Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Transcribed Image Text:### Problem Statement:
**Q.4)** Determine the maximum allowable weight of the drum for the system shown below if the system is to be in equilibrium. The block weighs 50 lb and the coefficient of static friction for all surfaces is 0.35.
### Diagram Explanation:
- The system comprises a block and a drum connected by a horizontal bar. The block rests on an inclined plane while the drum is placed at the bottom of the incline.
- Measurements provided in the diagram:
- The block has a height of 20 inches and a width of 12 inches.
- The distance from the bottom-left corner of the block to the center of the drum is 15 inches horizontally.
- The drum has a diameter of 8 inches.
- The rod connecting the drum and the block is 4 inches from the top of the block.
- The incline makes an angle with the horizontal, with a tangent value of \( \frac{5}{12} \).
- Coefficients of friction:
- Between the drum and the plane: \( \mu = 0.6 \)
- Between the block and the plane: \( \mu = 0.35 \)
### Given Data:
- Weight of the block (\( W_b \)): \( 50 \) lbs
- Coefficient of static friction for all surfaces (\( \mu \)): \( 0.35 \)
### Objective:
To determine the maximum allowable weight of the drum (\( W_d \)) to ensure the system remains in equilibrium.
### Key Considerations:
- Analyze forces acting on both the block and the drum.
- Consider frictional forces, normal forces, and gravitational forces to set up equilibrium equations.
- Ensure to account for the incline’s angle in force calculations for both normal and frictional components.
### Solution Approach:
1. *Components of Forces on the Inclined Plane*:
- Resolve the weight of the block and drum into components parallel and perpendicular to the inclined plane.
- Consider static friction forces opposing the motion where required.
2. *Equilibrium Conditions*:
- Set up force balance equations in the directions parallel and perpendicular to the inclined plane.
- Ensure torque equilibrium around appropriate pivot points where moments are balanced.
By using principles of static equilibrium, solve the resulting equations to find the maximum allowable weight of the drum (\( W_d \)).
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