A bead of mass 0.5 kg is threaded on a smooth straight wire. The forces acting on the bead are a constant force \(( 2 \mathbf { i } + 3 \mathbf { j } + \chi \mathbf { k } ) \mathrm { N }\), its weight \(( - 4.9 \mathbf { k } ) \mathrm { N }\), and the reaction on the bead from the wire.
Explain why the reaction on the bead from the wire does no work as the bead moves along the wire.
The bead moves from the point \(A\) with position vector \(( \mathbf { i } + \mathbf { j } - 3 \mathbf { k } ) \mathrm { m }\) relative to a fixed origin \(O\) to the point \(B\) with position vector \(( 3 \mathbf { i } - \mathbf { j } + 2 \mathbf { k } ) \mathrm { m }\). The speed of the bead at \(A\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of the bead at \(B\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).