Is more work required for this spring?

In summary, the conversation discusses the work required to stretch a spring from two different points, x0=0 to x1=10 cm and x1=10 cm to x2=20 cm. It is determined that more work is required to stretch the spring from x1 to x2, and this is justified mathematically using the equation for work as the difference between final and initial elastic potential energies. The concept of elastic potential energy is also clarified.
  • #1
endeavor
176
0
A spring with a force constant of 50 N/m is stretched continuously from x0=0 to x2=20 cm. Is more work required to stretch the spring from x1=10 cm to x2=20 cm than from x0 to x1? Justify your answer mathematically.

I thought the work required is the same because the displacements are equal for both work equations... but I think I'm wrong.
 
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  • #2
work = 1/2 kx^2

so then the difference would be greater between 20cm and 10cm

w= EPEf-EPEi = 0.5(k)400-0.5(k)100 = 150k
w0->1 = 0.5(k)(100) - 0.5k(0) = 50k
 
  • #3
but wouldn't it be:
work1 = 1/2 k (10cm)^2
work2 = 1/2 k (20cm - 10cm)^2=work1
?
 
  • #4
no, the work is the difference between energies.

[tex] EPE_i + W = EPE_f [/tex]
[tex] W = EPE_f - EPE_i [/tex]
[tex] W = 0.5kx_f^2 - 0.5kx_i^2 [/tex]
 
  • #5
I remember now...

what does EPE mean?
 
  • #6
elastic potential energy
 

1. Is more work required for this spring?

The amount of work required for any given spring will depend on several factors, including the type of work, the complexity of the project, and the available resources. It is important to carefully assess these factors before determining the amount of work required.

2. How do I know if more work is required for this spring?

To determine if more work is required for a spring, it is important to thoroughly review the project goals and objectives, assess the progress made so far, and identify any potential challenges or roadblocks. This will help determine if more work is needed to achieve the desired outcome.

3. Can I complete this spring with the current amount of work?

This will depend on the specific requirements and goals of the spring. If the current amount of work is not enough to achieve the desired outcome, it may be necessary to reassess and potentially increase the amount of work required.

4. What if I am unable to complete the required work for this spring?

If you are unable to complete the required work for a spring, it is important to communicate this as soon as possible. This will allow for adjustments to be made and a plan to be put in place to ensure the project can still be successfully completed.

5. How can I efficiently manage the required work for this spring?

To efficiently manage the required work for a spring, it is important to prioritize tasks, set clear goals and deadlines, and regularly assess progress. Effective communication and delegation can also help ensure that the work is completed efficiently and effectively.

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