Question

Figure shows a man of mass 60 kg standing on a light weighing machine in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight shows by the machine? What force should he exert on the rope to get his correct weight on the machine?

Answer 1

i) Given Mass of man $=60kg$

Let $R$= apparent weight of man in this case.

Now $R+T-60g=0$ [From FBD of man]

$\Rightarrow T=60g-R$ ...(I)

$T-R-30g=0$ ...(ii) [ From FBD of box]

$\Rightarrow 60g-R-R-30g=0$ [From (I)]

$\Rightarrow R=15g$ The weight shown by the machine is $15kg$

(ii) To get his correct weight suppose the applied force is $T$ and so acclerates upwards with $a$in this case, given that correct weight $=R=60g$, where $g=acc$ due to gravity

From the FBD of the man

$T^1+R-60g-60a=0$

$\Rightarrow T_1-60a=0[\therefore R=60g]$

$\Rightarrow T^1=60a$ ...(I)

From the FBD of the box

$T^1-R-30g-30a=0$

$\Rightarrow T^1-60g-30g-30a=0$

$\Rightarrow T^1-30a=90g=900$

$\Rightarrow T^1-30a-900$

From eqn (i) and eqn (ii) we get $T^1=2T^1-1800\Rightarrow T^1=1800N$

$\therefore$ So, he sould exert $1800N$ force on the rope of get correct reading