A raft of wood of density $0.8 \cdot 10^{3} k g m^{- 3}$ $0.8 * 10^3 kg m^-3$ and mass $120 k g$ $120kg$ floats in water. How much weight should be put on the raft to make it just sink?

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Answer 1 · 2016-11-24T14:00:44

Given

$the mass of the raft m = 120 k g$ $"the mass of the raft "m=120kg$

$the density of the raft d = 0.8 \times 10^{3} k g m^{- 3}$ $"the density of the raft "d=0.8xx10^3kgm^-3$
So

$the volume of the raft v = \frac{m}{d}$ $"the volume of the raft "v=m/d$

$= \frac{120 k g}{0.8 \times 10^{3} k g m^{- 3}} = 0.15 m^{3}$ $=(120kg)/(0.8xx10^3kgm^-3)=0.15m^3$

Let $w k g$ $wkg$ be the weight that should be put on the raft to make it just sink.

By condition of floatation we know that the total wt of raft and the weight put on it is equal to the wt of displaced water by the raft.

Taking density of water $d_{w} = 1000 k g m^{- 3}$ $d_w=1000kgm^-3$ we can write

$w + m = v \times d_{w}$ $w+m=vxxd_w$

$\Rightarrow w + 120 = 0.15 m^{3} \times 1000 k g m^{- 3}$ $=>w+120=0.15m^3xx1000kgm^-3$

$\Rightarrow w = (150 - 120) k g = 30 k g$ $=>w=(150-120)kg=30kg$

A raft of wood of density 0.8⋅103kgm−30.8 * 10^3 kg m^-3 and mass 120kg120kg floats in water. How much weight should be put on the raft to make it just sink?