Understanding the Relationship between Spring Constant and Energy

In summary, the conversation discusses the energy stored in two springs, Y and X, with different spring constants. It is determined that the energy stored in X must be half of that in Y due to its stiffer spring constant, but a mistake is made in the calculation at first.
  • #1
ravsterphysics
57
1

Homework Statement



1.JPG

Homework Equations

The Attempt at a Solution



EPE is (0.5)kx^2

Let Y have spring constant of K then X has spring constant of 2K

So EPE of Y is (0.50kx^2 which is E

So EPE of X must be (0.5)2kx^2 which is kx^2 which is 2E? But correct answer is E/2??
 
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  • #2
It looks like you've assumed that x is the same for both springs. Is that going to be the case?
 
  • #3
gneill said:
It looks like you've assumed that x is the same for both springs. Is that going to be the case?

Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
 
  • #4
ravsterphysics said:
Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
Check the expression you've just used for the energy. Did you forget something?
 
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  • #5
gneill said:
Check the expression you've just used for the energy. Did you forget something?

Argh such a silly mistake! Thanks for your help : )
 

Related to Understanding the Relationship between Spring Constant and Energy

What is the definition of spring constant?

Spring constant, also known as force constant, is a physical property that describes the stiffness of a spring. It is the amount of force required to stretch or compress a spring by a certain distance. It is denoted by the letter k and its unit is N/m (newton per meter).

How is spring constant related to energy?

Spring constant is directly related to the potential energy stored in a spring. The higher the spring constant, the more energy it can store. This can be seen in the equation for potential energy: PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement of the spring from its equilibrium position.

What factors affect the spring constant?

The spring constant is affected by the material and dimensions of the spring. A thicker and shorter spring will have a higher spring constant compared to a thinner and longer spring. The type of material used also plays a role, as some materials are more elastic than others and can stretch or compress more easily.

Can the spring constant change?

Yes, the spring constant can change depending on the conditions of the spring. It can change if the material of the spring is altered, if the dimensions of the spring are changed, or if the temperature of the spring changes. Additionally, when a spring is stretched or compressed beyond its elastic limit, the spring constant may change.

How is spring constant measured?

The spring constant can be measured by applying a known force to a spring and measuring the resulting displacement. The spring constant can then be calculated using the equation k = F/x, where F is the applied force and x is the displacement of the spring. This process can be repeated with different forces to determine the average spring constant.

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