Answer:
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:
[tex]K_i + U_i = K_f + U_f[/tex] (1)
where we have
[tex]K_i[/tex] is the initial kinetic energy of the spring, which is zero because the spring starts from rest (2)
[tex]U_i[/tex] is the elastic potential energy of the spring when it is fully stretched
[tex]K_f[/tex] is the kinetic energy of the spring when it reaches the natural length
[tex]U_f[/tex] 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
[tex]U_i = \frac{1}{2}k(\Delta x_i)^2[/tex]
where
k = 440 N/m is the spring constant
[tex]\Delta x_i = 0.3 m[/tex] is the initial stretching of the spring
Substituting,
[tex]U_i = \frac{1}{2}(440)(0.3)^2=19.8 J[/tex]
And so using eq.(1) and keeping in mind (2) and (3) we find
[tex]K_f= U_i = 19.8 J[/tex]
