A 0.220-kg block resting on a frictionless, horizontal surface is attached to a spring having force constant 83.8 N/m as in the figure below. A horizontal force F causes the spring to stretch at a distance of 5.49 cm from its equilibrium position.   (a) Find the value of F. (Enter the magnitude of the force only.)  N (b) What is the total energy stored in the system when the spring is stretched?  J (c) Find the magnitude of the acceleration of the block immediately after the applied force is removed.  m/s2

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)...
icon
Related questions
icon
Concept explainers
Question

A 0.220-kg block resting on a frictionless, horizontal surface is attached to a spring having force constant 83.8 N/m as in the figure below. A horizontal force F causes the spring to stretch at a distance of 5.49 cm from its equilibrium position.

 
(a) Find the value of F. (Enter the magnitude of the force only.)
 N

(b) What is the total energy stored in the system when the spring is stretched?
 J

(c) Find the magnitude of the acceleration of the block immediately after the applied force is removed.
 m/s2

(d) Find the speed of the block when it first reaches the equilibrium position.
 m/s

(e) If the surface is not frictionless but the block still reaches the equilibrium position, how would your answer to part (d) change?
The block would arrive at a greater speed.
The block would arrive at a lower speed.    
The block would arrive at the same speed.

(f) What other information would you need to know to find the actual answer to part (d) in this case?
 
### Hooke's Law and Spring Force

This image illustrates the concept of Hooke's Law and the force exerted by a spring. 

- **Spring**: The left side of the image shows a coiled spring attached to a fixed surface.
- **Mass/Block**: Adjacent to the spring is a blue block, which represents a mass that is being acted upon by the spring.
- **Force (F)**: The arrow pointing to the right with the label \(\vec{F}\) indicates the direction of the force applied to the block.

#### Explanation of the Diagram

- **Fixed Surface**: On the left side, the spring is attached to a fixed point which does not move.
- **Spring**: The coiled structure represents the spring, which can compress or stretch.
- **Block**: The block (colored in blue) is attached to the spring and moves when the force is applied.
- **Force Direction**: The blue arrow labeled \(\vec{F}\) represents the force applied to the block, causing a displacement.

### Hooke's Law
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as:

\[ \vec{F} = -k \vec{x} \]

Where:
- \( \vec{F} \) is the force exerted by the spring,
- \( k \) is the spring constant, a measure of the stiffness of the spring,
- \( \vec{x} \) is the displacement of the spring from its equilibrium position,
- The negative sign indicates that the direction of the force exerted by the spring is opposite to the direction of displacement.

### Practical Application
Understanding Hooke's Law is crucial in various applications, including mechanical system design, material science, and even biomechanics. It helps in designing objects that involve springs and elastic components, ensuring they can withstand the forces during operation.
Transcribed Image Text:### Hooke's Law and Spring Force This image illustrates the concept of Hooke's Law and the force exerted by a spring. - **Spring**: The left side of the image shows a coiled spring attached to a fixed surface. - **Mass/Block**: Adjacent to the spring is a blue block, which represents a mass that is being acted upon by the spring. - **Force (F)**: The arrow pointing to the right with the label \(\vec{F}\) indicates the direction of the force applied to the block. #### Explanation of the Diagram - **Fixed Surface**: On the left side, the spring is attached to a fixed point which does not move. - **Spring**: The coiled structure represents the spring, which can compress or stretch. - **Block**: The block (colored in blue) is attached to the spring and moves when the force is applied. - **Force Direction**: The blue arrow labeled \(\vec{F}\) represents the force applied to the block, causing a displacement. ### Hooke's Law Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as: \[ \vec{F} = -k \vec{x} \] Where: - \( \vec{F} \) is the force exerted by the spring, - \( k \) is the spring constant, a measure of the stiffness of the spring, - \( \vec{x} \) is the displacement of the spring from its equilibrium position, - The negative sign indicates that the direction of the force exerted by the spring is opposite to the direction of displacement. ### Practical Application Understanding Hooke's Law is crucial in various applications, including mechanical system design, material science, and even biomechanics. It helps in designing objects that involve springs and elastic components, ensuring they can withstand the forces during operation.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Potential energy
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.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON