College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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At the presentation ceremony, a championship bowler is presented a 1.80-kg trophy which he holds at arm's length, a distance of 0.655 m from his shoulder joint.

(a) Determine the torque the trophy exerts about the shoulder joint when his arm is horizontal. (Enter the magnitude only.)

[ ] N · m

(b) Determine the torque the trophy exerts about the shoulder joint when his arm is at an angle of 20.0° below the horizontal. (Enter the magnitude only.)

[ ] N · m
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Transcribed Image Text:At the presentation ceremony, a championship bowler is presented a 1.80-kg trophy which he holds at arm's length, a distance of 0.655 m from his shoulder joint. (a) Determine the torque the trophy exerts about the shoulder joint when his arm is horizontal. (Enter the magnitude only.) [ ] N · m (b) Determine the torque the trophy exerts about the shoulder joint when his arm is at an angle of 20.0° below the horizontal. (Enter the magnitude only.) [ ] N · m
**Problem Statement:**

Calculate the torque (in N·m) about the z-axis that is out of the page at the origin in the following figure, given that \( F_1 = 8.0 \, \text{N} \), \( F_2 = 6.0 \, \text{N} \), \( F_3 = 8.0 \, \text{N} \), \( F_4 = 5.7 \, \text{N} \). (Indicate the direction with the sign of your answer.)

**Diagram Explanation:**

- The diagram shows an x-y coordinate system with four force vectors \( \vec{F_1} \), \( \vec{F_2} \), \( \vec{F_3} \), and \( \vec{F_4} \), each applied at various points and angles relative to vertical and horizontal lines.
  
- Origin is denoted as point O.

- Distances from the origin to points of force applications:
  - A horizontal distance of 2 m is marked along the positive x-axis.
  - A vertical distance of 2 m is marked along the positive y-axis.
  - A diagonal distance of 3 m is marked at an angle above the positive x-axis.

- Forces and angles:
  - \( \vec{F_1} \) is directed along the 3 m diagonal line, creating a 90° angle with the line.
  - \( \vec{F_2} \) acts at a 30° angle above the horizontal (x-axis) at a distance of 2 m on the y-axis.
  - \( \vec{F_3} \) acts downward along the extended y-axis at a 2 m distance from the origin.
  - \( \vec{F_4} \) acts at a 20° angle from the vertical line downward and to the right, 2 m from the y-axis.

- Each vector is represented by a red arrow and labeled by its respective force magnitude.
- The axes and certain force angles are dotted to assist in understanding the force directions and angles. 

**Calculation Section:**

- An empty box is provided at the bottom for the torque value in N·m.
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Transcribed Image Text:**Problem Statement:** Calculate the torque (in N·m) about the z-axis that is out of the page at the origin in the following figure, given that \( F_1 = 8.0 \, \text{N} \), \( F_2 = 6.0 \, \text{N} \), \( F_3 = 8.0 \, \text{N} \), \( F_4 = 5.7 \, \text{N} \). (Indicate the direction with the sign of your answer.) **Diagram Explanation:** - The diagram shows an x-y coordinate system with four force vectors \( \vec{F_1} \), \( \vec{F_2} \), \( \vec{F_3} \), and \( \vec{F_4} \), each applied at various points and angles relative to vertical and horizontal lines. - Origin is denoted as point O. - Distances from the origin to points of force applications: - A horizontal distance of 2 m is marked along the positive x-axis. - A vertical distance of 2 m is marked along the positive y-axis. - A diagonal distance of 3 m is marked at an angle above the positive x-axis. - Forces and angles: - \( \vec{F_1} \) is directed along the 3 m diagonal line, creating a 90° angle with the line. - \( \vec{F_2} \) acts at a 30° angle above the horizontal (x-axis) at a distance of 2 m on the y-axis. - \( \vec{F_3} \) acts downward along the extended y-axis at a 2 m distance from the origin. - \( \vec{F_4} \) acts at a 20° angle from the vertical line downward and to the right, 2 m from the y-axis. - Each vector is represented by a red arrow and labeled by its respective force magnitude. - The axes and certain force angles are dotted to assist in understanding the force directions and angles. **Calculation Section:** - An empty box is provided at the bottom for the torque value in N·m.
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