A pipe system consists of three pipes with lengths L1 = 1.50 m, L2 = 0.500 m, and L3 = 2.60 m. A plumber pulls on the end of the pipe system, at the point P, with a force = -21.0 Ni + 49.0 Nj + 31.5 Nk. Po What is the torque 7 due to Fp about the origin?

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

A pipe system consists of three pipes with lengths:
- \( L_1 = 1.50 \, \text{m} \)
- \( L_2 = 0.500 \, \text{m} \)
- \( L_3 = 2.60 \, \text{m} \)

A plumber pulls on the end of the pipe system, at the point \( P \), with a force:
\[
\vec{F}_P = -21.0 \, \text{N} \, \hat{i} + 49.0 \, \text{N} \, \hat{j} + 31.5 \, \text{N} \, \hat{k}
\]

### Diagram Explanation

The diagram shows a coordinate system with axes labeled \( x \), \( y \), and \( z \). The origin \( O \) is where the three axes intersect. The pipes form a right-angled triangular shape in the \( xy \)-plane with the base along the \( x \)-axis, extending from the origin. The point \( P \) is shown where the force is applied, and the pipes are depicted with lengths \( L_1 \), \( L_2 \), and \( L_3 \), making up the sides of the triangle.

## Question

What is the torque \( \vec{\tau} \) due to \( \vec{F}_P \) about the origin?

Enter your expression using \( \hat{i}, \hat{j}, \text{ and } \hat{k} \) unit vector notation.

\[
\vec{\tau} = \, \boxed{\phantom{aaaaaaaaaaaa}}
\]

(N·m)
Transcribed Image Text:## Problem Statement A pipe system consists of three pipes with lengths: - \( L_1 = 1.50 \, \text{m} \) - \( L_2 = 0.500 \, \text{m} \) - \( L_3 = 2.60 \, \text{m} \) A plumber pulls on the end of the pipe system, at the point \( P \), with a force: \[ \vec{F}_P = -21.0 \, \text{N} \, \hat{i} + 49.0 \, \text{N} \, \hat{j} + 31.5 \, \text{N} \, \hat{k} \] ### Diagram Explanation The diagram shows a coordinate system with axes labeled \( x \), \( y \), and \( z \). The origin \( O \) is where the three axes intersect. The pipes form a right-angled triangular shape in the \( xy \)-plane with the base along the \( x \)-axis, extending from the origin. The point \( P \) is shown where the force is applied, and the pipes are depicted with lengths \( L_1 \), \( L_2 \), and \( L_3 \), making up the sides of the triangle. ## Question What is the torque \( \vec{\tau} \) due to \( \vec{F}_P \) about the origin? Enter your expression using \( \hat{i}, \hat{j}, \text{ and } \hat{k} \) unit vector notation. \[ \vec{\tau} = \, \boxed{\phantom{aaaaaaaaaaaa}} \] (N·m)
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