Discussion
A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is
Answer: B
The milling time is about 170 seconds.
The cutter diameter equals the slot width, so one straight pass along the diagonal from (0, 0) to (100, 100) cuts the slot:
\[ \begin{aligned} L &= \sqrt{100^{2}+100^{2}} = 141.42\ \text{mm} \\ t &= \frac{141.42}{50} = 2.828\ \text{min} \\ &= 169.7\ \text{s} \approx 170\ \text{s} \end{aligned} \]
120 s is the time for 100 mm, the travel along one axis only, which ignores that the tool moves diagonally. 180 s and 240 s overstate the path.
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