Solve for Fv ### Statics and Forces in Equilibrium#### Problem StatementYou use a board that is 60 cm long, and the cable makes an angle of 40 degrees with the board when the board is held horizontally. You place the spider a distance \( r = 29 \) cm from the hinge. The board has a mass of \( 3.0 \) kg, and the spider has a mass of \( 1.2 \) kg. The hinge applies both a horizontal force and a vertical force. You will be asked to determine the direction of both of these forces (left, right, up, down).1. **What is the magnitude of the tension in the cable in Newtons?** \[ T = \boxed{25.92 \text{ N}} \] (The provided value is incorrect.)2. **What is the magnitude and direction of the horizontal force from the hinge? Enter a positive number for the magnitude.** \[ F_H = \boxed{19.86 \text{ N}} \] Direction: \(\boxed{\text{to the left}}\)3. **What is the magnitude and direction of the vertical force from the hinge? Enter a positive number for the magnitude.** \[ F_V = \boxed{24.50 \text{ N}} \] Direction: \(\boxed{\text{upward}}\)#### Explanation of Diagram1. **Board Setup:** - The board is shown horizontally with a hinge at one end and a cable attached at an angle of 40° to the other end. - The board's length is marked as 60 cm. - A spider is placed at 29 cm from the hinge.2. **Angles and Forces:** - The angle of 40° is marked at the point where the cable is attached to the board. - Forces are indicated (not drawn) but are part of the problem to be solved.The answers to the questions involve calculating the tension in the cable, and both horizontal and vertical components of the force applied by the hinge. The problem requires an understanding of statics, specifically force equilibrium, where the sum of forces and the sum of moments acting on the system must be zero.

Answered: Solve for Fv

Engineering

Mechanical Engineering

Solve for Fv

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

Solve for Fv

### Statics and Forces in Equilibrium

#### Problem Statement

You use a board that is 60 cm long, and the cable makes an angle of 40 degrees with the board when the board is held horizontally. You place the spider a distance \( r = 29 \) cm from the hinge. The board has a mass of \( 3.0 \) kg, and the spider has a mass of \( 1.2 \) kg. The hinge applies both a horizontal force and a vertical force. You will be asked to determine the direction of both of these forces (left, right, up, down).

1. **What is the magnitude of the tension in the cable in Newtons?**
\[
T = \boxed{25.92 \text{ N}}
\]
(The provided value is incorrect.)

2. **What is the magnitude and direction of the horizontal force from the hinge? Enter a positive number for the magnitude.**
\[
F_H = \boxed{19.86 \text{ N}}
\]
Direction: \(\boxed{\text{to the left}}\)

3. **What is the magnitude and direction of the vertical force from the hinge? Enter a positive number for the magnitude.**
\[
F_V = \boxed{24.50 \text{ N}}
\]
Direction: \(\boxed{\text{upward}}\)

#### Explanation of Diagram

1. **Board Setup:**
- The board is shown horizontally with a hinge at one end and a cable attached at an angle of 40° to the other end.
- The board's length is marked as 60 cm.
- A spider is placed at 29 cm from the hinge.

2. **Angles and Forces:**
- The angle of 40° is marked at the point where the cable is attached to the board.
- Forces are indicated (not drawn) but are part of the problem to be solved.

The answers to the questions involve calculating the tension in the cable, and both horizontal and vertical components of the force applied by the hinge. The problem requires an understanding of statics, specifically force equilibrium, where the sum of forces and the sum of moments acting on the system must be zero.

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