- \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors.]
A small smooth ring of mass 0.5 kg moves along a smooth horizontal wire. The only forces acting on the ring are its weight, the normal reaction from the wire, and a constant force ( \(5 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }\) ) N. The ring is initially at rest at the point with position vector \(( \mathbf { i } + \mathbf { j } + \mathbf { k } ) \mathrm { m }\), relative to a fixed origin.
Find the speed of the ring as it passes through the point with position vector \(( 3 \mathbf { i } + \mathbf { k } ) \mathrm { m }\).