# Calculating Work Needed to Stretch a Spring: 100J to 0.75m

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• iPhotonHQ
In summary, the conversation discusses the calculation of work needed to stretch a spring from its equilibrium position. It is determined that the work required is not constant and an integral must be used to find the accurate value. It is also mentioned that Hooke's law can be applied to find the solution, which involves solving for the constant k. The final conclusion is that the work needed to stretch the spring an additional 0.75m is 525 J.
iPhotonHQ
"It takes 100J of work to stretch a spring 0.5m from its equilibrium position. How much work is needed to stretch it an additional 0.75m."
Attempt: w = ⌠abF(x)dx
work = F x D
100J = F x 0.5m
F = 200J

0.75 + 0.5 = 1.25
w = ⌠0.51.25 200dx
w = 150 J

The correct answer: w = 525 J

what did I do wrong? Thanks!

Nevermind, I found the exact problem online, so sorry!

Work is not constant in spring.You can't use W=Fd.You should take an integral
(Carefull for the signs when you take an integral).
Another thing that Questions ask "The work done by our force".

Arman777 said:
Work is not constant in spring.You can't use W=Fd.You should take an integral
(Carefull for the signs when u take an integral).
Another thing that Questions ask "The work done by our force".
My problem was that I forgot hooke's law.
F = kx
I can apply it to the given information to find the target solution.

Any ideas How ?

Arman777 said:
Any ideas How ?
w = ⌠.51.25 kx dx
you can solve for k by plugging in known integral...
100 = ⌠0.5kxdx

you should get k = 800

great

## 1. How do you calculate the work needed to stretch a spring from 100J to 0.75m?

To calculate the work needed to stretch a spring, you can use the formula W = (1/2)kx^2, where W is the work, k is the spring constant, and x is the displacement. In this case, the work would be equal to 100J and the displacement would be 0.75m. By rearranging the formula, you can solve for the spring constant (k) and then plug in the values to find the work needed.

## 2. What is the unit of measurement for the work needed to stretch a spring?

The unit of measurement for work is joules (J). This unit is commonly used to measure energy and is equivalent to the amount of work done when a force of one newton is applied over a distance of one meter.

## 3. Can the work needed to stretch a spring be negative?

Yes, the work needed to stretch a spring can be negative if the spring is released and returns to its original position. This is because the displacement in this case would be in the opposite direction of the force, resulting in negative work.

## 4. How does the work needed to stretch a spring change if the displacement is doubled?

The work needed to stretch a spring is directly proportional to the displacement. This means that if the displacement is doubled, the work needed would also double. This is because a larger displacement requires more force to stretch the spring, resulting in more work being done.

## 5. Can the work needed to stretch a spring be greater than the potential energy stored in the spring?

Yes, the work needed to stretch a spring can be greater than the potential energy stored in the spring. This can happen if the spring is stretched beyond its elastic limit, which is the point at which the spring can no longer return to its original position. In this case, additional work would be needed to stretch the spring further, but the potential energy stored would remain the same.

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