Calculating Work Done by a Confusing Force Function | F=ma, W=Fd

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Homework Help Overview

The problem involves calculating the work done by a force function defined as F = F_0(x/x_0 - 1) as a particle moves along the x-axis from x = 0 to x = 2x_0. Participants express confusion regarding the interpretation of the constants F_0 and x_0 within the context of the problem.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the meaning of the constants in the force function, particularly whether x_0 represents the initial position and F_0 the initial force. There is also discussion about how to graph the function before integrating and what values to choose for the constants.

Discussion Status

The discussion is ongoing, with some participants providing clarifications about the constants and suggesting how to approach graphing the function. However, there remains a lack of consensus on the best way to visualize the function and the implications of the constants.

Contextual Notes

Participants note that x_0 should not be zero to avoid division by zero issues, and there is a suggestion to place it at a positive value on the x-axis for ease of integration.

DrummingAtom
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Homework Statement


The force on a particle is directed along an x-axis and given by [tex]F = F_0(\frac {x}{x_0} -1)[/tex]. Find the work done by the force in moving the particle from x = 0 to [tex]x = 2x_0[/tex]


Homework Equations


F=ma, W=Fd, etc.


The Attempt at a Solution


I don't even know how to interpret that function. Does the [tex]x_0[/tex] mean the initial position? Does [tex]F_0[/tex] mean the initial force? I'm so confused. Any help would be appreciated.
 
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Hi DrummingAtom! :smile:

(try using the X2 tag just above the Reply box :wink:)
DrummingAtom said:
I don't even know how to interpret that function. Does the [tex]x_0[/tex] mean the initial position? Does [tex]F_0[/tex] mean the initial force?

That's right :smile:

a "0" subscript always means a constant (usually the value at t = 0). :wink:

(oh … except in relativity, where x0 means time! :rolleyes: :biggrin:)
 
I'm still confused on this one. So, if x0 F0 are constants then how would the graph of this function look? Because they want you to graph F(x) before integrating. I mean what do you pick for your constant in a situation like this? I know it's going to be a linear function.
 
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DrummingAtom said:
I'm still confused on this one. So, if x0 F0 are constants then how would the graph of this function look? Because they want you to graph F(x) before integrating. I mean what do you pick for your constant in a situation like this? I know it's going to be a linear function.

It doesn't really matter, as long as x0 is not 0 (otherwise you'll have a divide by zero problem). But if you want to make your life easier, put it on the positive x-axis somewhere. I suggest putting it at x = 1. That way you'll integrate from 0 to 2. But don't label you x-axis with '1' and '2'; rather label you x-axis to go from

0...x0...2x0...3x0...

Now when you consider your graph's labels, you are integrating from 0 to 2x0, as the problem specifies! :cool:

The y-axis is F. So where does F0 fit into your graph? I'll let you do that.
 
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