Work done to move spring displacement

In summary, the conversation discusses the problem of finding the amount of work needed to change the length of a spring from 2 cm to 10 cm, given its relaxed length of 5 cm and stiffness of 95 N/m. The attempt at a solution involves using the equation W = Fdcostheta, but it is incorrect since the force is a function of x. The correct approach would be to use integration or an energy approach.
  • #1
gunster
7
0

Homework Statement


A spring has a relaxed length of 5 cm and a
stiffness of 95 N/m. How much work must you
do to change its length from 2 cm to 10 cm?

k=95
Lnull=0.05
delta x = .1-.02 = 0.08


Homework Equations



F=-kx
W=Fdcostheta


The Attempt at a Solution



I honestly have tried everything and am beginning to think I am way off the mark and missed something. But what i tried was

W = Fdcostheta where F = -kx

Therefore, since force changes direction after the displacement is past the relaxed spring length, i used:

W = -95 * (0.05-0.02) * (0.05-0.02) cos 0 + -95 * (0.1-0.5) * (0.1-0.5) cos 180


But that was apparently completely wrong. any help please?
 
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  • #2
[itex] F = F d \cos \theta [/itex] is only valid if the force is constant over the distance (not a function of x in this case). Your force is a function of x, so you will have to integrate to get the work. It's possible you can solve the problem with a energy approach if integrals are beyond your course material.

[tex] W = \int F(x) dx [/tex]
 
  • #3
EDIT: nvm realized my mistake was suppose to subtract

Thanks a lot for reminding me force is not constant XD
 
Last edited:

1. What is work done to move spring displacement?

Work done to move spring displacement refers to the amount of energy required to compress or stretch a spring from its original position to a new position. It is a measure of the force applied and the distance the spring is moved.

2. How is work done to move spring displacement calculated?

The work done to move spring displacement is calculated by multiplying the force applied to the spring by the distance the spring is moved. This can be represented by the equation W = Fd, where W is the work done, F is the force, and d is the distance.

3. Why is work done to move spring displacement important?

Work done to move spring displacement is important because it is directly related to the potential energy stored in the spring. This potential energy can be converted into kinetic energy and used to perform work, making springs useful in various applications such as in mechanical devices and toys.

4. What factors affect the work done to move spring displacement?

The work done to move spring displacement is affected by the force applied to the spring, the distance the spring is moved, and the stiffness of the spring. A stiffer spring would require more force and distance to be moved, resulting in a higher work done.

5. How does work done to move spring displacement relate to Hooke's Law?

Work done to move spring displacement is directly related to Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its original position. This means that as the spring is compressed or stretched, the force and the work done to move the spring displacement will also increase proportionally.

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