### Static Equilibrium of a Square Plate#### Problem StatementA square plate is acted on by the three forces shown in the diagram. Is the plate in static equilibrium?*Yes.** No, the net torque is zero but the net force is not zero.* No, the net force is zero but the net torque is not zero.* No, neither the net force nor the net torque is zero.#### Diagram ExplanationThe diagram accompanying the problem shows a square plate subjected to three forces:1. A horizontal force \( F \) acting to the left at the top-left corner of the plate.2. A vertical downward force \( F \) applied at the bottom-center of the plate.3. A force \( \sqrt{2}F \) acting at a 45° angle from the top-center of the plate.The diagram visually represents the position and direction of these three forces. The force \( \sqrt{2}F \) is represented with dashed lines showing its components: one horizontal component to the right and one vertical component upwards.### Concept of Static EquilibriumStatic equilibrium of a rigid body requires that both the net force and the net torque acting on the body be zero.1. **Net Force**: The vector sum of all the forces acting on the plate must be zero.2. **Net Torque**: The sum of torques (moments) produced by all the forces about any point must be zero.On analyzing the given forces:- **Horizontal Forces**: There is a force \( F \) to the left and a horizontal component of \( \sqrt{2}F \cos 45° = F \) to the right. These forces cancel each other out, resulting in a net horizontal force of zero. - **Vertical Forces**: There is a force \( F \) downward and a vertical component of \( \sqrt{2}F \sin 45° = F \) upward. These forces also cancel each other out, resulting in a net vertical force of zero.Since both the horizontal and vertical force components add up to zero, the net force on the plate is zero.#### Verification of Net TorqueFor the net torque, consider calculating the torque around the center of the square plate. Since the forces are visually balanced and each pair of equal and opposite forces are aligned such that their torques cancel each other out:- The forces acting at symmetric positions (equal distances from the center

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. A square plate is acted on by the three forces shown. Is the plate in static equilibrium? VEF Yes. No, the net torque is zero but the net force is not zero. No, the net force is zero but the net torque is not zero. F No, neither the net force nor the net torque is zero.

. A square plate is acted on by the three forces shown. Is the plate in static equilibrium? VEF Yes. No, the net torque is zero but the net force is not zero. No, the net force is zero but the net torque is not zero. F No, neither the net force nor the net torque is zero.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Angular Momentum

Section: Chapter Questions

Problem 5P: Two forces F1 and F2 act along the two sides of an equilateral triangle as shown in Figure P11.5....

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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

### Static Equilibrium of a Square Plate

#### Problem Statement
A square plate is acted on by the three forces shown in the diagram. Is the plate in static equilibrium?

*Yes.*

* No, the net torque is zero but the net force is not zero.
* No, the net force is zero but the net torque is not zero.
* No, neither the net force nor the net torque is zero.

#### Diagram Explanation
The diagram accompanying the problem shows a square plate subjected to three forces:
1. A horizontal force \( F \) acting to the left at the top-left corner of the plate.
2. A vertical downward force \( F \) applied at the bottom-center of the plate.
3. A force \( \sqrt{2}F \) acting at a 45° angle from the top-center of the plate.

The diagram visually represents the position and direction of these three forces. The force \( \sqrt{2}F \) is represented with dashed lines showing its components: one horizontal component to the right and one vertical component upwards.

### Concept of Static Equilibrium
Static equilibrium of a rigid body requires that both the net force and the net torque acting on the body be zero.

1. **Net Force**: The vector sum of all the forces acting on the plate must be zero.
2. **Net Torque**: The sum of torques (moments) produced by all the forces about any point must be zero.

On analyzing the given forces:

- **Horizontal Forces**: There is a force \( F \) to the left and a horizontal component of \( \sqrt{2}F \cos 45° = F \) to the right. These forces cancel each other out, resulting in a net horizontal force of zero.

- **Vertical Forces**: There is a force \( F \) downward and a vertical component of \( \sqrt{2}F \sin 45° = F \) upward. These forces also cancel each other out, resulting in a net vertical force of zero.

Since both the horizontal and vertical force components add up to zero, the net force on the plate is zero.

#### Verification of Net Torque
For the net torque, consider calculating the torque around the center of the square plate. Since the forces are visually balanced and each pair of equal and opposite forces are aligned such that their torques cancel each other out:

- The forces acting at symmetric positions (equal distances from the center

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