### Topic: Moments and Vectors#### Problem Statement3. Make sure to use i, j, and k unit vectors.a. Determine the moment vector $ M_1 $ exerted on the pipe by the left couple. b. Determine the moment vector $ M_2 $ exerted on the pipe by the right couple. c. Determine the sum of the couples’ moment vectors $ M_1 $ and $ M_2 $.**You have to be very clear about the directions.**#### Diagram Description: The diagram features a pipe subjected to forces at different points:- The x-axis extends horizontally to the right, and the y-axis extends vertically upwards. - There is a force $ \vec{F_1} $ of 40 N acting at a point located 2 meters above the horizontal pipe and directed upwards along the y-axis.- Another force $ \vec{F_2} $ of 50 N is acting at a 60° angle with the horizontal, 4 meters to the right along the x-axis from the point of application of $ \vec{F_1} $.- The horizontal pipe has a force of 40 N directed along the negative x-axis.- An additional force of 50 N acts downward, making a 60° angle with the horizontal at a distance of 4 meters along the x-axis from the point where $ \vec{F_2} $ is applied.##### Graph Explanation:- The pipe is represented as a horizontal line (along the x-axis) with several forces acting on it.- Labels on the diagram indicate the specific distances and angles at which these forces act relative to the origin point on the pipe.#### Solution Steps1. **Identify the coordinates and forces acting on the pipe**: - $\vec{F_1} = 40\ \mathrm{N}$ in the j-direction at (0, 2, 0). - $\vec{F_2} = 50\ \mathrm{N}$ making a 60° angle with the positive x-axis at (4, 4, 0). - $\vec{F_3} = 40\ \mathrm{N}$ along negative x-direction at the origin. - $\vec{F_4} = 50\ \mathrm{N}$ downward making

Answered: Image /qna-images/answer/b42903f2-b38e-4c92-ae0b-86aa9a6719ce.jpg

3. Make sure to use i, j and k unit vectors. a. Determine the moment vector M1 exerted on the pipe by the left couple. b. Determine the moment vector M2 exerted on the pipe by the right couple. c. Determine the sum of the couples' moment vectors M1 and M2. You have to be very clear about the directions. F1-40N F2-50 N 50N 2 m 4 m 4 m 60° 60° 40N

3. Make sure to use i, j and k unit vectors. a. Determine the moment vector M1 exerted on the pipe by the left couple. b. Determine the moment vector M2 exerted on the pipe by the right couple. c. Determine the sum of the couples' moment vectors M1 and M2. You have to be very clear about the directions. F1-40N F2-50 N 50N 2 m 4 m 4 m 60° 60° 40N

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

### Topic: Moments and Vectors

#### Problem Statement
3. Make sure to use i, j, and k unit vectors.
a. Determine the moment vector $ M_1 $ exerted on the pipe by the left couple.
b. Determine the moment vector $ M_2 $ exerted on the pipe by the right couple.
c. Determine the sum of the couples’ moment vectors $ M_1 $ and $ M_2 $.

**You have to be very clear about the directions.**

#### Diagram Description:
The diagram features a pipe subjected to forces at different points:

- The x-axis extends horizontally to the right, and the y-axis extends vertically upwards.
- There is a force $ \vec{F_1} $ of 40 N acting at a point located 2 meters above the horizontal pipe and directed upwards along the y-axis.
- Another force $ \vec{F_2} $ of 50 N is acting at a 60° angle with the horizontal, 4 meters to the right along the x-axis from the point of application of $ \vec{F_1} $.
- The horizontal pipe has a force of 40 N directed along the negative x-axis.
- An additional force of 50 N acts downward, making a 60° angle with the horizontal at a distance of 4 meters along the x-axis from the point where $ \vec{F_2} $ is applied.

##### Graph Explanation:
- The pipe is represented as a horizontal line (along the x-axis) with several forces acting on it.
- Labels on the diagram indicate the specific distances and angles at which these forces act relative to the origin point on the pipe.

#### Solution Steps
1. **Identify the coordinates and forces acting on the pipe**:
- $\vec{F_1} = 40\ \mathrm{N}$ in the j-direction at (0, 2, 0).
- $\vec{F_2} = 50\ \mathrm{N}$ making a 60° angle with the positive x-axis at (4, 4, 0).
- $\vec{F_3} = 40\ \mathrm{N}$ along negative x-direction at the origin.
- $\vec{F_4} = 50\ \mathrm{N}$ downward making

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