Work done by springs in a series

In summary, the question asks for the amount of work needed to stretch a system consisting of two springs connected in series, with force constants k1 and k2, a distance x from the equilibrium position. The attempted solution involves using the elastic potential energy equation and substituting 1/kt=1/k1+1/k2, but this is incorrect. The problem lies in the fact that the distances stretched by the two springs are not equal due to their different force constants.
  • #1
sillybean
18
0

Homework Statement


Two springs, with force constants k1 and k2, are connected in series, as shown in the figure
Walker.7.68.jpg


How much work is required to stretch this system a distance x from the equilibrium position?

Homework Equations



W=1/2kx^2

The Attempt at a Solution



I have no idea how to derive this. I mean I've looked on the wikipedia article on hooke's law and figured that I just change the equation to W=1/2 (1/k1 + 1/k2)x^2

I'm guessing the problem with this is that the distances that the two stretch are not equal because of the different spring constants but I don't know how to go about showing this in an equation.
 
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  • #2
is that 1/(2kx^2) or (1/2k)x^2
 
  • #3
it is (1/2k)x^2
 
  • #4
using 1/kt=1/k1+1/k2. Substitute into elastic potential energy equation.

Edit: forget that... Misunderstood your question I think.
 
Last edited:
  • #5
i did that
W=1/2 (1/k1 + 1/k2)x^2

and this was wrong
 
  • #6
sillybean said:
i did that
W=1/2 (1/k1 + 1/k2)x^2

and this was wrong

I know. That'd why I edited and said forget it, Lol.
 
  • #7
ah i see. so any other takers.
 
  • #8
still need help. is my theory about distances being different right?
 

Related to Work done by springs in a series

What is the concept of work done by springs in a series?

The concept of work done by springs in a series refers to the total amount of energy required to compress or stretch multiple springs connected in a series. This is calculated by multiplying the force exerted by each spring by the distance it is compressed or stretched.

How is work done by springs in a series calculated?

To calculate work done by springs in a series, you need to know the force exerted by each spring and the distance it is compressed or stretched. The total work done is equal to the sum of the work done by each spring, which can be calculated using the formula W = 0.5 * k * x^2, where k is the spring constant and x is the distance.

What is the relationship between the spring constant and work done by springs in a series?

The spring constant, also known as the stiffness coefficient, is directly proportional to the work done by springs in a series. This means that as the spring constant increases, the amount of work done by the springs also increases.

What factors can affect the work done by springs in a series?

The work done by springs in a series can be affected by several factors, including the number of springs in the series, the spring constant of each spring, and the distance each spring is compressed or stretched. Additionally, external factors such as temperature and humidity can also impact the work done by springs.

Why is understanding work done by springs in a series important?

Understanding work done by springs in a series is important in various fields of science and engineering. This concept is used in designing and analyzing structures and machines that use springs, such as shock absorbers and suspension systems. It also helps in understanding the behavior of materials and their elastic properties.

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