Three forces are applied to a tree sapling, as shown in (Figure 1) , to stabilize it. Suppose that FA = 325 N an FB = 505 N . %3D

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Chapter1: Units, Trigonometry. And Vectors
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### Problem Description

Three forces are applied to a tree sapling to stabilize it, as shown in the provided figure. The forces are denoted as \(\vec{F}_A\), \(\vec{F}_B\), and \(\vec{F}_C\). The magnitudes of the forces are as follows:

- \(\vec{F}_A = 325 \, \text{N}\)
- \(\vec{F}_B = 505 \, \text{N}\)

### Figure Explanation

The diagram illustrates a tree sapling with three force vectors acting on it:

- \(\vec{F}_A\) is directed towards the right.
- \(\vec{F}_B\) is directed upwards, forming an angle of \(105^\circ\) with \(\vec{F}_A\).
- \(\vec{F}_C\) is directed downwards and to the left, forming an angle \(\theta\) with \(\vec{F}_A\), moving clockwise.

### Tasks

**Part A**

Determine the magnitude of \(\vec{F}_C\).

- Express your answer to three significant figures and include the appropriate units.

\[ F_C = \text{Value} \, \text{Units} \]

Provide your answer by clicking “Submit.”

**Part B**

Determine the angle \(\theta\) between \(\vec{F}_A\) and \(\vec{F}_C\), measured clockwise.

- Express your answer using three significant figures.

\[ \theta = \text{Value} \]

Provide your answer by clicking “Submit.”
Transcribed Image Text:### Problem Description Three forces are applied to a tree sapling to stabilize it, as shown in the provided figure. The forces are denoted as \(\vec{F}_A\), \(\vec{F}_B\), and \(\vec{F}_C\). The magnitudes of the forces are as follows: - \(\vec{F}_A = 325 \, \text{N}\) - \(\vec{F}_B = 505 \, \text{N}\) ### Figure Explanation The diagram illustrates a tree sapling with three force vectors acting on it: - \(\vec{F}_A\) is directed towards the right. - \(\vec{F}_B\) is directed upwards, forming an angle of \(105^\circ\) with \(\vec{F}_A\). - \(\vec{F}_C\) is directed downwards and to the left, forming an angle \(\theta\) with \(\vec{F}_A\), moving clockwise. ### Tasks **Part A** Determine the magnitude of \(\vec{F}_C\). - Express your answer to three significant figures and include the appropriate units. \[ F_C = \text{Value} \, \text{Units} \] Provide your answer by clicking “Submit.” **Part B** Determine the angle \(\theta\) between \(\vec{F}_A\) and \(\vec{F}_C\), measured clockwise. - Express your answer using three significant figures. \[ \theta = \text{Value} \] Provide your answer by clicking “Submit.”
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