The fishing pole in the figure below makes an angle of 20.0° with the horizontal, What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force F = 125 N at an angle 37.0° below the horizontąl? The force is applied at à point L = 1.92 m from the angler's hands. N-m

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
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Chapter10: Rotational Motion
Section: Chapter Questions
Problem 22P: The fishing pole in Figure P10.22 makes an angle of 20.0 with the horizontal. What is the torque...
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**Problem Description:**

The fishing pole in the figure makes an angle of 20.0° with the horizontal. You need to determine the magnitude of the torque exerted by the fish around an axis perpendicular to the page, which passes through the angler's hand. The fish pulls on the fishing line with a force **F** = 125 N at an angle 37.0° below the horizontal. The force is applied at a distance **L** = 1.92 m from the angler's hands.

**Diagram Explanation:**

- A person is shown holding a fishing pole at an angle of 20.0° above the horizontal.
- The line extends from the pole at an angle of 37.0° below the horizontal, where the force **F** is applied.
- The point where the force is applied is labeled as **L** = 1.92 m from the angler's hands.
- The angles and force vectors are clearly marked on the diagram, along with a fish depicted underwater pulling on the line.

**Solution Approach:**

To find the torque (\( \tau \)), use the formula:

\[
\tau = r \times F \times \sin(\theta)
\]

Where:
- \( r = 1.92 \text{ m} \) (distance from the pivot point)
- \( F = 125 \text{ N} \) (force exerted by the fish)
- \( \theta = 57.0° \) (the angle between **r** and **F** is the sum of the angle of the pole and the angle of the force, i.e., \( 20.0° + 37.0° \))

**Calculation:**

\[
\tau = 1.92 \times 125 \times \sin(57.0°)
\]

By calculating this, you obtain the magnitude of the torque.
Transcribed Image Text:**Problem Description:** The fishing pole in the figure makes an angle of 20.0° with the horizontal. You need to determine the magnitude of the torque exerted by the fish around an axis perpendicular to the page, which passes through the angler's hand. The fish pulls on the fishing line with a force **F** = 125 N at an angle 37.0° below the horizontal. The force is applied at a distance **L** = 1.92 m from the angler's hands. **Diagram Explanation:** - A person is shown holding a fishing pole at an angle of 20.0° above the horizontal. - The line extends from the pole at an angle of 37.0° below the horizontal, where the force **F** is applied. - The point where the force is applied is labeled as **L** = 1.92 m from the angler's hands. - The angles and force vectors are clearly marked on the diagram, along with a fish depicted underwater pulling on the line. **Solution Approach:** To find the torque (\( \tau \)), use the formula: \[ \tau = r \times F \times \sin(\theta) \] Where: - \( r = 1.92 \text{ m} \) (distance from the pivot point) - \( F = 125 \text{ N} \) (force exerted by the fish) - \( \theta = 57.0° \) (the angle between **r** and **F** is the sum of the angle of the pole and the angle of the force, i.e., \( 20.0° + 37.0° \)) **Calculation:** \[ \tau = 1.92 \times 125 \times \sin(57.0°) \] By calculating this, you obtain the magnitude of the torque.
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