Jwin2k15
contestada

A spring is compressed to a displacement of -3.9 m from equilibrium. Then the spring is released and allowed to stretch to a displacement of -1.5 m from equilibrium. The spring constant is 11 N/m. What best describes the work involved as the spring stretches? 71 J of work is performed on the spring. The spring performs 140 J of work The spring performs 71 J of work. 140 J of work is performed on the spring.

Respuesta :

The elastic potential energy stored by a spring is
[tex]U= \frac{1}{2} k x^2 [/tex]
where [tex]k=1.1 N/m[/tex] is the spring's constant and x is the displacement of the spring with respect its rest position.

In the problem we have two situations: situation 1 (initial condition), where the spring has a displacement of [tex]x_1 = -3.9 m[/tex], and situation 2 (final condition), where the spring has a displacement of [tex]x_2 = -1.5 m[/tex]. The work performed by the spring corresponds to its loss in elastic potential energy:
[tex]W=U_1- U_2 = \frac{1}{2}kx_1^2- \frac{1}{2}kx_2^2 = \frac{1}{2}k[x_1^2-x_2^2]= [/tex]
[tex]= \frac{1}{2}(1.1 N/m)[(-3.9m)^2-(-1.5m)^2]=71 J [/tex]
this work has positive sign, because it is performed by the spring (in factm the spring is releasing from a position of higher potential energy to a position with less potential energy). 

Therefore, the correct answer is The spring performs 71 J of work.