From the given information in the question, the correct option is Option 1: 14 cm.
A non-stretched elastic spring has a conserved potential energy which gives it the ability to perform work. The elastic potential energy can be expressed as:
PE = [tex]\frac{1}{2}[/tex] k [tex]x^{2}[/tex]
Where PE is the energy, k is the spring constant and x is extension.
i. Given that: PE = 10 J and x = 10 cm, then;
PE = [tex]\frac{1}{2}[/tex] k [tex]x^{2}[/tex]
10 = [tex]\frac{1}{2}[/tex] k [tex]10^{2}[/tex]
20 = 100k
k = 0.2 J/cm
ii. To determine how far the spring is needed to be stretched, given that PE = 20 J.
PE = [tex]\frac{1}{2}[/tex] k [tex]x^{2}[/tex]
20 = [tex]\frac{1}{2}[/tex] (0.2) [tex]x^{2}[/tex]
40 = 0.2 [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 200
x = [tex]\sqrt{200}[/tex]
= 14.1421
x = 14.14 cm
So that;
x is approximately 14.00 cm.
Thus, the spring need to be stretched to 14.00 cm to give the spring 20 J of elastic potential energy.
For more information, check at: https://brainly.com/question/1352053.
