Answer
The tension in the cable that supports the elevator is $16,700~N$
Work Step by Step
We can find the net force on the elevator:
$\sum F = ma = (2010~kg)(1.50~m/s^2) = 3015~N$
We can find the tension $F_T$ in the cable that supports the elevator:
$\sum F = mg-F_T$
$F_T = mg - \sum F$
$F_T = (2010~kg)(9.8~m/s^2)-3015~N$
$F_T = 16,700~N$
The tension in the cable that supports the elevator is $16,700~N$
