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60.0° 0 F₁ F3 W N S E F2

60.0° 0 F₁ F3 W N S E F2

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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Question: At a picnic , there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result , three forces act on the

### Diagram Analysis: Concurrent Force System on a Point #### Description and Components The diagram illustrates a concurrent force system acting on a spherical object at its center, with three different forces denoted by \(\vec{F}_1\), \(\vec{F}_2\), and \(\vec{F}_3\). These forces are represented by arrows, showing both the direction and the line of action of each force. #### Force Vectors 1. **Force \(\vec{F}_1\)**: - Directed obliquely from the top-left towards the sphere. - The angle between the horizontal axis and \(\vec{F}_1\) is 60.0°. 2. **Force \(\vec{F}_2\)**: - Directed horizontally towards the sphere from the right. 3. **Force \(\vec{F}_3\)**: - Directed obliquely from the bottom-left towards the sphere. #### Angle and Directions - The angle \(\theta\) is formed between the line of action of \(\vec{F}_1\) and the line of action of \(\vec{F}_3\) through the center of the sphere. - The directional compass rose shows the cardinal directions, providing a reference for the directions of the forces. - The compass indicates North (N) at the top, East (E) to the right, South (S) at the bottom, and West (W) to the left. ### Explanation #### Force Vector Representation The forces are applied to the spherical object, with their directions clearly shown using the arrows. The lengths of the arrows generally represent the magnitudes of the forces qualitatively. #### Angle Measurement - The \(60.0°\) angle between the horizontal line and \(\vec{F}_1\) shows the inclination of \(\vec{F}_1\) relative to the x-axis. - The angle \(\theta\) demonstrates the relative positioning of \(\vec{F}_3\) with respect to \(\vec{F}_1\) and \(\vec{F}_2\). #### Cardinal Directions - The compass rose aids in visualizing the forces' orientations relating to standard geographical directions, ensuring clarity in understanding the directional components of each force. ### Application This system can be used to study and resolve forces in static equilibrium. By breaking these forces
Transcribed Image Text:### Diagram Analysis: Concurrent Force System on a Point #### Description and Components The diagram illustrates a concurrent force system acting on a spherical object at its center, with three different forces denoted by \(\vec{F}_1\), \(\vec{F}_2\), and \(\vec{F}_3\). These forces are represented by arrows, showing both the direction and the line of action of each force. #### Force Vectors 1. **Force \(\vec{F}_1\)**: - Directed obliquely from the top-left towards the sphere. - The angle between the horizontal axis and \(\vec{F}_1\) is 60.0°. 2. **Force \(\vec{F}_2\)**: - Directed horizontally towards the sphere from the right. 3. **Force \(\vec{F}_3\)**: - Directed obliquely from the bottom-left towards the sphere. #### Angle and Directions - The angle \(\theta\) is formed between the line of action of \(\vec{F}_1\) and the line of action of \(\vec{F}_3\) through the center of the sphere. - The directional compass rose shows the cardinal directions, providing a reference for the directions of the forces. - The compass indicates North (N) at the top, East (E) to the right, South (S) at the bottom, and West (W) to the left. ### Explanation #### Force Vector Representation The forces are applied to the spherical object, with their directions clearly shown using the arrows. The lengths of the arrows generally represent the magnitudes of the forces qualitatively. #### Angle Measurement - The \(60.0°\) angle between the horizontal line and \(\vec{F}_1\) shows the inclination of \(\vec{F}_1\) relative to the x-axis. - The angle \(\theta\) demonstrates the relative positioning of \(\vec{F}_3\) with respect to \(\vec{F}_1\) and \(\vec{F}_2\). #### Cardinal Directions - The compass rose aids in visualizing the forces' orientations relating to standard geographical directions, ensuring clarity in understanding the directional components of each force. ### Application This system can be used to study and resolve forces in static equilibrium. By breaking these forces
**Physics Problem: Forces Acting on a Ball** Consider a ball subject to three forces, \(\vec{F}_1\), \(\vec{F}_2\), and \(\vec{F}_3\) (refer to the accompanying drawing - not provided). The magnitudes of the forces \(\vec{F}_1\) and \(\vec{F}_2\) are given as: \[ F_1 = 50.0 \text{ newtons} \] \[ F_2 = 90.0 \text{ newtons} \] Using a scale drawing and the graphical technique, determine: (a) The magnitude of \(\vec{F}_3\). (b) The angle \(\theta\) such that the resultant force acting on the ball is zero. (Note: The exact drawing and diagrams are essential to fully solve and understand this problem. The use of graphical techniques refers to vector addition methods such as the head-to-tail method or parallelogram method to find the resultant force and equilibrium conditions.)
Transcribed Image Text:**Physics Problem: Forces Acting on a Ball** Consider a ball subject to three forces, \(\vec{F}_1\), \(\vec{F}_2\), and \(\vec{F}_3\) (refer to the accompanying drawing - not provided). The magnitudes of the forces \(\vec{F}_1\) and \(\vec{F}_2\) are given as: \[ F_1 = 50.0 \text{ newtons} \] \[ F_2 = 90.0 \text{ newtons} \] Using a scale drawing and the graphical technique, determine: (a) The magnitude of \(\vec{F}_3\). (b) The angle \(\theta\) such that the resultant force acting on the ball is zero. (Note: The exact drawing and diagrams are essential to fully solve and understand this problem. The use of graphical techniques refers to vector addition methods such as the head-to-tail method or parallelogram method to find the resultant force and equilibrium conditions.)
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