Calculating Work Needed to Change Spring Length

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Homework Help Overview

The problem involves calculating the work required to change the length of a spring from 10 cm to 14 cm, given its relaxed length and stiffness. The context is within the subject area of mechanics, specifically focusing on spring dynamics and work-energy principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the work formula and the need to consider the variable nature of spring force. There is an exploration of using potential energy to calculate work, with questions about the correct interpretation of the spring stretch in relation to the unstretched length.

Discussion Status

Participants are actively engaging with the problem, clarifying the correct use of formulas and discussing the necessary steps to calculate work. Some guidance has been provided regarding the need to compare energy at different positions of the spring.

Contextual Notes

There is an emphasis on understanding the definitions of variables in the formulas being used, particularly the concept of stretch in relation to the spring's relaxed length. Participants are also navigating the implications of integrating force over a distance versus using potential energy formulas.

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Homework Statement



A spring has a relaxed length of 5 cm and a stiffness of 50 N/m. How much work must you do to change its length from 10 cm to 14 cm?


Homework Equations



W= -U = F(delta R) = (Ks)(s)


The Attempt at a Solution




-attempted solving this problem using the formula above
-got a value of 0.08 J
-value is apparently incorrect
-not quite sure where I went wrong
 
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The spring force is not constant, so you can't just use W = Fx. You'll have to integrate the force over the distance.

Alternatively, you can use the formula for the potential energy stored in a stretched spring.
 
so is the formula (0.5) K s^2 ?

K=stiffness = 50
s= 14-10 = 4

is this an accurate calculation?
 
The formula is correct but your use of it is not. In the formula, s stands for the amount of stretch beyond the unstretched length.

When the spring has length 10, how much is it stretched?
When the spring has length 14, how much is it stretched?

Compare the energy at each of those positions.
 
oh ok... I think I understand

so essentially, I should use that formula separately to find work at 10cm (s=5) and 14cm(s=9)

and then find the difference of the too work values?
 
That's correct.
 

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