You stretch a spring by a distance of 0.3 m. the spring has a spring constant of 440 n/m. when you release the spring, it snaps back. what is the kinetic energy of the springs as it reaches its natural length?

19.8 J

Explanation:

According to the law of conservation of energy, the total mechanical energy of the spring (sum of kinetic energy and elastic potential energy) must be conserved:

(1)

where we have

is the initial kinetic energy of the spring, which is zero because the spring starts from rest (2)

is the elastic potential energy of the spring when it is fully stretched

is the kinetic energy of the spring when it reaches the natural length

is the elastic potential energy of the spring when it reaches its natural length, which is zero because the stretch in this case is zero (3)

So

where

k = 440 N/m is the spring constant

is the initial stretching of the spring

Substituting,

And so using eq.(1) and keeping in mind (2) and (3) we find

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