Answer
(a) The mass of box B is 4.34 kg.
(b) The mass of box A is 5.30 kg.
Work Step by Step
(a) We can find the downward acceleration of the boxes.
$y = \frac{1}{2}at^2$
$a = \frac{2y}{t^2} = \frac{(2)(12.0~m)}{(4.00~s)^2}$
$a = 1.5~m/s^2$
We can use a force equation to find the mass of box B.
$\sum F = ma$
$mg - T = ma$
$m(g-a) = T$
$m = \frac{T}{g-a} = \frac{36.0~N}{(9.80~m/s^2)-(1.5~m/s^2)}$
$m = 4.34~kg$
The mass of box B is 4.34 kg.
(b) Since the boxes are tied together, the downward acceleration of box A is also $a = 1.5~m/s^2$. We can use a force equation to find the mass of box A.
$\sum F = ma$
$mg + T - F = ma$
$m(g-a) = F-T$
$m = \frac{F-T}{g-a} = \frac{(80.0~N)-(36.0~N)}{(9.80~m/s^2)-(1.5~m/s^2)}$
$m = 5.30~kg$
The mass of box A is 5.30 kg.
