Question

When the displacement of a mass on a spring is 12 A, what percentage of the energy is kinetic energy?

Answer 1

Answer:

1.44%

Explanation:

The potential energy of a spring is given by

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

The kinetic energy is

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

Now x = 12 A

Applying in the first equation

$U=\dfrac{1}{2}k(12A)^2\\\Rightarrow U=\dfrac{1}{2}k144A^2\\\Rightarrow U=144\dfrac{1}{2}kA^2\\\Rightarrow U=144E$

The percentage would be 14400%

at $x=\dfrac{1}{2}A$ (makes more sense)

$U=\dfrac{1}{2}k(\dfrac{1}{2}A)^2\\\Rightarrow U=\dfrac{1}{2}k\dfrac{1}{4}A^2\\\Rightarrow U=\dfrac{1}{4}\times \dfrac{1}{2}kA^2\\\Rightarrow U=0.25E$

The percentage is 25 % of the kinetic energy