How Do Compression Distances Affect Spring Work Calculations?

The limits of integration in part 2 should be from 5 to 9, since x represents the compression distance, not the length of the spring. This can be found using the equation Work = Force * Distance, and substituting in F = kx. In summary, the limits of integration in part 2 should be from 5 to 9, as x represents the compression distance in this problem.
  • #1
ecoo
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2

Homework Statement



I reference the problem posted here: https://www.physicsforums.com/threads/work-and-spring-problem.194531/

Homework Equations



Work = Force * Distance

F = kx

The Attempt at a Solution



Wouldn't the limits of integration in part 2 be from 5 to 9, since x is the compression distance, not the length of the spring?

Thanks!
 
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  • #2
ecoo said:

Homework Statement



I reference the problem posted here: https://www.physicsforums.com/threads/work-and-spring-problem.194531/

Homework Equations



Work = Force * Distance

F = kx

The Attempt at a Solution



Wouldn't the limits of integration in part 2 be from 5 to 9, since x is the compression distance, not the length of the spring?

Thanks!
Yes, I agree with you.
 
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Related to How Do Compression Distances Affect Spring Work Calculations?

1. What is work done on a spring?

The work done on a spring is the amount of energy required to stretch or compress it from its initial position to a new position. This work is typically measured in joules (J) and is equal to the force applied to the spring multiplied by the distance it is stretched or compressed.

2. How is work done on a spring calculated?

The work done on a spring can be calculated using the formula W = 1/2kx², where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What is the relationship between work done and the potential energy of a spring?

The work done on a spring is equal to the change in potential energy of the spring. This means that when work is done on a spring, its potential energy increases or decreases depending on whether it is being stretched or compressed.

4. Can work be done on a spring without changing its potential energy?

No, work cannot be done on a spring without changing its potential energy. This is because the work done is directly related to the change in potential energy of the spring.

5. How does the work done on a spring vary with the spring constant?

The work done on a spring is directly proportional to the spring constant. This means that as the spring constant increases, the amount of work required to stretch or compress the spring also increases.

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