portion \(AB\) of mass \(1.4 \text{ kg}\), and a uniform taut string of mass \(m \text{ kg}\) which joins \(A\) and \(B\). The curved portion \(AB\) is an arc of a circle centre \(O\) and radius \(0.8 \text{ m}\). Angle \(AOB\) is \(\frac{2}{3}\pi\) radians (see diagram). The centre of mass of the bow (including the string) is \(0.65 \text{ m}\) from \(O\). Calculate \(m\). [6]
\includegraphics{figure_2}
A bow consists of a uniform curved portion $AB$ of mass $1.4 \text{ kg}$, and a uniform taut string of mass $m \text{ kg}$ which joins $A$ and $B$. The curved portion $AB$ is an arc of a circle centre $O$ and radius $0.8 \text{ m}$. Angle $AOB$ is $\frac{2}{3}\pi$ radians (see diagram). The centre of mass of the bow (including the string) is $0.65 \text{ m}$ from $O$. Calculate $m$. [6]
\hfill \mbox{\textit{CAIE M2 2010 Q2 [6]}}