Answer
(a) The tension in the upper cord is 63 N and the tension in the lower cord is 31 N.
(b) The tension in the upper cord is 71 N and the tension in the lower cord is 35 N.
Work Step by Step
(a) The upper cord is holding the weight of both buckets.
$F_T = mg$
$F_T = (6.4 ~kg)(9.8 ~m/s^2)$
$F_T = 63 ~N$
The lower cord is holding up the weight of the lower bucket.
$F_T = mg$
$F_T = (3.2 ~kg)(9.8 ~m/s^2)$
$F_T = 31 ~N$
(b) The upper cord is causing both buckets to accelerate.
$F_T - mg = ma$
$F_T = m(g+a)$
$F_T = (6.4 ~kg)(1.25 ~m/s^2 + 9.8 ~m/s^2)$
$F_T = 71 ~N$
The lower cord is causing the lower bucket to accelerate.
$F_T - mg = ma$
$F_T = m(g+a)$
$F_T = (3.2 ~kg)(1.25 ~m/s^2 + 9.8 ~m/s^2)$
$F_T = 35 ~N$
