Let's focus on **Question 2** and go through the step-by-step calculations: --- ### Given Data: - **Undermined chip thickness** = .125 inch - **Chip thickness** = .15 inch - **Back rake angle** = 8° - **Cutting speed** = 300 ft/min --- ### **a. Cutting Ratio** **Cutting ratio** is the ratio of the uncut chip thickness to the chip thickness: \[ \text{Cutting ratio} = \frac{\text{Uncut chip thickness}}{\text{Chip thickness}} \] \[ = \frac{.125}{.15} \approx .833 \] **Final answer:** \[ \boxed{ \text{Cutting ratio} \approx .83 } \] --- ### **b. Shear angle** The shear angle \(\phi\) can be calculated using the relation: \[ \text{tan} \phi = \frac{\text{r} \cos \alpha}{1 - r \sin \alpha} \] where: - \( r \) = ratio of uncut chip thickness to chip thickness = .83 - \( \alpha \) = back rake angle = 8° First, convert \(\alpha\) to radians or use degrees directly in the calculator: \[ \cos 8^\circ \approx .9903 \] \[ \sin 8^\circ \approx .1392 \] Now, substitute: \[ \text{tan} \phi = \frac{.83 \times .9903}{1 - .83 \times .1392} = \frac{.8226}{1 - .1154} = \frac{.8226}{.8846} \approx .929 \] Calculate \(\phi\): \[ \phi = \arctan(.929) \approx 42.1^\circ \] **Final answer:** \[ \boxed{ \text{Shear angle} \approx 42.1^\circ } \] --- ### **c. Chip velocity** The **chip velocity** \( V_c \) can be calculated using the relation with cutting speed: \[ V_c = \frac{\text{Cutting speed}}{\cos \phi} \] Given: - Cutting speed \( V_s = 300 \text{ ft/min} \) - Shear angle \( \phi \approx 42.1^\circ \) Calculate: \[ V_c = \frac{300}{\cos 42.1^\circ} \] \[ \cos 42.1^\circ \approx .743 \] \[ V_c \approx \frac{300}{.743} \approx 403.4 \text{ ft/min} \] **Final answer:** \[ \boxed{ \text{Chip velocity} \approx 403.4 \text{ ft/min} } \] --- ### **Summary of results:** | **Parameter** | **Value** | |---------------------------|----------------------------------| | a. Cutting ratio | **~.83** | | b. Shear angle | **~42.1°** | | c. Chip velocity | **~403.4 ft/min** | Let me know if you'd like additional explanations!