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https://texercises.com/exercise/work-required-to-stretch-a-spring/
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The following quantities appear in the problem: Kraft \(F\) / Arbeit \(W\) / Strecke \(s\) / Federkonstante \(D\) /
The following formulas must be used to solve the exercise: \(W = \int F(s)\,\text{d}s \quad \) \(F = Ds \quad \)
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Exercise:
A spring DO is to be stretched from its resting position of length saO to sbO. How much work is required to do this?

Solution:
According to Hooke's Law for springs FDs we get for the required work to stretch a spring from s_ to s_: W _s_^s_ Fs dd s _s_^s_ Ds dd s D _s_^s_ s dd s D left frac s^ right_s_^s_ fracD left s_^ - s_^ right fracD leftqtysb^-qtysa^ W approx WS WP- There is another method to solve this exercise: The initial force to hold the spring at saO is F_ Ds_ D sa and the force the hold the completely stretched spring at sbO is F_ Ds_ D sb The average force during the stretch of the spring is hence bar F fracF_+F_ fracDs_+Ds_ and the work required becomes: W bar F s bar F s_-s_ fracDs_+s_s_-s_ fracD s_^-s_^
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Exercise:
A spring DO is to be stretched from its resting position of length saO to sbO. How much work is required to do this?

Solution:
According to Hooke's Law for springs FDs we get for the required work to stretch a spring from s_ to s_: W _s_^s_ Fs dd s _s_^s_ Ds dd s D _s_^s_ s dd s D left frac s^ right_s_^s_ fracD left s_^ - s_^ right fracD leftqtysb^-qtysa^ W approx WS WP- There is another method to solve this exercise: The initial force to hold the spring at saO is F_ Ds_ D sa and the force the hold the completely stretched spring at sbO is F_ Ds_ D sb The average force during the stretch of the spring is hence bar F fracF_+F_ fracDs_+Ds_ and the work required becomes: W bar F s bar F s_-s_ fracDs_+s_s_-s_ fracD s_^-s_^
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Tags
federgesetz, mechanik, physik
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Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration