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A man of mass $70 \mathrm{~kg}$ stands on a weighing scale in a lift, which is moving (a) upwards with a uniform speed of 10 $\mathrm{ms}^{-1}$, (b) downwards with a uniform acceleration of $5 \mathrm{~ms}^{-2}$, (c) upwards with a uniform acceleration of $5 \mathrm{~ms}^{-2}$. What would be the readings on the scale in each case (d) what would be the reading if the lift mechanism failed and it hurted down freely under gravity?
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Given $m=70 \mathrm{~kg}, a=10 \mathrm{~ms}^{-2}$
The weighing machine gives the reading of the reaction force, $R$, which is apparent weight.
(a) When lift is moving upwards with a uniform speed, acceleration $=0$, $\therefore R=m \mathrm{~g}=70 \times 9.8=700 \mathrm{~N}$
(b) When lift is moving downwards with acceleration $=5 \mathrm{~ms}^{-2}$,
$\therefore R=m(\mathrm{~g}-a)=70 \times(10-5)=350 \mathrm{~N}$
(c) When lift is moving upwards with acceleration $=5 \mathrm{~ms}^{-2}$, $\therefore R=m(\mathrm{~g}+a)=70 \times(10+5)=1050 \mathrm{~N}$
(d) When lift is coming down freely under gravity, acceleration, $a=g$,
$$
\therefore R=m(g-g)=0
$$
The weighing machine gives the reading of the reaction force, $R$, which is apparent weight.
(a) When lift is moving upwards with a uniform speed, acceleration $=0$, $\therefore R=m \mathrm{~g}=70 \times 9.8=700 \mathrm{~N}$
(b) When lift is moving downwards with acceleration $=5 \mathrm{~ms}^{-2}$,
$\therefore R=m(\mathrm{~g}-a)=70 \times(10-5)=350 \mathrm{~N}$
(c) When lift is moving upwards with acceleration $=5 \mathrm{~ms}^{-2}$, $\therefore R=m(\mathrm{~g}+a)=70 \times(10+5)=1050 \mathrm{~N}$
(d) When lift is coming down freely under gravity, acceleration, $a=g$,
$$
\therefore R=m(g-g)=0
$$
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