A question about the spring constant equation?

Question

On my assignment I have been asked a question about a ball suspended from a ceiling by a spring. The information I have is the spring constant is 6.0 Nm^-1, the extension of the spring from its equalibrium is 0.10m. The question asks for the mass of the ball. I think the answer is 6.1*10^-2 Kg.

I know that m*a = -ks * x, the problem I seem to be having is with (a) and (ks) if they are positive or negative when I try to show my working. Can anybody help.

Answer 1

The negative sign is denoting direction. It's there because the force on the object due to the spring is in the opposite direction to the acceleration of the object

Answer 2

spring constant is 6.0 Nm^-1,  That means a force of 6 N will expand the spring by 1 mt.

increase in length = 0.1 mt

force needed to create this increase in length length = 6*0.1 = 0.6 N = 0.6/9.81 = 0.06116 KG = 61.16 grams = mass of the ball

Answer 3

Your answer is correct.

To avoid the confusion related to sign, it is best to assume any direction as positive.

Let us take upward direction as positive. Then downward becomes negative.

Tension in the spring = kx = 6.0 * 0.1 = 0.6 N

Weight = -mg

For equilibrium, total force = 0

0.6 - mg = 0

mg = 0.6

m = 0.6/g = 0.6/9.8 = 6.1 * 10^-2 kg

Note: Tension is upward, so I took that as positive. Weight is downward, so I took that as negative.

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Another way. It is actually the same method but written differently.

Tension in the spring =  kx = 6.0 * 0.1 = 0.6 N vertically upward

Weight = mg vertically downward

For equilibrium

total upward force = total downward force

Or

0.6 N = mg

Rest is as earlier. In this, you do not have to put signs because you are explicitly mentioning upward or downward.