An elevator car weighs 5500 N. If the car accelerates upwards at a rate of 4.0 m/s2, what is the tension in the support cable lifting the car?

Thanks for helping.

Dec 18, 2016

$\text{The tension in the support cable is 7755 Newtons.}$

Explanation:

$G : \text{represents weight of elevator(the red vector)}$
$F : \text{Force by inertia(the blue vector)}$
$T : \text{Tension in the cable}$

$T = F + G$

$T = m \cdot a + G$

$m : \text{represents mass of elevator}$
$G = m \cdot g$

$5500 = m \cdot g$

$m = \frac{5500}{9.81}$

$T = \frac{5500}{9.81} \cdot 4 + 5500$

$T = 5500 \left(\frac{4}{9.81} + 1\right)$

$T = 5500 \left(0.41 + 1\right)$

$T = 5500 \cdot 1.41$

$T = 7755 \text{ } N$