Dependence of extention on length

In summary, the conversation discusses a light uniform spring that is tied between the ceiling and the floor. A bead of finite mass is attached to the spring and allowed to slowly move down, causing a shift in distance. The question is how the distance (y) depends on the distance (l) between the bead and the upper end of the spring. The attempted solution involves calculating the changes in length of the upper and lower parts of the spring, but the answer is said to be incorrect due to the partial spring having a different spring constant than the full spring.
  • #1
Brilli
48
0

Homework Statement


A light uniform spring is tied between the ceiling and the floor keeping the spring vertical as shown in the figure. A bead of finite mass is glued at a distance l from the upper end and then allowed to go slowly down. The bead shifts a distance y.How does the y depend on l?

The Attempt at a Solution

I put that k(change in length of the spring upper part) +k ( change in legth of the lower part)=mg
And that both changes are same thus the changes in legth =(mgk)/2. But the answer says its wrong.
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  • #2
The spring constant of a partial spring is not the same as the spring constant of the full spring.
 
  • #3
Orodruin said:
The spring constant of a partial spring is not the same as the spring constant of the full spring.
Thanks you so much!
 

1. How does the length of an object affect its extension?

The length of an object directly affects its extension. When a force is applied to an object, it will stretch or compress in the direction of the force. The amount of stretch or compression is directly proportional to the length of the object.

2. What is the relationship between extension and length?

The relationship between extension and length is a linear one. This means that as the length of an object increases, its extension or deformation also increases in a proportional manner.

3. Does the material of an object affect the dependence of extension on length?

Yes, the material of an object does affect the dependence of extension on length. Different materials have different elastic properties, which determine how much they will stretch or compress when a force is applied. Therefore, the dependence of extension on length may vary for different materials.

4. How is the dependence of extension on length measured in scientific experiments?

The dependence of extension on length is typically measured by conducting a tensile test. This involves applying a force to an object and measuring its extension at various lengths. The data collected is then used to plot a stress-strain curve, which shows the relationship between extension and length.

5. Can the dependence of extension on length be used to predict the behavior of objects under different forces?

Yes, the dependence of extension on length can be used to predict the behavior of objects under different forces. By understanding the relationship between extension and length, scientists can make accurate predictions about an object's behavior when different forces are applied to it. This is especially useful in engineering and design applications.

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