**Text Transcription for Educational Website:** --- **Problem 3:** Two blocks with unequal masses, \(M\) and \(m\) (\(M > m\)), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible. **a.** If one of your classmates calculated that, once released, the acceleration of the blocks would be \(\frac{g}{4}\), without doing any calculations, say whether or not this could be a reasonable value for the acceleration. **b.** Draw and label a free body diagram (FBD) for each block. (*Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.*) Rank the relative magnitudes of all forces in your FBDs. *(I’m looking for a single ranking that includes every different force drawn and labeled in both FBDs, separated by <, >, or =.)* - **Heavy block:** - **Light block:** Relative sizes of all forces in FBDs: _________________ **c.** Use the FBDs from the previous part, and Newton’s 2nd Law, to derive an expression (in terms of \(M\), \(m\), and \(g\)) for the acceleration of the blocks once they’re released. \[ a = \_\_\_\_\_\_\_\_\_ \] **Bonus:** If the blocks start a distance \(y\) above the ground, use kinematics to find what’s the maximum height above the ground that the small block reaches before falling back and hanging above the ground? (*Assume that pulley is high enough that the small block doesn’t touch it. Attach your own paper with work.*) --- **Diagram Explanation:** The diagram shows two blocks connected by a string over a pulley. The block with mass \(M\) is heavier than the block with mass \(m\). The pulley is depicted as a simple circle, indicating that it has negligible mass and friction. The focus of the problem is to calculate the forces and accelerations involved when the system is released.
**Text Transcription for Educational Website:** --- **Problem 3:** Two blocks with unequal masses, \(M\) and \(m\) (\(M > m\)), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible. **a.** If one of your classmates calculated that, once released, the acceleration of the blocks would be \(\frac{g}{4}\), without doing any calculations, say whether or not this could be a reasonable value for the acceleration. **b.** Draw and label a free body diagram (FBD) for each block. (*Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.*) Rank the relative magnitudes of all forces in your FBDs. *(I’m looking for a single ranking that includes every different force drawn and labeled in both FBDs, separated by <, >, or =.)* - **Heavy block:** - **Light block:** Relative sizes of all forces in FBDs: _________________ **c.** Use the FBDs from the previous part, and Newton’s 2nd Law, to derive an expression (in terms of \(M\), \(m\), and \(g\)) for the acceleration of the blocks once they’re released. \[ a = \_\_\_\_\_\_\_\_\_ \] **Bonus:** If the blocks start a distance \(y\) above the ground, use kinematics to find what’s the maximum height above the ground that the small block reaches before falling back and hanging above the ground? (*Assume that pulley is high enough that the small block doesn’t touch it. Attach your own paper with work.*) --- **Diagram Explanation:** The diagram shows two blocks connected by a string over a pulley. The block with mass \(M\) is heavier than the block with mass \(m\). The pulley is depicted as a simple circle, indicating that it has negligible mass and friction. The focus of the problem is to calculate the forces and accelerations involved when the system is released.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Text Transcription for Educational Website:**
---
**Problem 3:**
Two blocks with unequal masses, \(M\) and \(m\) (\(M > m\)), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible.
**a.** If one of your classmates calculated that, once released, the acceleration of the blocks would be \(\frac{g}{4}\), without doing any calculations, say whether or not this could be a reasonable value for the acceleration.
**b.** Draw and label a free body diagram (FBD) for each block. (*Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.*) Rank the relative magnitudes of all forces in your FBDs. *(I’m looking for a single ranking that includes every different force drawn and labeled in both FBDs, separated by <, >, or =.)*
- **Heavy block:**
- **Light block:**
Relative sizes of all forces in FBDs: _________________
**c.** Use the FBDs from the previous part, and Newton’s 2nd Law, to derive an expression (in terms of \(M\), \(m\), and \(g\)) for the acceleration of the blocks once they’re released.
\[ a = \_\_\_\_\_\_\_\_\_ \]
**Bonus:** If the blocks start a distance \(y\) above the ground, use kinematics to find what’s the maximum height above the ground that the small block reaches before falling back and hanging above the ground? (*Assume that pulley is high enough that the small block doesn’t touch it. Attach your own paper with work.*)
---
**Diagram Explanation:**
The diagram shows two blocks connected by a string over a pulley. The block with mass \(M\) is heavier than the block with mass \(m\). The pulley is depicted as a simple circle, indicating that it has negligible mass and friction. The focus of the problem is to calculate the forces and accelerations involved when the system is released.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18608e9e-bffe-4b38-84b4-3b337a037743%2F42208811-d9d8-4fea-b788-67828376f11b%2Flbtc9q.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website:**
---
**Problem 3:**
Two blocks with unequal masses, \(M\) and \(m\) (\(M > m\)), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible.
**a.** If one of your classmates calculated that, once released, the acceleration of the blocks would be \(\frac{g}{4}\), without doing any calculations, say whether or not this could be a reasonable value for the acceleration.
**b.** Draw and label a free body diagram (FBD) for each block. (*Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.*) Rank the relative magnitudes of all forces in your FBDs. *(I’m looking for a single ranking that includes every different force drawn and labeled in both FBDs, separated by <, >, or =.)*
- **Heavy block:**
- **Light block:**
Relative sizes of all forces in FBDs: _________________
**c.** Use the FBDs from the previous part, and Newton’s 2nd Law, to derive an expression (in terms of \(M\), \(m\), and \(g\)) for the acceleration of the blocks once they’re released.
\[ a = \_\_\_\_\_\_\_\_\_ \]
**Bonus:** If the blocks start a distance \(y\) above the ground, use kinematics to find what’s the maximum height above the ground that the small block reaches before falling back and hanging above the ground? (*Assume that pulley is high enough that the small block doesn’t touch it. Attach your own paper with work.*)
---
**Diagram Explanation:**
The diagram shows two blocks connected by a string over a pulley. The block with mass \(M\) is heavier than the block with mass \(m\). The pulley is depicted as a simple circle, indicating that it has negligible mass and friction. The focus of the problem is to calculate the forces and accelerations involved when the system is released.
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