I need help with a physics problem.?

Question

An unstretchd spring is 12 cm long. When you hang a 875g weight from it, it streeches to a length of 14.40 cm. What is the force constant in N/m of the spring? What total mass must you hang from the spring tp strech it to a total lenght of 17.72cm? The answers are 357 N/m and 2.08 kg. I don't know how to get there. I need to see the work to get the right answer. We are supposed to be using Hooke's law Fspr=-kx.

Answer 1

If at rest the spring is 12 cm, and the weight causes it to stretch to 14.4 cm, then it stretches 2.4 cm. We have the weight that causes the spring to stretch, so we can use Hooke's law to figure this one out:

Fs = -kx
(0.875 kg)(9.81 m/s^2) = -k(-0.024 m)
8.584 N = -k(-0.024 m)
k = 357.7 N/m

Now given this, we can use Hooke's law again to find the weight that will cause the spring to stretch to 17.72 cm. first, realize that this means the spring is stretching 5.72 cm. Using this, we can plug in numbers:

Fs = -kx
m(9.81 m/s^2) = -(357.7 N/m)(0.0572 m)
m = 2.09 kg

(My answers are slightly off from yours due to rounding.)