Certainly! Let's break down the questions in **two steps each**, with explanations at each step, and provide the final answers. --- ## **5.5** **Step 1:** **Task:** Move the rod to the hole shown at right. Draw an extended free-body diagram for the system. **Explanation:** - The rod is now at a different point, changing the **moment arm** for the spring scale. - The forces acting are: the weight of the rod (down), the reaction at the pivot (up), and the tension from the spring scale (up). - Draw arrows for these forces at their respective positions: weight at the center of mass, pivot at the support, tension at the cable location. **Step 2:** **Task:** Predict whether the tension in the cable will be greater or less than before, and why. **Explanation:** - Since the cable is now **closer to the pivot**, the lever arm for the tension is **shorter**. - To balance the **same torque** from the rod's weight, the tension must **increase** (since torque = force × distance, and distance is now less). **Final Answer (5.5):** - The tension in the cable will be **greater** than before, because moving the cable closer to the pivot requires a larger force to provide the same torque. --- ## **5.6** **Step 1:** **Task:** Set up the beam as shown and measure the tension in the spring scale. **Explanation:** - With the beam and spring scale set up as in the diagram (spring scale on the right end), measure the value shown on the scale. **Step 2:** **Task:** Is the measurement consistent with your prediction? **Explanation:** - If the tension is **greater** than before (when the cable was further from the pivot), it matches the prediction from 5.5. **Final Answer (5.6):** - Yes, the measurement should show a **greater tension**, consistent with the prediction in 5.5. --- ## **5.7** **Step 1:** **Task:** Hold the beam horizontally by pulling down on the left end with a spring scale, as shown. Draw an extended free-body diagram. **Explanation:** - Now, the **spring scale pulls down** on the left, while the pivot supports the beam, and the rod's weight acts down at the center. - Draw arrows: spring scale (down, left end), weight (down, center), pivot (up, under the beam). **Step 2:** **Task:** Predict and then measure the tension in the spring scale. **Explanation:** - The spring scale must balance the **torque** from the rod's weight around the pivot. - Since the lever arm (distance from pivot to spring scale) is **greater** on the left end, the required force (tension) will be **less** than when the spring scale was closer to the pivot (on the right end). **Final Answer (5.7):** - The tension measured on the left end with the spring scale will be **less** than when the scale was on the right end, because the lever arm is longer, requiring less force for the same torque. --- ## **Summary of All Answers** 1. **5.5:** The cable tension is **greater** when it is closer to the pivot (shorter lever arm). 2. **5.6:** The measurement is **consistent**; tension is greater as predicted. 3. **5.7:** When pulling down on the left end, the tension is **less** due to a longer lever arm. Let me know if you need the free-body diagrams or further details!

Certainly! Here’s a structured solution for all parts of the problem based on the provided image and explanations. --- # **Problem Solutions** ## **5.5** ### **Step 1: Free-Body Diagram** - **Task:** Move the rod to the indicated hole and draw an extended free-body diagram. - **Explanation:** - Forces acting on the rod include: - **Weight (W)** acting downward at the center of mass. - **Reaction force (R)** at the pivot acting upward. - **Tension (T)** from the spring scale acting upward. - Diagram should show arrows representing these forces at their respective positions. ### **Step 2: Tension Prediction** - **Task:** Predict the tension in the cable after moving it. - **Explanation:** - Since the cable is closer to the pivot, the lever arm for tension (distance from pivot to cable attachment) is shorter. - To maintain the same torque (which is the product of force and distance), the tension must increase because torque \( \tau = F \cdot d \). ### **Final Answer (5.5):** - The tension in the cable will be **greater** than before after moving it closer to the pivot. --- ## **5.6** ### **Step 1: Measure Tension** - **Task:** Set up the beam and measure the tension in the spring scale. - **Explanation:** - With the beam in position and the spring scale attached, take note of the reading on the scale. ### **Step 2: Consistency Check** - **Task:** Compare the measured tension with the prediction. - **Explanation:** - If the measured tension is indeed greater than when the scale was positioned further from the pivot, this confirms the prediction made in part 5.5. ### **Final Answer (5.6):** - Yes, the measurement shows a **greater tension**, consistent with the prediction. --- ## **5.7** ### **Step 1: Free-Body Diagram with Downward Pull** - **Task:** Hold the beam horizontally and draw the free-body diagram while pulling down on the left end. - **Explanation:** - Forces acting now include: - **Tension (T)** from the spring scale acting downward on the left end. - **Weight (W)** acting downward at the center of the rod. - **Reaction force (R)** at the pivot acting upward. - Diagram should indicate these forces clearly. ### **Step 2: Tension Prediction and Measurement** - **Task:** Predict and then measure the tension in the spring scale. - **Explanation:** - The lever arm from the pivot to the left end (where the spring scale is) is longer than when it was on the right. - Thus, less force (tension) is needed to balance the torque from the rod’s weight. ### **Final Answer (5.7):** - The tension measured on the left end will be **less** than when the scale was on the right end, due to the longer lever arm. --- ## **Summary of All Answers** 1. **5.5:** The cable tension is **greater** after moving it closer to the pivot. 2. **5.6:** The measurement is **consistent**; tension is greater as predicted. 3. **5.7:** Tension on the left end is **less** due to a longer lever arm. If you have any further questions or need clarifications, feel free to ask!