Question

If the displacement of a horizontal mass-spring system was doubled, the elastic potential energy in the system would change by a factor of

Answer 1

Answer:

K'=4K

Explanation:

The electric potential energy is given by :

$E=\dfrac{1}{2}kx^2$

Where

k is spring constant

x is compression or extension in the spring

If the displacement of a horizontal mass-spring system is doubled, x'= 2x

New elastic potential energy :

$E'=\dfrac{1}{2}kx'^2\\\\E'=\dfrac{1}{2}k(2x)^2\\\\=\dfrac{1}{2}k\times 4x^2\\\\K'=4\times \dfrac{1}{2}kx^2\\\\K'=4K$

So, new elastic potential energy 4 times the initial elastic potential energy.