D) Determine the true magnitude and direction of the forces acting on the cylinder

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Educational Content on Free Body Diagrams and Hand Calculations**

**Problem 4-3: Analyzing Forces on a Cylinder**

**Figure 4.3 Description:**
A cylinder resting on a smooth 45° incline is depicted. The cylinder has a weight of 200 lb. Two forces are labeled: one is the tension (T), directed at an angle of 40° above the horizontal, and the other is a reaction force at the point of contact, inclined at 25° to the horizontal plane.

**Diagram Explanation:**
The diagram shows a cylinder on an incline with two external forces impacting it. The tension force T is making an angle of 40° with the vertical while the inclined contact angle made by the reaction force is 25°.

**Instructions:**

a) **Free Body Diagram**
   - Apply all known and unknown forces to the free body diagram provided below the description.
   - The diagram illustrates the cylindrical object with a circle, awaiting annotation of force vectors.

b) **Hand Calculations**
   - Determine the true magnitude and direction of the forces acting on the cylinder.
   - A coordinate system is provided for clarity, with x-y axes depicted both in positive and negative directions (+x, +y, -x, -y).

c) **Balanced Free Body Diagram**
   - Revise the initial free body diagram to reflect the true magnitude and direction of all forces. This includes a balanced arrangement following the calculation in part (b).

This exercise aims to develop a comprehensive understanding of force dynamics through the visualization and calculation of force vectors on a cylindrical object resting on an inclined plane.
Transcribed Image Text:**Educational Content on Free Body Diagrams and Hand Calculations** **Problem 4-3: Analyzing Forces on a Cylinder** **Figure 4.3 Description:** A cylinder resting on a smooth 45° incline is depicted. The cylinder has a weight of 200 lb. Two forces are labeled: one is the tension (T), directed at an angle of 40° above the horizontal, and the other is a reaction force at the point of contact, inclined at 25° to the horizontal plane. **Diagram Explanation:** The diagram shows a cylinder on an incline with two external forces impacting it. The tension force T is making an angle of 40° with the vertical while the inclined contact angle made by the reaction force is 25°. **Instructions:** a) **Free Body Diagram** - Apply all known and unknown forces to the free body diagram provided below the description. - The diagram illustrates the cylindrical object with a circle, awaiting annotation of force vectors. b) **Hand Calculations** - Determine the true magnitude and direction of the forces acting on the cylinder. - A coordinate system is provided for clarity, with x-y axes depicted both in positive and negative directions (+x, +y, -x, -y). c) **Balanced Free Body Diagram** - Revise the initial free body diagram to reflect the true magnitude and direction of all forces. This includes a balanced arrangement following the calculation in part (b). This exercise aims to develop a comprehensive understanding of force dynamics through the visualization and calculation of force vectors on a cylindrical object resting on an inclined plane.
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