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I have the following question to answer :

A force of $160 \ \mathrm{N}$ stretches a spring $0.050 \ \mathrm{m}$ from its equilibrium position.

A. what is the spring constant of the spring?

The equation for Hooke's Law in my text is $F=-kx$ , where $k$ is the spring constant. So with some simple algebra we can find an equation for $k: k = -(f/x)$. After plugging all my values in I get $-3200$

My question: Am I supposed to disregard the negative sign when plugging in value?

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Kind of.

The negative sign indicates the direction of the force exerted by the spring on the mass. If you pull the mass to the right, the force from the spring is to the left. Since they go opposite directions, there is a minus sign.

The problem states an external force exerted on the mass displaces it, presumably to a new equilibrium. The spring must exert an equal and opposite force on the mass to keep the mass at rest. The force exerted by the spring is actually -1 times the external force on the mass.

However, the problem didn't really give the direction of the forces to begin with. So, in a more carefully-worded problem (a force of 160N to the right displaces the equilibrium point of a mass 0.05m to the right...), the minus sign becomes important. In this problem as it's written, it's fine to ignore the minus sign.

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