Calculating Work Done by a Variable Applied Force

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Homework Help Overview

The problem involves calculating the work done by a variable applied force defined by the equation F = k1*x^n - k2, with specific values for k1, k2, and n. The task is to determine the work done as an object moves between two positions.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integral formulation for work and share their calculations, noting discrepancies in their results. Some question whether their calculations were performed correctly.

Discussion Status

There is ongoing dialogue about the correct application of the work formula, with participants sharing their results and expressing confusion over differing outcomes. Some guidance has been offered regarding the importance of using sufficient precision in calculations.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is an acknowledgment of potential mistakes in calculations without resolving them.

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Homework Statement


An applied force varies with position according to F = k1xn - k2, where n = 3, k1 = 8.3 N/m3, and k2 = 87 N. How much work is done by this force on an object that moves from xi = 6.47 m to xf = 14.9 m? Answer in units of kJ.

Homework Equations



W = k1 x4/4 ]from the integral of x1 to x2
- k2x]from x1to x2

The Attempt at a Solution


I plugged in everything, and I got 96.778 at first, then I thought I should use x33/3, then I got 6.543478 kJ.
I got both them wrong, did I do the calculation wrong? Please help, thanks. :D
SOLVED
 
Last edited:
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Agree with W = k1 x^4/4 - k2x from x1 to x2.
I got about -15000.
 
Delphi51 said:
Agree with W = k1 x^4/4 - k2x from x1 to x2.
I got about -15000.

I still didn't get that answer. :(
 
It is really W = k1 x^4/4 - k2 x , and I got 97904, similar to your result. Use enough digits during the calculations. ehild
 
ehild said:
It is really W = k1 x^4/4 - k2 x , and I got 97904, similar to your result. Use enough digits during the calculations.


ehild

I found my mistake, thank you very much.
 

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