**Educational Content:**In this problem, we are given forces and couple moments acting on the toe and heel plates of a snow ski. Our task is to replace this system with an equivalent force and couple moment at a specific point \( P \).### Given Data- **For the toe plate:** - Force \( \mathbf{F}_t = \{-38i + 100j - 141k\} \, \text{N} \) - Moment \( \mathbf{M}_t = \{-5i + 4j + 2k\} \, \text{N} \cdot \text{m} \)- **For the heel plate:** - Force \( \mathbf{F}_h = \{-13i - 6j - 26k\} \, \text{N} \) - Moment \( \mathbf{M}_h = \{-24i + 8j + 13k\} \, \text{N} \cdot \text{m} \)### Objective- Calculate the equivalent force vector and couple moment vector at point \( P \).### Part A: Equivalent ForceFind the components of the equivalent force.1. Sum the x, y, and z components of the forces from both the toe and heel plates.2. Express the result as a Cartesian vector using components in newtons to three significant figures.**Input Box:**\[(F_R)_x, \, (F_R)_y, \, (F_R)_z = \boxed{\phantom{000}} \, \text{N}\]### Part B: Equivalent MomentFind the components of the couple moment acting at point \( P \).1. Sum the moments from both the toe and heel.2. Express the result as a Cartesian vector using components in newton-meters to three significant figures.**Input Box:**\[(M_P)_x, \, (M_P)_y, \, (M_P)_z = \boxed{\phantom{000}} \, \text{N} \cdot \text{m}\]This exercise helps in understanding vector addition and the replacement of force systems, fundamental concepts in physics and engineering dynamics. The image depicts a mechanical setup involving forces and moments acting on a slender beam. Here's a detailed explanation:1. **Axes**: - The diagram is oriented with three axes: x, y, and z for three-dimensional analysis.2. **Beam**: - A beam is shown with two supports along its length. The beam is lying approximately along the x-axis.3. **Forces**: - \( F_r \): A force acting perpendicular to the beam at one of the support points on the left. - \( F_h \): A horizontal force acting parallel to the beam at the same support point as \( F_r \).4. **Moments**: - \( M_l \): A moment (torque) indicated at the left support, represented by a curved arrow around the axis at that point. - \( M_h \): Another moment depicted near the right support, similar in representation to \( M_l \).5. **Support Points**: - The two support points are located at: - \( O \): The origin or reference point, marked at the right end of the beam. - Another point 120 mm to the left of \( O \), marked as the position of \( F_r \) and \( F_h \).6. **Dimensions**: - The total length from the reference point \( O \) to the point \( P \) at the left end is 800 mm.This setup can be used to analyze the static equilibrium of the beam, considering both translational and rotational effects. The forces and moments will induce stresses and deformations, which can be calculated using principles from mechanics and structural analysis.

Answered: m. nd Find the components of the…

m. nd Find the components of the equivalent force. Express the re Express the z, y, and z components of the force in new (FR)z. (FR)y. (FR)= =

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**Educational Content:**

In this problem, we are given forces and couple moments acting on the toe and heel plates of a snow ski. Our task is to replace this system with an equivalent force and couple moment at a specific point \( P \).

### Given Data

- **For the toe plate:**
- Force \( \mathbf{F}_t = \{-38i + 100j - 141k\} \, \text{N} \)
- Moment \( \mathbf{M}_t = \{-5i + 4j + 2k\} \, \text{N} \cdot \text{m} \)

- **For the heel plate:**
- Force \( \mathbf{F}_h = \{-13i - 6j - 26k\} \, \text{N} \)
- Moment \( \mathbf{M}_h = \{-24i + 8j + 13k\} \, \text{N} \cdot \text{m} \)

### Objective

- Calculate the equivalent force vector and couple moment vector at point \( P \).

### Part A: Equivalent Force
Find the components of the equivalent force.
1. Sum the x, y, and z components of the forces from both the toe and heel plates.
2. Express the result as a Cartesian vector using components in newtons to three significant figures.

**Input Box:**
\[
(F_R)_x, \, (F_R)_y, \, (F_R)_z = \boxed{\phantom{000}} \, \text{N}
\]

### Part B: Equivalent Moment
Find the components of the couple moment acting at point \( P \).
1. Sum the moments from both the toe and heel.
2. Express the result as a Cartesian vector using components in newton-meters to three significant figures.

**Input Box:**
\[
(M_P)_x, \, (M_P)_y, \, (M_P)_z = \boxed{\phantom{000}} \, \text{N} \cdot \text{m}
\]

This exercise helps in understanding vector addition and the replacement of force systems, fundamental concepts in physics and engineering dynamics.

The image depicts a mechanical setup involving forces and moments acting on a slender beam. Here's a detailed explanation:

1. **Axes**:
- The diagram is oriented with three axes: x, y, and z for three-dimensional analysis.

2. **Beam**:
- A beam is shown with two supports along its length. The beam is lying approximately along the x-axis.

3. **Forces**:
- \( F_r \): A force acting perpendicular to the beam at one of the support points on the left.
- \( F_h \): A horizontal force acting parallel to the beam at the same support point as \( F_r \).

4. **Moments**:
- \( M_l \): A moment (torque) indicated at the left support, represented by a curved arrow around the axis at that point.
- \( M_h \): Another moment depicted near the right support, similar in representation to \( M_l \).

5. **Support Points**:
- The two support points are located at:
- \( O \): The origin or reference point, marked at the right end of the beam.
- Another point 120 mm to the left of \( O \), marked as the position of \( F_r \) and \( F_h \).

6. **Dimensions**:
- The total length from the reference point \( O \) to the point \( P \) at the left end is 800 mm.

This setup can be used to analyze the static equilibrium of the beam, considering both translational and rotational effects. The forces and moments will induce stresses and deformations, which can be calculated using principles from mechanics and structural analysis.

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