Tension on a box made of stretchable material

[Yuppy]

Please take a look at the slides attached.

Suppose I apply a force F on the right hand side and another on the left hand side as shown in the following diagram. Suppose that the material can be stretched. Now one of my friends said that the extension is delta due to a force F while another friend said it is 2delta and they both gave me their reasons. The next slides shows their reasoning. Could you please tell me which reasoning is right?

 

[Doc Al]

Now one of my friends said that the extension is delta due to a force F while another friend said it is 2delta and they both gave me their reasons.

The tension created is F, not 2F. The extension, which is measured from end to end, is due to the tension F. If you measure from the center, then each end moves delta/2, of course. The total end-to-end extension is the same no matter how you think of it.

Point out to your second friend that if you measure from the center, the effective "spring constant" of the material is twice as much--since you are looking at only half of it--thus the extension of each end from the center is just half of the total extension.

Make sense?

 

[astrokreng]

I cannot definitively say which reasoning is correct without more information about the specific properties of the stretchable material and the forces being applied. However, I can provide some insights that may help clarify the situation.

Firstly, it is important to understand that the extension of a material is directly related to the applied force and the material's properties such as elasticity and stiffness. Different materials will behave differently when subjected to the same force, so it is important to know the specific properties of the material in question.

In the first reasoning, it is stated that the extension is equal to delta due to the force F. This suggests that the material is behaving in a linear manner, where the extension is directly proportional to the applied force. This is known as Hooke's Law and is applicable to certain materials such as springs. However, not all materials behave in a linear manner, so it is important to determine if the material in question follows this law.

In the second reasoning, it is stated that the extension is 2delta due to the force F. This suggests that the material is behaving in a non-linear manner, where the extension is not directly proportional to the applied force. This could be due to the material's properties such as non-linear elasticity or plastic behavior. Again, it is important to know the specific properties of the material to determine if this reasoning is correct.

In summary, the correct reasoning will depend on the specific properties of the stretchable material and the forces being applied. Without this information, it is difficult to determine which reasoning is correct. It may be helpful to conduct experiments or consult with experts in the field to determine the behavior of the material in question.