# How do I use the signs in the spring force equation?

The spring force equation is F = - (k)(x). Assuming right direction of axis to be +ve, and left to be -ve, should we use the values of force and displacement, accordingly? And also, in this question -

"When a block is pulled out to x = +4.0 cm from 0.0 cm, we must apply a force of magnitude of 360 N to hold it here. Then find the spring constant."

So using F = - (k) (x) , we get (k) = - (F) (x), substituting values, k = - (360N) (4.0cm) . I.e., the spring constant comes out to be negative, why is it so? Please help , I am really confused with the sign convention.

• You might not know about calculus yet, but compare the equation "acceleration = x" to the equation "acceleration = -x". One blows up, the other oscillates like a flicked spring. We want the oscillating behavior, and we don't want our physics to blow up, so that's why the sign is there :) – user12029 Oct 28 '16 at 6:55
• You haven't really answered my question but given some rhetorical statement. Please answer my question. The spring constant can never really be negative. – Sachin Chaudhary Oct 28 '16 at 6:57
• I haven't answered the question, which is why I posted it as a comment and not an answer. – user12029 Oct 28 '16 at 7:59

In the spring equation the force $F$ is the force exerted by the spring on another body, say it is you.
So you exert a force of $+360$ N on the spring.
Newton's third law states that the spring will exert a force of $-360$ N on you and that is the value you put into the equation.

• One more question, If I compress the spring, is spring force is +ve ? Since F = -kx and x (displacement) is negative . so f = - k (-x) i.e. f = kx – Sachin Chaudhary Oct 28 '16 at 7:05
• That is correct. With the x-direction as you have defined it to compress the spring you must apply a force in the negative x-direction which means the PhET the spring exerts a force in the positive X-direction. – Farcher Oct 28 '16 at 7:11

The spring force equation shows the relationship between the displacement and the force the spring exerts. But you have been given the force applied to hold the spring away from equilibrium. This applied force is in the opposite direction to the one exerted by the spring.

• So then how should I solve it? – Sachin Chaudhary Oct 28 '16 at 7:03
• Put in the spring's force (with the correct sign), not the force exerted on the spring. – BowlOfRed Oct 28 '16 at 7:06
• Thanks. If I compress the spring, is spring force is +ve ? Since F = -kx and x (displacement) is negative . so f = - k (-x) i.e. f = kx – Sachin Chaudhary Oct 28 '16 at 7:07
• If you compress the spring from the right, it will exert a force directed to the right. – BowlOfRed Oct 28 '16 at 7:12

NeuroFuzzy is correct in his comment. The negative sign is there to indicate opposite direction of force and displacement vector. Spring constant is never negative but you have forgotten a crucial point that restoring force times displacement is some negative number because they're in opposite direction.

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