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Determine the direction of the resultant force FR, measured counterclockwise from the positive axis. Express your answer to three significant figures and include the appropriate units.

Determine the direction of the resultant force FR, measured counterclockwise from the positive axis. Express your answer to three significant figures and include the appropriate units.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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F1=230lb

F2=370lb

### Force Vector Diagram The diagram illustrates forces acting on a hook, with two force vectors, \( F_1 \) and \( F_2 \), applied at specific angles relative to the Cartesian coordinate axes. #### Description: 1. **Coordinate Axes**: - The diagram is set on an \( x \)-\( y \) plane, with the origin placed at the center of the hook. - The positive \( y \)-axis is oriented vertically upwards. - The positive \( x \)-axis is oriented horizontally to the right. 2. **Forces Acting on the Hook**: - **Force \( F_1 \)**: - This force is represented by a vector pointing upwards and to the right, forming an angle of \( 30^\circ \) with the positive \( y \)-axis. - **Force \( F_2 \)**: - This force is represented by a vector pointing downwards and to the right, forming an angle of \( 45^\circ \) with the positive \( x \)-axis. #### Force Vector Analysis: - **Vector \( F_1 \)**: - The angle between \( F_1 \) and the positive \( y \)-axis is \( 30^\circ \). - \( F_1 \) can be decomposed into two components: - \( F_{1y} \): The vertical component of \( F_1 \), which is \( F_1 \cdot \cos{30^\circ} \). - \( F_{1x} \): The horizontal component of \( F_1 \), which is \( F_1 \cdot \sin{30^\circ} \). - **Vector \( F_2 \)**: - The angle between \( F_2 \) and the positive \( x \)-axis is \( 45^\circ \). - \( F_2 \) can similarly be decomposed into two components: - \( F_{2x} \): The horizontal component of \( F_2 \), which is \( F_2 \cdot \cos{45^\circ} \). - \( F_{2y} \): The vertical component of \( F_2 \), which is \( F_2 \cdot \sin{45^\circ} \). This diagram is essential for understanding how forces combine and act on objects in a
Transcribed Image Text:### Force Vector Diagram The diagram illustrates forces acting on a hook, with two force vectors, \( F_1 \) and \( F_2 \), applied at specific angles relative to the Cartesian coordinate axes. #### Description: 1. **Coordinate Axes**: - The diagram is set on an \( x \)-\( y \) plane, with the origin placed at the center of the hook. - The positive \( y \)-axis is oriented vertically upwards. - The positive \( x \)-axis is oriented horizontally to the right. 2. **Forces Acting on the Hook**: - **Force \( F_1 \)**: - This force is represented by a vector pointing upwards and to the right, forming an angle of \( 30^\circ \) with the positive \( y \)-axis. - **Force \( F_2 \)**: - This force is represented by a vector pointing downwards and to the right, forming an angle of \( 45^\circ \) with the positive \( x \)-axis. #### Force Vector Analysis: - **Vector \( F_1 \)**: - The angle between \( F_1 \) and the positive \( y \)-axis is \( 30^\circ \). - \( F_1 \) can be decomposed into two components: - \( F_{1y} \): The vertical component of \( F_1 \), which is \( F_1 \cdot \cos{30^\circ} \). - \( F_{1x} \): The horizontal component of \( F_1 \), which is \( F_1 \cdot \sin{30^\circ} \). - **Vector \( F_2 \)**: - The angle between \( F_2 \) and the positive \( x \)-axis is \( 45^\circ \). - \( F_2 \) can similarly be decomposed into two components: - \( F_{2x} \): The horizontal component of \( F_2 \), which is \( F_2 \cdot \cos{45^\circ} \). - \( F_{2y} \): The vertical component of \( F_2 \), which is \( F_2 \cdot \sin{45^\circ} \). This diagram is essential for understanding how forces combine and act on objects in a
### Problem Statement Determine the direction of the resultant force \( \mathbf{F_R} \), measured counterclockwise from the positive \( x \) axis. Express your answer to three significant figures and include the appropriate units.
Transcribed Image Text:### Problem Statement Determine the direction of the resultant force \( \mathbf{F_R} \), measured counterclockwise from the positive \( x \) axis. Express your answer to three significant figures and include the appropriate units.
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