Consider a bow and arrow. Suppose the bow is held vertically, and the string is drawn back from its midpoint so the arrow is horizontal. Each half of the string makes an angle θ with the vertical, as shown in the diagram. A horizontal force with magnitude F is applied to the tail of the arrow, and the system is motionless. Write an expression for the tension, T, in the string.

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Chapter1: Units, Trigonometry. And Vectors
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Consider a bow and arrow. Suppose the bow is held vertically, and the string is drawn back from its midpoint so the arrow is horizontal. Each half of the string makes an angle θ with the vertical, as shown in the diagram. A horizontal force with magnitude F is applied to the tail of the arrow, and the system is motionless.

Write an expression for the tension, T, in the string. 

 

The image is a diagram illustrating the mechanics of a bow and arrow. Here's a detailed description:

1. **Arrow and Force (F):** 
   - The arrow is depicted in the center, with its forward direction indicated by a black arrowhead.
   - A green arrow labeled "F" points leftward, representing the force applied to the bowstring by the user.

2. **Bow Structure:**
   - The bow is shown symmetrically around the arrow.
   - The curved structure of the bow is shaded on one side to give a three-dimensional impression.

3. **Angles (θ):**
   - Two angles marked as θ are illustrated at the points where the bowstring connects to the ends of the bow.
   - These angles highlight the deformation or bending of the bow when the string is drawn back.

This diagram visually explains the tension and mechanics involved when a bow is drawn and prepared to launch an arrow. The angle θ is significant in understanding the elasticity and potential energy stored in the bow.
Transcribed Image Text:The image is a diagram illustrating the mechanics of a bow and arrow. Here's a detailed description: 1. **Arrow and Force (F):** - The arrow is depicted in the center, with its forward direction indicated by a black arrowhead. - A green arrow labeled "F" points leftward, representing the force applied to the bowstring by the user. 2. **Bow Structure:** - The bow is shown symmetrically around the arrow. - The curved structure of the bow is shaded on one side to give a three-dimensional impression. 3. **Angles (θ):** - Two angles marked as θ are illustrated at the points where the bowstring connects to the ends of the bow. - These angles highlight the deformation or bending of the bow when the string is drawn back. This diagram visually explains the tension and mechanics involved when a bow is drawn and prepared to launch an arrow. The angle θ is significant in understanding the elasticity and potential energy stored in the bow.
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