Work: I am having problem determining the elongation in spring

In summary, the conversation discusses the calculation of elongation in a spring attached to an object on the ground. The spring is initially at its natural length, but is pulled by a force and a point on the spring moves l/5 units away from the top. The work done by the force is to be determined using the Work-Energy Theorem. The student initially calculates the elongation to be l/5, but the teacher corrects them, explaining that the elongation at each portion of the spring should be x/l. The student then realizes their mistake and correctly calculates the elongation to be 25% of the original length. The conversation ends with the student asking why it is important to consider the values from the bottom of the
  • #1
PhysicsBoi1908
50
12

Homework Statement



A spring has been attached to an object which is kept on the ground. The spring is initially in its natural length: 'l' when a force 'F' is applied on it. The force 'F' slowly pulls the object so it does not attain any acceleration. There's a point 'P' on the line which is positioned l/5 units away from the top of the spring when it was in its natural length. After a few moments, the point 'P' is at the same point where the end of the spring earlier was. We are required to determine the work done by the force. There's no air resistance.
I have also attached an image of the diagram.

Homework Equations


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I aim at solving this question via the Work-Energy Theorem for a system of particles.

The Attempt at a Solution


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We haven't been given the value for the constant of spring force, so to determine that, I thought about the elongation of the spring, I thought that elongation should be equal to l/5 but my teacher said I was wrong. What is wrong about the elongation that I calculated? I then thought that since when we pull a spring, each portion of the spring gets elongated equally, if the spring gets elongated by 'x', then the elongation at each portion will have to be x/l, but i don't know if I am right or wrong.
 

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  • #2
PhysicsBoi1908 said:
I thought that elongation should be equal to l/5 but my teacher said I was wrong. What is wrong about the elongation that I calculated?
How did you calculate it?

PhysicsBoi1908 said:
I then thought that since when we pull a spring, each portion of the spring gets elongated equally,
Sounds good to me. So by what factor does the spring stretch?
 
  • #3
I assumed that since point P on the spring is going up by l/5, elongation must be l/5 but my sir said that my logic is wrong, he would discuss the solution on Tuesday
 
  • #4
PhysicsBoi1908 said:
I assumed that since point P on the spring is going up by l/5, elongation must be l/5 but my sir said that my logic is wrong, he would discuss the solution on Tuesday
Your logic is wrong but easily fixable. Consider the section of spring from point P to the bottom. By what factor does its length change?
 
  • #5
Initially, P was 4l/5 away from the surface, then after elongation, it now is 5l/5 from the surface, I still see an l/5 change or 20% change.
 
  • #6
PhysicsBoi1908 said:
Initially, P was 4l/5 away from the surface, then after elongation, it now is 5l/5 from the surface, I still see an l/5 change or 20% change.
Try again: l/5 is what fraction of 4l/5?
 
  • #7
25%
 
  • #8
Oh! Now I see it, change in length =(5l/5-4l/5)/4l/5*100=25%
 
  • #9
PhysicsBoi1908 said:
Oh! Now I see it, change in length =(5l/5-4l/5)/4l/5*100=25%
There you go. :smile:
 
  • #10
Thank you very much, sir! I really appreciate how gracefully you led me to the answer without actually giving it out. However, I have one last question, why is it important to consider these values from down and not from the up?
 
  • #11
PhysicsBoi1908 said:
However, I have one last question, why is it important to consider these values from down and not from the up?
Simply because that's the only data given. The length from point P to the top of the spring stretches from l/5 to what? You aren't given that info. (But you can figure it out from what you are given.)
 

Related to Work: I am having problem determining the elongation in spring

1. What is the formula for calculating the elongation in a spring?

The formula for calculating the elongation in a spring is: elongation = (applied force * length of spring) / (spring constant).

2. How do I determine the spring constant?

The spring constant is determined by dividing the force applied to the spring by the resulting elongation. This is known as Hooke's Law, which states that the force applied to an elastic object is directly proportional to the resulting elongation or compression.

3. Can the elongation in a spring be negative?

Yes, the elongation in a spring can be negative if the force applied is in the opposite direction of the original force that caused the spring to stretch.

4. How does the material of the spring affect its elongation?

The material of the spring can affect its elongation by altering the spring constant. Different materials have different levels of stiffness, which can impact the spring constant and ultimately the amount of elongation for a given force.

5. What factors can affect the accuracy of determining the elongation in a spring?

The accuracy of determining the elongation in a spring can be affected by several factors, including the accuracy of measuring the applied force and the length of the spring, as well as any external forces acting on the spring, such as friction or gravity.

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