Question

An 800-kg elevator is lifted vertically by a strong rope. Find the acceleration of
the elevator if the rope tension is (a) 9000 N, (b) 7840 N, and (c) 2000N.

Answer 1

Explanation:

Given that,

Mass of an elevator, m = 800 kg

It is lifted vertically by a strong rope

The equation of motion, when the elevator is lifted vertically up is :

T-mg = ma

a is the acceleration of the elevator

We need to find the acceleration of the elevator if the rope tension is :

(a) 9000 N

Put T = 9000 N,

T-mg = ma

$a=\dfrac{T-mg}{m}\\\\a=\dfrac{9000-800(10)}{800}\\\\=1.25\ m/s^2$

(b) 7840 N

Put T = 7840 N,

T-mg = ma

$a=\dfrac{T-mg}{m}\\\\a=\dfrac{7840-800(10)}{800}\\\\=-0.2\ m/s^2$

(c) 2000 N

Put T = 2000 N,

T-mg = ma

$a=\dfrac{T-mg}{m}\\\\a=\dfrac{2000-800(10)}{800}\\\\=-7.5\ m/s^2$

Hence, this is the required solution.