Question

How much tension must a cable withstand if it used to accelerate a 1500 kg object vertically upward at 0.80 m/s²?

Answer 1

Let's apply the Newton's Second Law of Motion:

$$\sum F_y = ma_y,$$ $$T - mg = ma,$$

here, $T$ is the tension in the cable, $mg$ is the weight of the object, $m = 1500 \ kg$ is the mass of the object, $a = 0.80 \ \dfrac{m}{s^2}$ is the acceleration of the object and $g = 9.8 \ \dfrac{m}{s^2}$ is the acceleration due to gravity.

Then from this equation we can find the tension in the cable:

$$T = m(g+a),$$ $$T = 1500 \ kg \cdot (9.8 \ \dfrac{m}{s^2}+0.80 \ \dfrac{m}{s^2}) = 15900 \ N.$$

Answer:

$T = 15900 \ N.$