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

In summary, the conversation discusses the relationship between cross sectional area and the amount of work required to stretch a device. The concept of stress is brought up, with the equation stress = force applied / area being mentioned. It is noted that an increase in area leads to a decrease in stress and an increase in Young's modulus, meaning the material can handle more stress. The conversation also prompts the consideration of Hooke's law and how it relates to Young's modulus. Lastly, the hypothetical scenario of the cords having a cross sectional area of zero is suggested, questioning the amount of force needed to stretch them.
  • #1
ravsterphysics
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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)
 
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  • #2
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).
 
  • #3
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?
 
  • #4
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).
 
  • #5
Suppose the cross sectional area of the rubber cords was zero. How much force would it take to stretch them?
 

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

1. What is Hooke's Law?

Hooke's Law is a physical law that states the force exerted on a spring is directly proportional to the amount the spring is stretched or compressed.

2. How does Hooke's Law relate to work?

Hooke's Law relates to work by stating that the work done on a spring is equal to the force applied multiplied by the distance the spring is stretched or compressed.

3. How does increasing cross sectional area affect work in Hooke's Law?

Increasing cross sectional area decreases the amount of work done on a spring. This is because a larger cross sectional area results in a stronger spring, requiring less force to stretch or compress it.

4. Does increasing cross sectional area always reduce work in Hooke's Law?

No, increasing cross sectional area does not always reduce work in Hooke's Law. If the force applied to the spring is also increased, the work done will also increase, regardless of the cross sectional area.

5. What are some real-world applications of Hooke's Law?

Hooke's Law has many real-world applications, including in the design of springs for various machines and devices, such as trampolines, car suspensions, and pogo sticks. It is also used in the study of elasticity in materials, such as rubber bands and elastic clothing.

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