Q: The apparent weight of a man in a lift is W1 when lift moves upwards with some acceleration and is W2 when it is accelerating down with same acceleration. Find the true weight of the man and acceleration of lift.
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Sol: (a) W1 = m(g + a),
W2 = m(g – a)
W1 + W2 = 2 mg
⇒ W1 + W2 = 2 W (∵ W = mg)
$\large W = \frac{W_1 + W_2}{2}$
(b) $\large \frac{W_1}{W_2} = \frac{g+a}{g-a} $
$\large \frac{g}{a} = \frac{W_1 + W_2}{W_1 – W_2}$
$\large a = g( \frac{W_1 – W_2}{W_1 + W_2} ) $