Question

A 60kg man is inside a lift which is moving up with an acceleration of 2.45 m/s2
. The apparent
percentage change in his weight is

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Apparent\:change\:in\:weight\%=24.5\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Mass \: of \: man = 60 \: kg \\ \\ \tt: \implies Acceleration \: of \: lift = 2.45 \: m/{s}^{2} (upward) \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Apparent \: percentage \: change \: in \: weight = ?$

• According to given question :

$\bold{Forces \: required} \\ \tt \circ \: N = normal \: force \\ \\ \tt \circ \: mg = vertically \: downward \\ \\ \bold{As \: according \: to \:F.B.D} \\ \tt: \implies N - mg = ma \\ \\ \tt: \implies N = ma + mg \\ \\ \tt: \implies N=m(g + a) \\ \\ \tt: \implies N =60(10 + 2.45) \\ \\ \tt: \implies N =60 \times 12.45 \\ \\ \tt: \implies N =747 \: n \\ \\ \tt: \implies Reading\:weight=74.7 \: kg \\ \\ \bold{For \: apparent\: weight \: increase} \\ \tt : \implies Apparent \: weight \: increase = Reading \: weight - Actual \: weight \\ \\ \tt : \implies Apparent \: weight \: increase =74.7 - 60 \\ \\ \tt : \implies Apparent \: weight\: increase =14.7 \: kg \\ \\ \bold{For \: Apparent \: weight \:increase \: percentage} \\ \tt: \implies Increase\% = \frac{Increase \: Apparent \: weight}{Actual \: weight} \times 100 \\ \\ \tt: \implies Increase\% = \frac{14.7}{60} \times 100 \\ \\ \green{\tt: \implies Increase\% = 24.5\%}$

Answer 2

Given ,

• Mass of the man (m) is 60 kg
• So , weight of the man = 60 × 9.8 = 588 N

We know that ,

When a person of mass m climbs up a rope with acceleration a , the tension T in the rope is equal to the the apparent weight of the person

$\large \mathtt{ \fbox{</p><p>T = apparent \: weight= m(g + a) }}$

Thus ,

➡Apparent weight = 60 × (9.8 + 2.45)

➡Apparent weight = 60 × 12.25

➡Apparent weight = 735 N

Now , we have to calculate the percentage of change in his weight , so

$\mapsto \sf Weight \: change = \frac{(735 - 588)}{588} \times 100 \\ \\ \mapsto \sf Weight \: change = \frac{(147)}{588} \times 100 \\ \\ \mapsto \sf \: Weight \: change = 25 \: \: \% \: \: (Approx)$

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