Answer
(a) The amount of energy that was lost is 0.30 J
(b) The energy could have been transformed into heat inside the spring.
Work Step by Step
(a) We can find the initial amount of energy in the system.
$E_1 = \frac{1}{2}kA^2$
$E_1 = \frac{1}{2}(250~N/m)(0.060~m)^2$
$E_1 = 0.45~J$
We can find the amount of energy in the system after eight cycles.
$E_2 = \frac{1}{2}kA^2$
$E_2 = \frac{1}{2}(250~N/m)(0.035~m)^2$
$E_2 = 0.15~J$
We can find the amount of energy that was lost.
$E_1-E_2 = 0.45~J-0.15~J = 0.30~J$
(b) The energy could have been transformed into heat inside the spring.
