Calculating Work Done on a Spring with Given Stiffness and Length Changes

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Homework Help Overview

The problem involves calculating the work done on a spring when changing its length from 12 cm to 15 cm, given its relaxed length and stiffness. The context is rooted in the principles of mechanics related to springs.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between work and potential energy in springs, with one suggesting the use of integration to find the work done. There are attempts to apply the formula for force and work, as well as questions about the potential energy formula for springs.

Discussion Status

The discussion is active, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the use of integration and potential energy, but there is no explicit consensus on the solution yet.

Contextual Notes

Participants note the importance of using consistent units (meters instead of centimeters) and question the assumptions regarding the initial and final lengths of the spring.

karobins
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Homework Statement



A spring has a relaxed length of 7 cm and a stiffness of 150 N/m. How much work must you do to change its length from 12 cm to 15 cm?

Homework Equations



F=-kx, W=F(delta)x

The Attempt at a Solution



?? ((.12 m)-(.07 m) * (150 N/m)) = 7.5 N

((.15 m)-(.07 m) * (150 N/m)) = 12 N

(12-7.5 N) * (.15-.12 m) = .135 Nm
 
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You need to consider that W = ΔPE

What is the formula for the PE of a spring?
 
thanks much for the help!
 
i assume you got the answer but if not
a quick way to solve this problem is to
set up a integral.
integrate Kx where K is the stiffness
so it gives you 75x^2
act like relaxed length is initial (or 0) then find difference
from initial your two asking points are (make sure your in m not cm)
ex. rest is 7cm find work 13cm stretched to 15 cm
first limit would be (.13-.07)=.06 next (.15-.07)=.08
just plug these into 75x^2
do F(b)-F(a) and that gives you the answer
 

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