City Guilds Model Questions Vol1 2025 Engineering Question 48

In a turning operation the workpiece diameter is \(100\) mm. The depth of cut is \(2\) mm and the feed is \(0.2\) mm per revolution. Tool life follows Taylor's equation \( T = \dfrac{C}{V^{n}} \) with \( C = 2000\; \text{min·(m/min)}^{n} \) and \( n = 0.25 \). The power required is approximated by \( P = k V^{2} \) where \( k = 0.0005\; \text{kW·(m/min)}^{-2} \). The electricity cost is ₦0.5 per kWh and the tool cost is ₦2000. Assuming the spindle speed is related to cutting speed by \( N = \dfrac{V}{\pi D} \) (with \( D = 0.1\) m), determine the cutting speed \( V \) (in m min\(^{-1}\)) between \(50\) m min\(^{-1}\) and \(250\) m min\(^{-1}\) that minimises the total cost per part (tool cost plus energy cost). Also give the minimum cost per part in naira, rounded to three decimal places.