B Why Does Hooke's Law Use a Negative Sign in Scalar Form?

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Hooke's Law incorporates a negative sign in its scalar form to indicate that the spring force acts in the opposite direction to the displacement from equilibrium. This is consistent with the vector notation, where the force vector and displacement vector have opposite signs. The confusion arises when transitioning from vector equations to scalar components, leading to misinterpretations of magnitudes and signs. It is essential to maintain clarity in notation to differentiate between vector components and their magnitudes. Understanding that Hooke's Law is fundamentally a vector equation helps clarify the necessity of the negative sign in its scalar form.
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kuruman said:
And then there is the recurrent question, "if I substitute numbers for g in the equation, do I use +9.8 m/s2 or -9.8 m/s2 ?"
Years ago I was using a textbook that forced the students to make that choice. In other words, ##g=\pm 9.8 \ \mathrm{m/s^2}##. That was a huge mistake.
 

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