Final answer:
A spring is unstretched when it is at its natural length without compression or elongation, which is also the position where the spring's elastic potential energy is zero.
Step-by-step explanation:
The spring of constant k is unstretched when it is at its natural length, which means it has not been compressed or elongated due to external forces. In terms of physics and energy, this is usually considered the position where the elastic potential energy of the spring is zero.
According to Hooke's Law, the elastic potential energy (U(x)) in the spring at a displacement x from its unstretched length is given by U(x) = (1/2)kx². If the spring is at its unstretched length (x=0), the value of the elastic potential energy U is zero as the equation simplifies to U(x) = 0.
In scenario 38, where it takes 500 J of work to compress a spring 10 cm, we can use this equation to determine the force constant of the spring by rearranging the equation to solve for k: k = 2U / x². Here the U is 500 J and the x is 0.1 m, resulting in the calculation of the force constant k.