Answer
(a) Please refer to the free-body diagram.
(b) The length of the bottom spring is 13.07 cm.
The length of the middle spring is 14.14 cm.
The length of the top spring is 15.20 cm.
Work Step by Step
(a) Please refer to the free-body diagram.
(b) bottom spring:
$kx = mg$
$x = \frac{mg}{k}$
$x = \frac{(8.50~kg)(9.80~m/s^2)}{7800~N/m}$
$x = 0.0107~m = 1.07~cm$
The length of the bottom spring is 13.07 cm.
middle spring:
$kx = 2mg$
$x = \frac{2mg}{k}$
$x = \frac{(2)(8.50~kg)(9.80~m/s^2)}{7800~N/m}$
$x = 0.0214~m = 2.14~cm$
The length of the middle spring is 14.14 cm.
top spring:
$kx = 3mg$
$x = \frac{3mg}{k}$
$x = \frac{(3)(8.50~kg)(9.80~m/s^2)}{7800~N/m}$
$x = 0.0320~m = 3.20~cm$
The length of the top spring is 15.20 cm.
