A $550\;N$ physics student stands on a bathroom scale in an elevator. As the elevator starts moving the scale reads $450\;N$. Draw a free body diagram of the problem and find the magnitude and direction of the acceleration of the elevator.

Given,

Weight of the body $(w = mg = 550\;N)$

Normal Reaction $(R) = 450\;N$

Acceleration $(a) = \;?$

We have,

Here, the weight of the body is greater than the normal reaction, hence the elevator is moving downward with acceleration $(a)$. Then for downward motion,

$F = mg - R = 550 - 450 = 100\;N$ 

$m = $$\frac{W}{g} = \frac{550}{10}$$ = 55$

Again,

$F = ma$    ⇒    $a = $$\frac{F}{m}$   =   $\frac{100}{55}$ $= 1.8$

ஃ a = $1.8 m/s^2$ in downward motion.

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