You find that if you hang a 1.25kg weight from a vertical spring, it stretches 3.75cm.

a) What is the force constant of this spring?

b) How much mass should hang from this spring so it will stretch 8.13 cm from its original unstretched length?

(A) k = 327N/m

(B) m = 2.71kg

Explanation:

The weight of the 1.25kg is the force acting on the spring. W= weight = mg =F = kx

That is

mg = kx

Therefore k = mg/x

Given m = 1.25kg and x = 3.75cm = 0.0375m

k = 1.25 ×9.8 / 0.0375 = 327N/m

(B) from the relation mg =kx

Given x = 8.13cm = 0.0813m.

m = kx / g = 327 × 0.0813 / 9.8 = 2.17kg.

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