A lift of mass $1000 ext{ kg}$ is moving with an acceleration of $1 ext{ m/s}^2$ in the upward direction.

Question

A lift of mass $1000 	ext{ kg}$ is moving with an acceleration of $1 	ext{ m/s}^2$ in the upward direction. Tension developed in the string, which is connected to the lift, is:

Accepted Answer

According to Newton's second law of motion, the net force on an object moving upward with acceleration $a$ is the result of the upward tension ($T$) overcoming the downward weight ($mg$).

The equation of motion is:
$$ T - mg = ma $$
$$ T = m(g + a) $$

Given:
*   Mass, $m = 1000 	ext{ kg}$
*   Acceleration, $a = 1 	ext{ m/s}^2$
*   Acceleration due to gravity, $g = 9.8 	ext{ m/s}^2$ (standard value)

Substituting the values:
$$ T = 1000 	ext{ kg} 	imes (9.8 	ext{ m/s}^2 + 1 	ext{ m/s}^2) $$
$$ T = 1000 	imes 10.8 	ext{ N} $$
$$ T = 10,800 	ext{ N} $$

(Note: This concept relates to apparent weight in a lift and effective gravity as seen in Source 73 and 126).

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