Question

A CNC water jet cutting machine is used to cut a straight slot between the points (2, 1) and (10, 10) on the XY plane (dimensions are in mm). If the feed rate is 1.5 mm/s, the time, in s, required to machine the slot following the shortest path, is ................. (round off to 2 decimal places).

Hint:

To calculate the time for a CNC machine to cut a straight path, find the Euclidean distance between the points and divide by the feed rate.

Answer 1

- To find the time required to machine the slot, we need to calculate the distance between the two points on the XY plane. The formula for the Euclidean distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the given values \((x_1, y_1) = (2, 1)\) and \((x_2, y_2) = (10, 10)\): \[ d = \sqrt{(10 - 2)^2 + (10 - 1)^2} = \sqrt{8^2 + 9^2} = \sqrt{64 + 81} = \sqrt{145} \approx 12.04 \, \text{mm} \] - The time \(t\) required to cut the slot is given by: \[ t = \frac{\text{Distance}}{\text{Feed rate}} = \frac{12.04}{1.5} \approx 8.03 \, \text{seconds} \] Thus, the time required is approximately \(8.03 \, \text{s}\).