Final answer:
When a spring is completely compressed by 10 cm, its elastic potential energy will be 0.2 J.
Step-by-step explanation:
To calculate the elastic potential energy of a spring, we can use the equation: PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the spring. In this case, the spring is stretched by 5 cm, so the displacement would be 0.05 m. We are given that the potential energy is 1 J, so we can solve for the spring constant: 1 = (1/2)k(0.05^2). Solving for k, we find that k = 40 N/m.
Now, if the spring is completely compressed by 10 cm, the displacement would be -0.1 m. Plugging this value into the equation for potential energy, we get: PE = (1/2)(40 N/m)(-0.1^2) = 0.2 J. Therefore, the elastic potential energy of the completely compressed spring would be 0.2 J.