# Internal Torque Diagram for Shaft (Step-by-Step Solution) ## **Given Data** - \( T_1 = 100 \) N·cm (at section B) - \( T_2 = 500 \) N·cm (at section C) - Lengths: \( L_1, L_2 \) (not numerically specified) - The shaft is fixed at A. --- ## **Step 1: Analyze and Calculate Internal Torque** ### **A. Section AB (from A to B, \( < x < L_1 \))** - **At A**: The shaft is fixed, so the internal torque must balance all external torques to the right. - **To the right of A (just before B):** Only \( T_1 \) acts to the right of the section. - **Internal Torque in AB:** \( T_{AB} = T_1 = 100 \) N·cm (constant across AB) --- ### **B. Section BC (from B to C, \( L_1 < x < L_1 + L_2 \))** - **At B:** Both \( T_1 \) and \( T_2 \) are to the right. - **Internal Torque in BC:** \( T_{BC} = T_1 - T_2 = 100 - 500 = 500 \) N·cm (constant across BC) --- ## **Step 2: Draw the Internal Torque Diagram** Below is a simple representation: ``` Torque (N·cm) ^ | _________ | | | | | | |--------| |_________ | | | | 100 | 500 | |________|_________|_________> x L1 L1+L2 ``` ### **Explanation:** - From A to B (\( < x < L_1 \)), torque = **100 N·cm**. - From B to C (\( L_1 < x < L_1 + L_2 \)), torque = **500 N·cm**. - At C, the torque drops to zero (shaft free end or torque is balanced). --- ## **Summary Table** | Section | Internal Torque (N·cm) | |---------|-----------------------| | AB | 100 | | BC | 500 | --- ## **Final Answer** - **Internal torque in AB:** \( 100 \) N·cm - **Internal torque in BC:** \( 500 \) N·cm ### **Internal Torque Diagram:** See the plot above for the step decrease at \( B \). --- **Example Values:** If \( L_1 = 10 \) cm, \( L_2 = 15 \) cm, - From to 10 cm: torque = 100 N·cm - From 10 to 25 cm: torque = 500 N·cm --- **Let me know if you need the diagram in another format or with specific lengths!**