The mass of the elevator with passengers is 800 kg, determine the magnitude and direction of acceleration

The mass of the elevator with passengers is 800 kg, determine the magnitude and direction of acceleration of the elevator movement, if it is known that the tension of the cable is 12,000 newtons

m = 800 kg.

g = 10 m / s2.

N = 12000 N.

a -?

The lift is acted upon by 2 forces: the gravity force m * g directed vertically downward and the cable tension force N directed vertically upward.

2 Newton’s law in projections on the vertical axis directed upwards will look like: m * a = N – m * g.

a = (N – m * g) / m.

a = (12000 N – 800 kg * 10 m / s2) / 800 kg = 5 m / s2.

Since the acceleration has a “+” sign, it is also directed vertically upward.

Answer: an elevator with passengers moves with an acceleration a = 5 m / s2, which is directed vertically upwards.