Hooke's law lab report question

[elihid98]

I am doing a lab report on Hooke's law, and I'm trying to find the constant "k" of a spring. I am having an issue with the positive and negative signs. To do the experiment, we placed different weights on a spring and measured how much it stretched out. 

So now, the force we got was mass (the one we placed to stretch the spring out) times gravity, should the force be negative since the acceleration due to gravity is negative? 
I understand that the - sign in F=-kx is not because the constant is negative, but because x is negative? 

I am assuming that the constant is meant to be positive. 

Could you please clarify what is negative and what is positive? I am a bit lost.

Thanks in advance!

[Vioh]

Very good question, i must say. Lots of people got confused about this, but often tend to ignore. Now let’s me clarify this. Whether a force is negative or positive is not important (because it depends entirely on the perspective of the observer). However, you must be consistent. For example, if you happen to choose North to be positive, then you can’t say that South is positive later on in your problem.

 

It is very often that people choose F = mg (where ‘g’ is positive), simply because the force of gravity is always pointing down, and taking away the minus sign would make it much simpler in most cases. Now, we know from the free-body diagram that the spring force counteracts the force of gravity, so it must be in the opposite direction, i.e. it is F = -kx (where both ‘k’ and ‘x’ are positive). Remember the minus sign here only accounts for the fact that the spring force is in the opposite direction compared to gravity. And it is not to indicate that ‘x’ negative, because in Hooke’s law, ‘x’ is defined to be the stretched length of the spring (which of course is always positive)

 

Having said that, you can obviously choose gravity to be negative; in other words, F = -mg, and F = kx; but this doesn’t affect anything. Besides it is not conventional to do so.

 

I am assuming that the constant is meant to be positive.

 

No, constant isn’t meant to be negative. In fact, one of the most important constants in physics is a negative value, which is the charge of an electron. However, most constants are made to be positive, because positive values make the problems much simpler.

 

Hope that helps! Cheers

Edited November 7, 2014 by Vioh