Hooke's Law Q3: Does Increasing Cross Sectional Area Reduce Work?

  • Thread starter Thread starter ravsterphysics
  • Start date Start date
  • Tags Tags
    Hooke's law Law
Click For Summary

Homework Help Overview

The discussion revolves around the implications of increasing the cross-sectional area of cords in the context of Hooke's Law and the work done in stretching them. Participants are exploring the relationship between cross-sectional area, stress, and the work required for extension.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether increasing the cross-sectional area of the cords would lead to more or less work required to stretch them. Some suggest that heavier cords would require more work, while others argue that a larger area results in less extension and therefore less work. The concept of stress and its relationship to area is also being examined, with inquiries into how Young's modulus relates to these changes.

Discussion Status

The discussion is active, with participants offering different perspectives on the relationship between cross-sectional area and work done. Some guidance has been provided regarding the irrelevance of cord weight and the need to consider the elasticity of the cords in relation to their cross-sectional area. Multiple interpretations of the problem are being explored.

Contextual Notes

There is an ongoing examination of assumptions regarding the weight of the cords and the definition of stress in the context of Hooke's Law. The discussion includes hypothetical scenarios, such as the implications of a zero cross-sectional area.

ravsterphysics
Messages
57
Reaction score
1
1.JPG
2.JPG

3. The Attempt at a Solution

My thinking is that if cross sectional area of the cords increase wouldn't the cords be heavier and thus it would require more work to pull/stretch the device? So more work is done?

(But the answers say less work is done because there is a smaller extension/won't stretch as much)
 
Physics news on Phys.org
What concepts and equations are involved? Note that the weight of the cords is irrelevant here, it can be taken as negligible compared to the force associated with stretching them (think massless springs).
 
gneill said:
What concepts and equations are involved? Note that the weight of the cords is irrelevant here, it can be taken as negligible compared to the force associated with stretching them (think massless springs).

Okay can we then look at stress = force applied / area ?

So if area (cross sectional area) increases then stress decreases which means youngs modulus of the material increases? so it can handle more stress on it?
 
Young's constant for a given material will be constant. Look into how the elasticity of the cords would vary with the cross sectional area (i.e., investigate how the Hooke's law spring constant is related to Young's modulus for a material).
 
Suppose the cross sectional area of the rubber cords was zero. How much force would it take to stretch them?
 

Similar threads

Spring characteristics when loaded with a mass
  • · Replies 4 ·
Replies
4
Views
2K
What is the Hooke's Law Constant for a Stretched Muscle?
  • · Replies 5 ·
Replies
5
Views
5K
Bungee Jumping Physics: Hooke's Law & Potential Energy
  • · Replies 9 ·
Replies
9
Views
3K
Calculating the elastic potential energy from a force-extension investigation
  • · Replies 16 ·
Replies
16
Views
4K
Calculating Distance Using SHM & Hookes Law
  • · Replies 7 ·
Replies
7
Views
5K
Hooke's Law applied to a bungee cord
  • · Replies 1 ·
Replies
1
Views
10K
Young's Modulus and Hooke's Law
  • · Replies 6 ·
Replies
6
Views
11K
How Is the Spring Constant Derived from Young's Modulus, Length, and Area?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad A smaller cross-sectional area increases the resistance of a conductor?
  • · Replies 7 ·
Replies
7
Views
2K
Hooke's Law/Work done on a spring system
  • · Replies 3 ·
Replies
3
Views
3K