A picture of mass m = 11 kg is hung on a wall from a hook with a piece of wire. The picture hangs level and is centered on the hook. The tension in the wire is the same on both sides of the hook. Each section of wire makes the same angle with the horizontal. Refer to the figure. Initially the picture is hung with a short wire, such that θ1 = 11°. What is the tension in the wire, in newtons. FT = The wire is replaced with a longer wire. The picture now hangs with θ2 = 48°. What is the new tension in the wire, in newtons. FT =

Physics for Scientists and Engineers: Foundations and Connections
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Chapter6: Applications Of Newton’s Laws Of Motion
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A picture of mass m = 11 kg is hung on a wall from a hook with a piece of wire. The picture hangs level and is centered on the hook. The tension in the wire is the same on both sides of the hook. Each section of wire makes the same angle with the horizontal. Refer to the figure.

 Initially the picture is hung with a short wire, such that θ1 = 11°. What is the tension in the wire, in newtons. 
FT =

 

The wire is replaced with a longer wire. The picture now hangs with θ2 = 48°. What is the new tension in the wire, in newtons. 
FT = 
### Understanding Tension in Picture Hanging

This image illustrates the forces involved in hanging a picture with a wire. It depicts a wooden-framed picture suspended by a wire, showing important physical concepts.

**Key Elements:**

- **Forces (FT):** The tension forces in the wire are represented by \( F_T \). There are two components of tension acting on the wire, one on each side of the frame.

- **Angle (\(\theta\)):** The angle between the vertical centerline and each side of the wire is denoted by \(\theta\). This angle is crucial in determining the distribution of forces along the wire.

- **Diagram Explanation:** 
  - The wire forms two symmetrical angles \(\theta\) with the vertical centerline, creating an inverted "Y" shape.
  - The vertical dashed line represents the line of symmetry, providing a balance point for the forces.

Understanding these factors is essential in physics and engineering, as they help in calculating the correct support needed to prevent the frame from falling. This involves applying knowledge of tension forces and angles in practical scenarios.
Transcribed Image Text:### Understanding Tension in Picture Hanging This image illustrates the forces involved in hanging a picture with a wire. It depicts a wooden-framed picture suspended by a wire, showing important physical concepts. **Key Elements:** - **Forces (FT):** The tension forces in the wire are represented by \( F_T \). There are two components of tension acting on the wire, one on each side of the frame. - **Angle (\(\theta\)):** The angle between the vertical centerline and each side of the wire is denoted by \(\theta\). This angle is crucial in determining the distribution of forces along the wire. - **Diagram Explanation:** - The wire forms two symmetrical angles \(\theta\) with the vertical centerline, creating an inverted "Y" shape. - The vertical dashed line represents the line of symmetry, providing a balance point for the forces. Understanding these factors is essential in physics and engineering, as they help in calculating the correct support needed to prevent the frame from falling. This involves applying knowledge of tension forces and angles in practical scenarios.
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