Finding Work from Force Equation

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Homework Help Overview

The discussion revolves around calculating work from a force equation, specifically using the relationship W = F*d. Participants are exploring the implications of a changing force and the integration required to find work in such scenarios.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various expressions for work and question their validity, particularly regarding the presence of variables in the results. There is an exploration of how to handle a changing force and the need to integrate the force over a displacement.

Discussion Status

The discussion is active, with participants questioning initial attempts and clarifying the need for integration when dealing with a changing force. Some guidance has been offered regarding the integration process and the use of limits based on positions.

Contextual Notes

Participants note the complexity of the problem and the potential for misunderstanding the requirements, particularly in relation to the integration of force and the assumptions about the force being constant versus changing.

mintsnapple
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Homework Statement


b7f66x.png



Homework Equations


W = F*d


The Attempt at a Solution


a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...
 
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mintsnapple said:

Homework Statement


b7f66x.png


Homework Equations


W = F*d

The Attempt at a Solution


a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...
Those results don't look right.

What do you get for the indefinite integral ## \displaystyle \int C e^{\alpha x}\ dx \ \ ? ##
 
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SammyS said:
Those results don't look right.
... in particular, there should not be any x in the answers.
 
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Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?
 
mintsnapple said:
Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?
dW = F dx .

You need to integrate to integrate the force with respect to x .
 
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SammyS said:
dW = F dx .

You need to integrate to integrate the force with respect to x .

Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.
 
mintsnapple said:
Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.

Yes.
 

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