Standard +0.8 This M5 question requires applying the work-energy theorem in 3D vector form, finding displacement vectors, computing dot products, and solving for an unknown force vector. While the individual techniques are standard, the multi-step coordination of vector mechanics with energy principles and the 9-mark allocation indicate this is moderately challenging, requiring more synthesis than routine M1-M3 questions but less insight than proof-based problems.
A particle of mass 0.5 kg is at rest at the point with position vector \((2\mathbf{i} + 3\mathbf{j} - 4\mathbf{k})\) m. The particle is then acted upon by two constant forces \(\mathbf{F}_1\) and \(\mathbf{F}_2\). These are the only two forces acting on the particle. Subsequently, the particle passes through the point with position vector \((4\mathbf{i} + 5\mathbf{j} - 5\mathbf{k})\) m with speed 12 m s\(^{-1}\). Given that \(\mathbf{F}_1 = (\mathbf{i} + 2\mathbf{j} - \mathbf{k})\) N, find \(\mathbf{F}_2\). [9]
A particle of mass 0.5 kg is at rest at the point with position vector $(2\mathbf{i} + 3\mathbf{j} - 4\mathbf{k})$ m. The particle is then acted upon by two constant forces $\mathbf{F}_1$ and $\mathbf{F}_2$. These are the only two forces acting on the particle. Subsequently, the particle passes through the point with position vector $(4\mathbf{i} + 5\mathbf{j} - 5\mathbf{k})$ m with speed 12 m s$^{-1}$. Given that $\mathbf{F}_1 = (\mathbf{i} + 2\mathbf{j} - \mathbf{k})$ N, find $\mathbf{F}_2$. [9]
\hfill \mbox{\textit{Edexcel M5 2006 Q2 [9]}}