### Determining Vertical Acceleration of a Cylinder#### Problem Statement:Determine the vertical acceleration of the cylinder with a weight \( W_A = 71 \, \text{lb} \) for each of the two cases. Neglect friction and the mass of the pulleys. The acceleration is positive if up, negative if down.Assume \( W_B = 46 \, \text{lb} \).#### Diagram Explanation:- **Case (a):** - Two pulleys are attached to a fixed point. - One pulley is connected to weight \( W_A \). - A second string going through both pulleys is connected to weight \( W_B \). - The diagram indicates an arrow pointing downwards, signaling the direction of \( W_B \).- **Case (b):** - Two pulleys are fixed to a support, with a continuous string going through them. - One end of the string is attached to weight \( W_A \) and the other to weight \( W_B \).#### Calculations:The text does not provide detailed calculations, but the results for the vertical accelerations are given as follows:- **Answers:** - (a) \( a = 9.5162 \, \text{ft/sec}^2 \) - (b) \( a = 5.2992 \, \text{ft/sec}^2 \)These accelerations are positive, indicating upward motion under the specified conditions.### Conclusion:By understanding the diagrams and the specified weights, one can derive the vertical accelerations of the system in both scenarios. Given the weights and system setup, the accelerations have been determined and provided for educational reference.

Answered: Image /qna-images/answer/b42983bc-3041-4817-80b5-58efe1918251.jpg

Determine the vertical acceleration of the cylinder with a weight WA = 71 lb for each of the two cases. Neglect friction and the mass of the pulleys. The acceleration is positive if up, negative if down. Assume WB = 46 lb. WA WB W Answers: (a) a = (b) a = (a) 9.5162 i 5.2992 WA (b) ft/sec² ft/sec²

Determine the vertical acceleration of the cylinder with a weight WA = 71 lb for each of the two cases. Neglect friction and the mass of the pulleys. The acceleration is positive if up, negative if down. Assume WB = 46 lb. WA WB W Answers: (a) a = (b) a = (a) 9.5162 i 5.2992 WA (b) ft/sec² ft/sec²

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Author:Sadiku, Matthew N. O.

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Conservation of Energy

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Question

### Determining Vertical Acceleration of a Cylinder
#### Problem Statement:
Determine the vertical acceleration of the cylinder with a weight \( W_A = 71 \, \text{lb} \) for each of the two cases. Neglect friction and the mass of the pulleys. The acceleration is positive if up, negative if down.

Assume \( W_B = 46 \, \text{lb} \).

#### Diagram Explanation:
- **Case (a):**
- Two pulleys are attached to a fixed point.
- One pulley is connected to weight \( W_A \).
- A second string going through both pulleys is connected to weight \( W_B \).
- The diagram indicates an arrow pointing downwards, signaling the direction of \( W_B \).

- **Case (b):**
- Two pulleys are fixed to a support, with a continuous string going through them.
- One end of the string is attached to weight \( W_A \) and the other to weight \( W_B \).

#### Calculations:
The text does not provide detailed calculations, but the results for the vertical accelerations are given as follows:

- **Answers:**
- (a) \( a = 9.5162 \, \text{ft/sec}^2 \)
- (b) \( a = 5.2992 \, \text{ft/sec}^2 \)

These accelerations are positive, indicating upward motion under the specified conditions.

### Conclusion:
By understanding the diagrams and the specified weights, one can derive the vertical accelerations of the system in both scenarios. Given the weights and system setup, the accelerations have been determined and provided for educational reference.

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