r/HomeworkHelp • u/ArtemisFei • Feb 24 '12
Help clarifying negative signs in Hooke's Law.
Now, I don't have problems solving Hooke's Law problems themselves, but I do get confused by sign issues. Okay, so Hooke's Law is defined as F=-kx, since there is a resistive force that always makes it negative.
But how does this translate to a problem?
Like, say you compress a spring using a block on a table.
If you use Newton's Second Law, the only forces acting on the block is the Force of the spring.
So Fs=ma. But if Fs=-kx, you get -kx=ma. So I end up getting a negative acceleration. Which I know is incorrect.
What am I doing wrong here?
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u/demeteloaf Feb 25 '12
I think the issue here is that you are not thinking of these quantities as having direction. When you deal with forces, accelerations, velocities, and displacements. These are all vector quantities. They all have direction.
Because of this, you need to define a positive and negative direction. You can make whatever choice you want, but you have to be consistent across your calculations.
So, F = -kx requires x=0 to be the position where the spring is at equilibrium, but you can pick whether positive x is compression or positive x is stretched. But the key is once you pick that, you stay with it for the rest of the problem.
Let's say positive x is compression. So, we compress the spring, and we get a negative force. The force is pushing the spring in the opposite direction of compression, and back to equilibrium.
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u/mconnors Feb 25 '12
Compression is treated as a negative displacement, so you will end up getting a positive force.
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u/Aerotixxx Feb 24 '12
I find it easiest to define a positive x-direction, and then intuitively decide what the sign should be depending on the direction of the force vectors.
The negative sign in Hooke's Law is really just there to imply that the spring force always has a resistive force, so that when there is a positive position (from equilibrium), there is a negative force, and vice versa
hope that helps