earning Goal: particle of mass M moves along a straight line with initial speed v₁. A force of magnitude F pushes the particle a distance s along the direction of its motion.
earning Goal: particle of mass M moves along a straight line with initial speed v₁. A force of magnitude F pushes the particle a distance s along the direction of its motion.
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
Related questions
Question
![**Learning Goal:**
A particle of mass \( M \) moves along a straight line with initial speed \( v_i \). A force of magnitude \( F \) pushes the particle a distance \( s \) along the direction of its motion.
---
**Concept Explanation:**
The scenario describes a fundamental problem in classical mechanics concerning the motion of a particle when an external force is applied. Let's break down the components:
- **Initial Conditions:**
- The particle has a mass \( M \).
- It begins with an initial speed \( v_i \) along a straight path.
- **External Influence:**
- A force of magnitude \( F \) acts on the particle.
- This force causes the particle to move a distance \( s \) in the same direction as the force.
**Key Concepts:**
1. **Newton's Second Law of Motion:**
- This law states that the force acting on an object is equal to the mass of that object times its acceleration (\( F = ma \)).
2. **Work-Energy Principle:**
- The work done by a force on an object is equal to the change in kinetic energy of that object.
- The work done by the force \( F \) over a distance \( s \) is \( W = F \cdot s \).
3. **Kinetic Energy:**
- The initial kinetic energy of the particle is given by \( KE_i = \frac{1}{2} M v_i^2 \).
- After the force has done work on the particle, the final kinetic energy \( KE_f \) can be calculated.
**Applications:**
From the provided information, we can explore several physical concepts, such as:
- Calculating the acceleration of the particle due to the force \(F\).
- Determining the final speed of the particle after it has traveled the distance \(s\).
- Understanding how the energy imparted by the force changes the particle’s kinetic energy.
This foundational problem is crucial for understanding more complex physics scenarios involving forces and motion.
---
**Additional Resources:**
- **Videos:** Watch demonstrations of Newton’s laws.
- **Textbooks:** Refer to introductory physics textbooks for detailed explanations on work and energy.
- **Interactive Simulations:** Use online simulations to visualize the effects of force on a moving particle.
---
**Weather Information:**
- [Weather Icon: Sunny]
99°F
Note: In](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe62c7a88-b129-4d03-954b-a75b918bc43a%2Fd2d15339-9adf-4406-89f3-43aa67819d1a%2F8s8a43l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Learning Goal:**
A particle of mass \( M \) moves along a straight line with initial speed \( v_i \). A force of magnitude \( F \) pushes the particle a distance \( s \) along the direction of its motion.
---
**Concept Explanation:**
The scenario describes a fundamental problem in classical mechanics concerning the motion of a particle when an external force is applied. Let's break down the components:
- **Initial Conditions:**
- The particle has a mass \( M \).
- It begins with an initial speed \( v_i \) along a straight path.
- **External Influence:**
- A force of magnitude \( F \) acts on the particle.
- This force causes the particle to move a distance \( s \) in the same direction as the force.
**Key Concepts:**
1. **Newton's Second Law of Motion:**
- This law states that the force acting on an object is equal to the mass of that object times its acceleration (\( F = ma \)).
2. **Work-Energy Principle:**
- The work done by a force on an object is equal to the change in kinetic energy of that object.
- The work done by the force \( F \) over a distance \( s \) is \( W = F \cdot s \).
3. **Kinetic Energy:**
- The initial kinetic energy of the particle is given by \( KE_i = \frac{1}{2} M v_i^2 \).
- After the force has done work on the particle, the final kinetic energy \( KE_f \) can be calculated.
**Applications:**
From the provided information, we can explore several physical concepts, such as:
- Calculating the acceleration of the particle due to the force \(F\).
- Determining the final speed of the particle after it has traveled the distance \(s\).
- Understanding how the energy imparted by the force changes the particle’s kinetic energy.
This foundational problem is crucial for understanding more complex physics scenarios involving forces and motion.
---
**Additional Resources:**
- **Videos:** Watch demonstrations of Newton’s laws.
- **Textbooks:** Refer to introductory physics textbooks for detailed explanations on work and energy.
- **Interactive Simulations:** Use online simulations to visualize the effects of force on a moving particle.
---
**Weather Information:**
- [Weather Icon: Sunny]
99°F
Note: In
![**Increase in Initial Speed**
For the final two parts, assume that the initial speed of the particle is increased to \( 3v_i \), with the particle's mass once again equal to \( M \).
### Part D
By what factor, \( R_T \), does the initial kinetic energy increase (with respect to the first scenario, with mass \( M \) and speed \( v_i \)), and by what factor, \( R_U \), does the work done by the force increase?
**Express your answers numerically separated by a comma.**
\[ R_T, R_U = \]
**Submit** [Submit Button Image]
[Request Answer Button Image]
### Part E
The particle’s change in speed over the distance \( s \) will be ________ the change in speed when the particle had an initial speed equal to \( v_i \).
[View Available Hint(s) Button Image]
[Submit Answer Button Image]
[Close Hint Button Images]
---
Please insert values for \( R_T \) and \( R_U \) as per the analysis of the initial scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe62c7a88-b129-4d03-954b-a75b918bc43a%2Fd2d15339-9adf-4406-89f3-43aa67819d1a%2F1ygbjgi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Increase in Initial Speed**
For the final two parts, assume that the initial speed of the particle is increased to \( 3v_i \), with the particle's mass once again equal to \( M \).
### Part D
By what factor, \( R_T \), does the initial kinetic energy increase (with respect to the first scenario, with mass \( M \) and speed \( v_i \)), and by what factor, \( R_U \), does the work done by the force increase?
**Express your answers numerically separated by a comma.**
\[ R_T, R_U = \]
**Submit** [Submit Button Image]
[Request Answer Button Image]
### Part E
The particle’s change in speed over the distance \( s \) will be ________ the change in speed when the particle had an initial speed equal to \( v_i \).
[View Available Hint(s) Button Image]
[Submit Answer Button Image]
[Close Hint Button Images]
---
Please insert values for \( R_T \) and \( R_U \) as per the analysis of the initial scenario.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY