Our goal is to calculate the tensions in the two ropes if the person is momentarily motionless (Part 3).**Set up Newton's 2nd Law in the x and y directions when the system is at rest. What should the sum of the forces add up to?**1. **Set-up Newton's 2nd Law is in terms of symbols and notations only.** Please do not substitute any numerical values except for the angles. Write expressions for \( \Sigma F_x \) and \( \Sigma F_y \) in terms of \( T_1, T_2, m, g, \) and the numerical values of the angles. For example, you may express the x-component of \( T_1 \) as \( -T_1 \sin(15^\circ) \) or \( T_1 \cos(105^\circ) \).2. **Take the upward direction to be the +y-direction, and to the right to be the +x-direction.****Diagram Explanation:**- The diagram shows a firefighter using a rope to aid a person hanging against a burning wall.- \( T_1 \): Tension in the left rope, making an angle of \( 15^\circ \) with the wall.- \( T_2 \): Tension in the right rope, making an angle of \( 10^\circ \) with the horizontal.- \( w \): Weight of the person, directed vertically downward. These tensions balance the vertical and horizontal forces, keeping the person momentarily motionless. ## Transcription for Educational Website### Using Math Editor for Angles and Tensions in Physics ProblemsWhen solving physics problems involving angles and tensions, it's crucial to use the correct notations. Follow these guidelines for accuracy:### 3. Add Degree Signs and SubscriptsMake sure to include the degree sign for angles and the subscripts for tensions. This can be done using the math editor.#### How to Access the Degree Symbol:The degree symbol can be found in the math type menu. Click the arrow to the right of the division sign as shown in the images below. For instance, when entering an angle, you should write it as \( \cos(32^\circ) \).### Diagram ExplanationThe diagram shows a toolbar from the math editor. Key elements highlighted are:1. The degree symbol option, located next to basic arithmetic symbols.### EquationsTwo equations are presented for balancing forces in different directions:1. **Horizontal (x) Direction:** \[ \Sigma F_x = T_2 \cos(10^\circ) - T_1 \sin(15^\circ) = 0 \] - This equation is correct, as indicated by the green box with a check mark. - Positive x direction is defined as to the right.2. **Vertical (y) Direction:** \[ \Sigma F_y = T_2 \cos(10^\circ) = T_1 \sin(15^\circ) = 0 \] - This equation is incorrect, as indicated by the red box with a cross mark. - Positive y direction is defined as upwards.By adhering to these guidelines, calculations become clearer and more precise, aiding in accurate problem-solving.

The given figure depicts a person dangling from a cable. Two tension forces are applied to the cable…

Answered: 15° T₁ T₂ J.10°

Science

Physics

15° T₁ T₂ J.10°

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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