Question

Uma mola tem constante elástica de 10000 N/m. De quanto essa mola deve ser esticada para que sua energia potencial elástica seja:
a) 50 J
b) 100 J

Answer 1

a)

$E_{el} = 50J\\k = 10000N/m\\\\\\ E_{el} = \frac{k\Delta x^2}{2}\\\\\frac{10000\Delta x^2}{2} = 50\\10000\Delta x^2 = 100\\\Delta x^2 = \frac{100}{10000}\\\Delta x = \sqrt{\frac{1}{100}}\\\Delta x = \frac{1}{10}\\\boxed{\Delta x = 0,1m = 10cm}$

b)

$E_{el} = 100J\\k = 10000N/m\\\\\frac{10000\Delta x^2}{2} = 100\\10000\Delta x^2 = 200\\\Delta x^2 = \frac{200}{10000}\\\Delta x = \sqrt{\frac{1}{50}}\\\Delta x = \frac{1}{\sqrt{50}}\\\boxed{\Delta x = \frac{\sqrt50}{50}m \approx 0,14m \approx 14cm }$