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

[ravsterphysics]

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)

 

[gneill]

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).

 

[ravsterphysics]

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?

 

[gneill]

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).

 

[Chestermiller]

Suppose the cross sectional area of the rubber cords was zero. How much force would it take to stretch them?