Question

there is a 5,000 kg elevator hanging from a cable. calculate the force of tension in order to accelerate the elevator up at a rate of 1m/s^2 (assume g is 10 m/s^2)
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Explanation:

Step1: Identify forces acting on elevator

The forces acting on the elevator are the force of gravity $F_g = mg$ acting down - ward and the tension force $T$ acting upward. According to Newton's second - law $F_{net}=ma$, and $F_{net}=T - F_g$.

Step2: Calculate the force of gravity

Given $m = 5000$ kg and $g = 10$ m/s², then $F_g=mg=5000\times10 = 50000$ N.

Step3: Apply Newton's second - law

Since $F_{net}=T - F_g$ and $F_{net}=ma$, we can rewrite the equation as $T - F_g=ma$. Then $T=ma + F_g$.
Given $a = 1$ m/s², $m = 5000$ kg, and $F_g = 50000$ N. Substitute the values: $T=5000\times1+50000$.
$T = 5000+50000=55000$ N.

Answer:

55000 N