Calculating Work with a Variable Force

AI Thread Summary
The discussion revolves around calculating the work done by a variable force defined by the function F(x) = 50(5 - √x) as an object moves from 0 to 9 meters. The original poster consistently arrives at a work value of 1350 J, while the expected answer is 1700 J. Participants emphasize the importance of showing detailed calculations to identify potential errors, noting that F(x) is positive in the given range. There is also a mention of the conservative nature of the force, indicating that work is path-independent. The conversation highlights the need for careful evaluation of integrals in variable force problems.
physics79
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Homework Statement


An object is moved from 0 to 9 meters with a force varying according to the function F(x)= 50(5-square root x). What is the work done.



Homework Equations





The Attempt at a Solution



I tried to take the integral and evaluate it from 0 to 9. I get 1350J no matter what I do, which is not correct. The correct answer is given as 1700 J. Any help?
 
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physics79 said:

Homework Statement


An object is moved from 0 to 9 meters with a force varying according to the function F(x)= 50(5-square root x). What is the work done.



Homework Equations





The Attempt at a Solution



I tried to take the integral and evaluate it from 0 to 9. I get 1350J no matter what I do, which is not correct. The correct answer is given as 1700 J. Any help?

It sometimes happens that the given "answer" is not correct. If you show your work in detail then we can see if your method produces a correct result.
 
I will only say that F(x) is not always positive.
 
ZxcvbnM2000 said:
I will only say that F(x) is not always positive.

Yes, but it is positive over the spatial domain in question. Furthermore, since this is a conservative force, the work done from the starting point to the ending point will be independent of the path.

My calculation yields the same number as the OP's.
 
Steely Dan said:
Yes, but it is positive over the spatial domain in question. Furthermore, since this is a conservative force, the work done from the starting point to the ending point will be independent of the path.

My calculation yields the same number as the OP's.


Yeah you are right..sorry . This must definitely be the most useless hint ever ! :P
 

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