Calculating Potential Energy of a Spring: A Case Study in Newtonian Dynamics

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Homework Help Overview

The discussion revolves around calculating the potential energy of a spring described by a specific restoring force function. The problem involves Newtonian dynamics and includes multiple parts, such as finding the potential energy function, determining the speed of an object attached to the spring, and calculating instantaneous power.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential energy function and its relation to work done. There is mention of using calculus to derive the potential energy from the force function. Some express confusion regarding the concepts involved, particularly in relation to the equations provided.

Discussion Status

The discussion is ongoing, with some participants offering hints related to the relationship between force and potential energy. Others are seeking clarification on the mathematical concepts involved, indicating a mix of understanding and confusion.

Contextual Notes

There is an indication that the original poster may be struggling with calculus concepts, particularly in relation to the equations of motion and energy. The problem is set within the constraints of a homework assignment, which may limit the information available for discussion.

xshezsciencex
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A certain spring exerts a restoring force F{sub x}(x)= -alpha x - beta x^2 if it is stretched or compressed, where alpha= 60N/m and beta=18N. The mass of the spring is negligible.

How would I : (a) Find the potential energy function U(x) for the spring. Let U=0 when x=0. (b) An object with mass, m = 0.900kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00m to the right to stretch the spring and released. What is the speed of the object when it is 0.500m to the right of the equilibrium position? (c) Use Newtonian dynamics to find the speed at this position. (d) What is the instantaneous power when x= 0.500m?
 
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Hi xshezsciencex! Welcome to PF! :wink:

Hint: potential energy is (minus) work done = -∫ … ? :smile:
 
im even more confused >_<
 
Are you familiar with calculus, or with the equation F=-dU/dx where U is potential energy?
 

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