#### Answer

(a) T = 490 N
(b) T = 490 N
(c) T = 740 N
(d) T = 240 N

#### Work Step by Step

(a) If the box is at rest, then the tension is equal in magnitude to the weight.
$T = mg$
$T = (50~kg)(9.80~m/s^2)$
$T = 490~N$
(b) If the box is moving at a steady speed, then the acceleration is zero. Then the tension must be equal in magnitude to the weight.
$T = mg$
$T = (50~kg)(9.80~m/s^2)$
$T = 490~N$
(c) $\sum F = ma$
$T - mg = ma$
$T = m(a+g)$
$T = (50~kg)(5.0~m/s^2+9.8~m/s^2)$
$T = 740~N$
(d) $\sum F = ma$
$mg - T= ma$
$T = m(g-a)$
$T = (50~kg)(9.8~m/s^2-5.0~m/s^2)$
$T = 240~N$