Figure shows a man of mass 60 kg standing on a light weighting machine kept 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 shown by the machine? What force should he exert on the rope to get his correct weight on the machine?

Answer

A

Explanation

i. given Mass of man = 60 kg
Let R'= Apparent weight of man in this case
From free body diagram of man,
`R'+T-60g=0`
`rarr T= 60g=R'` …………..i. `
From free body diagram of box,
`T-R'-30g=0` ……..ii.
From equation i.
` 60g-R'-R-30g=0`
`R'=15g`
)
Hence weight shown by the machine is 15 kg.
ii. To get his correct wight, suppose the applied force is T and so, accelerates upward with a in this case
Given that correct weight = R= 60g where g= acceleratioin due to gravity Form the free body diagram of the man
` T'+R-60g-60a=0`
`T'-60a=0` [since R=60g]
`rarr T'=60a` ...i.
From the free body diagram of the box,
`T'-R-30g-30a=0`
`rarr T' -60g-30g-30a=0`
rarr T'-30a+90g=0`
`rarr T'=30a-900`.......ii.
From equation i. and ii we get
`T'=2T'-1800`
`rarr T'=1800N` So he should exert 1800 N force on the rope to get correct reading.