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i m thinking about a project to evaluate the magnitude of work done on a spring by an agent.But i m facing much problem by the positive or negative value of work.i think that if work done by an agent while elongating a spring is positive then work done by the same agent for same amount of compression should be negative. but in my text book it is written that ''THE WORK DONE IS SAME FOR SAME AMOUNT OF OF COMPRESSION OR ELONGATION AND BOTH OF THEM ARE POSITIVE.''........how????? they have given the expression of the formula for work done for elongating the spring through integration but didnt do that for compression.pls help me to find out the limit for integration for the compression

I hope the following explaination helps...

One form of work is force times distance. Note: Force and Distance can both be positive or negative. By convention, work is ALWAYS positive. The logic/philosophy of this convention is something can do work (positive >0 ) or not (0) , but undoing work is still work, so negative work does not exist!

The ideal spring relationship is a linear equation with spring length times a spring coefficient (constant for a given spring) equaling force.
Typically positive force represents compression and negative force represents expansion (but this is arbitrary).
With the typical positive force being compression, the compression distance must be positive for the work to come out positive.
This means makes the opposite (expansion) direction negative which multiplied by the negative force causes the work to also come out positive.

Note: You can just easily assign the compression force to be negative if you make the compression distance negative.

I agree with Craig, but I'd like to add something. You can do work on a system, or the system can do work on you. Imagine a pulley with a rope attached to a weight. You grasp the rope and pull down. The weight goes up. Your arm is doing work on the weight. Now you relax a little and the weight comes down, and your arm goes up. The weight is doing work on you. The convention holds that both are regarded as positive work. If you get deeper into the work concept there is always the "system" and its definition is important. I hope this is helpful.

Craig_Bridge wrote: By convention, work is ALWAYS positive

Then from where the idea of''Positive andNegative work done by gravitational force'' comes from

I found this definition of positive and negative work that should help answer your latest question:

http://tutor4physics.com/positivenegativework.htm