Potential energy:

$\overline{){\mathbf{P}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

The energy required, E = ΔPE

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{\mathbf{(}}{{\mathbf{d}}}^{{\mathbf{2}}}{\mathbf{-}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{)}}}$

**a)**

E = (1/2)k(d^{2} - 0^{2}) = **(1/2)kd ^{2} **

During which interval is the largest amount of energy required to stretch the spring?

a) From x = 0 to x = d

b) From x = d to x = 2d

c) From x = 2d to x = 3d

d) The energy required is the same in all three intervals

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Springs & Elastic Potential Energy concept. You can view video lessons to learn Springs & Elastic Potential Energy. Or if you need more Springs & Elastic Potential Energy practice, you can also practice Springs & Elastic Potential Energy practice problems.