Let's break down the information: ### Given: - **Dimensions:** - \( a = 60 \text{ mm} \) - \( b = 80 \text{ mm} \) - \( c = 40 \text{ mm} \) - \( d_A = 80 \text{ mm} \) - \( d_B = 120 \text{ mm} \) - \( d_{\text{shaft}} = 14 \text{ mm} \) - **Pulley B:** - \( T_1 = 200 \text{ N} \) (tight-side tension) - \( T_2 = 50 \text{ N} \) (slack-side tension) - **Pulley A:** - Slack-side tension is \( \frac{1}{6} \) of tight-side tension ### Question: **The tight-side tension on pulley A is?** Let: - \( T_3 \) = tight-side tension on pulley A - \( T_4 \) = slack-side tension on pulley A Given: \( T_4 = \frac{1}{6} T_3 \) #### Step 1: Find Torques on Each Pulley **Pulley B:** \[ \tau_B = (T_1 - T_2) \cdot \frac{d_B}{2} \] \[ \tau_B = (200 - 50) \cdot \frac{120}{2} = 150 \cdot 60 = 9000 \text{ Nmm} \] **Pulley A:** \[ \tau_A = (T_3 - T_4) \cdot \frac{d_A}{2} \] But since shaft is in equilibrium: \[ \tau_A = \tau_B \] #### Step 2: Substitute \( T_4 \) in terms of \( T_3 \): \[ T_4 = \frac{1}{6} T_3 \] So, \[ (T_3 - T_4) \cdot \frac{80}{2} = 9000 \] \[ (T_3 - \frac{1}{6}T_3) \cdot 40 = 9000 \] \[ (\frac{5}{6}T_3) \cdot 40 = 9000 \] \[ \frac{200}{6}T_3 = 9000 \] \[ T_3 = \frac{9000 \cdot 6}{200} \] \[ T_3 = \frac{54000}{200} \] \[ T_3 = 270 \text{ N} \] ### **Final Answer:** > **B. \( T_3 = 270 \, N \)** --- **Let me know if you want to proceed with Question 6!**

### Question 6 **Given:** - The tight-side tension on pulley A, \( T_3 = 270 \, N \). - Slack-side tension on pulley A, \( T_4 = \frac{1}{6} T_3 \). #### Calculate Slack-Side Tension \( T_4 \): \[ T_4 = \frac{1}{6} T_3 = \frac{1}{6} \cdot 270 = 45 \, N \] ### **Final Answer:** > **Slack-side tension on pulley A, \( T_4 = 45 \, N \)** --- ### Question 7 **Determine the resultant torque on the shaft.** #### Formula for Resultant Torque: \[ \tau_{\text{total}} = \tau_A + \tau_B \] Where: - \( \tau_A = (T_3 - T_4) \cdot \frac{d_A}{2} \) - \( \tau_B = (T_1 - T_2) \cdot \frac{d_B}{2} \) #### Calculating Each Torque: 1. **For Pulley A:** \[ \tau_A = (270 - 45) \cdot \frac{80}{2} = 225 \cdot 40 = 9000 \, \text{Nmm} \] 2. **For Pulley B:** \[ \tau_B = (200 - 50) \cdot \frac{120}{2} = 150 \cdot 60 = 9000 \, \text{Nmm} \] #### Total Torque: \[ \tau_{\text{total}} = 9000 + 9000 = 18000 \, \text{Nmm} \] ### **Final Answer:** > **Resultant torque on the shaft, \( \tau_{\text{total}} = 18000 \, \text{Nmm} \)** --- ### Question 8 **Identify the section with the worst bending stress.** #### Given Sections: - Section P - Section Q - Section R The section with the worst bending stress is typically where the maximum moment occurs, which is usually at the points of maximum load. **Conclusion on Section P:** If Section P is at the midpoint of the shaft where the torques from both pulleys act, it will likely experience the worst bending stress. ### **Final Answer:** > **The section with the worst bending stress is Section P.** --- Let me know if you need further assistance or clarification!