Mining Drill Polar Coordinates

A tracked mining dril raises its wireline tower to begin excavating. \(OAB\) moves about point \(O\), while section \(AB\) extends out from \(OA\).

For the following conditions: \(d = {{params.d}} ft\), \(\theta = {{params.theta}}^{\circ}\), \(\dot{\theta} = {{params.dot_theta}} deg/s\), \(\ddot{\theta} = {{params.ddot_theta}} deg/s^2\), \(l = {{params.l}} ft\), \(\dot{l} = {{params.dot_l}} ft/s\), \(\ddot{l} = {{params.ddot_l}} ft/s^2\)

\(\dot{l}\) and \(\ddot{l}\) are the first and second-time derivatives of the extending section AB.

Part 1

Determine the \(\hat{r}\) component of the velocity of the wireline tower at \(B\).

Answer Section

Part 2

Determine the \(\hat{\theta}\) component of the velocity of the wireline tower at \(B\).

Answer Section

Part 3

Determine the \(\hat{r}\) component of the acceleration of the wireline tower at \(B\).

Answer Section

Part 4

Determine the \(\hat{\theta}\) component of the acceleration of the wireline tower at \(B\).

Answer Section

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.