We know that
• The mass of the elevator is 5000 kg.
Let's draw a free-body diagram.
As you can observe, there are just two forces involved, the weight of the elevator and the tension force. Let's use Newton's Second Law.
[tex]\begin{gathered} \Sigma F_y=ma_y \\ T-W=ma_y \end{gathered}[/tex]
But, W = mg = 5000kg*9.8m/s^2 = 49,000 N, and m = 5000 kg, a = 0 (because the speed is constant).
[tex]\begin{gathered} T-49,000N=5000\operatorname{kg}\cdot0 \\ T=49,000N \end{gathered}[/tex]
Therefore, the tension in the cable is 49,000 N.
