. 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.
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)...
Related questions
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f5b5be0-3b24-4105-92aa-f99f327c1089%2Fb9223549-99d4-4e27-a3fe-844034ca5afd%2F7ugh9hm.jpeg&w=3840&q=75)
Transcribed Image Text:### 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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON