Question

If you hang a 3 kg mass vertically from a certain (idea) spring, the spring stretches from 10 cm (unstretched length) to 15 cm. If the mass is removed and the spring is stretched horizontally to a total length of 20 cm, how much potential energy is stored?

(A) 0.3 J

(B) 1.2 J

(C) 3 J

(D) 12 J

(E) 30 J

Answer 1

We know that 

F = kx

K = f/x

\(K=\frac{mg}{x}\)

\(K=\frac{3\times9.8}{0.05}\)

K = 588

Stared potential energy E = 1/2 kx²

= 1/2 x 588 x (.20) x (0.20)

= 11.98 J

≅ 12J

Answer 2

Mg=kx  

30=k×5×10^-2

K=600

PE=1/2k(xf^2-xi^2)+mgh

1/2×600(0.04-0.01)+30×10×10^-2

9+3=12J