A stepladder of negligible weight is constructed as shown in the figure below, with AC = BC = { = 4.40 m. A painter of mass m = 73.0 kg stands on the ladder d = 3.00 m from the bottom.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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A stepladder of negligible weight is constructed as shown in the figure below, with \( AC = BC = \ell = 4.40 \, \text{m} \). A painter of mass \( m = 73.0 \, \text{kg} \) stands on the ladder \( d = 3.00 \, \text{m} \) from the bottom.

**Diagram Explanation:**
The diagram shows a stepladder in the shape of an inverted "V". The ladder sections \( AC \) and \( BC \) are equal in length. A painter stands at point \( C \), and a horizontal bar \( DE \) connects the two halves of the ladder. The points \( A \) and \( B \) are at the bottom, and point \( C \) is at the top hinge. The height from the bottom to where the painter stands is marked as \( d \).

**Assuming the floor is frictionless, find the following.** 
*(Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.)*

(a) The tension in the horizontal bar \( DE \) connecting the two halves of the ladder:  
\(\_\_\_\_\_\) N

(b) The normal forces at \( A \) and \( B \):  
at \( A \) \(\_\_\_\_\_\) N  
at \( B \) \(\_\_\_\_\_\) N

(c) The components of the reaction force at the single hinge \( C \) that the left half of the ladder exerts on the right half:  
rightward component \(\_\_\_\_\_\) N  
upward component \(\_\_\_\_\_\) N

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Transcribed Image Text:A stepladder of negligible weight is constructed as shown in the figure below, with \( AC = BC = \ell = 4.40 \, \text{m} \). A painter of mass \( m = 73.0 \, \text{kg} \) stands on the ladder \( d = 3.00 \, \text{m} \) from the bottom. **Diagram Explanation:** The diagram shows a stepladder in the shape of an inverted "V". The ladder sections \( AC \) and \( BC \) are equal in length. A painter stands at point \( C \), and a horizontal bar \( DE \) connects the two halves of the ladder. The points \( A \) and \( B \) are at the bottom, and point \( C \) is at the top hinge. The height from the bottom to where the painter stands is marked as \( d \). **Assuming the floor is frictionless, find the following.** *(Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.)* (a) The tension in the horizontal bar \( DE \) connecting the two halves of the ladder: \(\_\_\_\_\_\) N (b) The normal forces at \( A \) and \( B \): at \( A \) \(\_\_\_\_\_\) N at \( B \) \(\_\_\_\_\_\) N (c) The components of the reaction force at the single hinge \( C \) that the left half of the ladder exerts on the right half: rightward component \(\_\_\_\_\_\) N upward component \(\_\_\_\_\_\) N **Need Help?** Master It **Additional Materials** eBook
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