Question

A raft 3.5m long and 1.75m wide is constructed of timber 0.25 m thick having a relative density of 0.7. The raftfloats in water of density 1019kg/m3. Calculate the minimum mass which must be placed on top of raft to sink it.Ans:

Answer 1

Answer:

m = 488.46 Kg

Explanation:

given,

Length of raft,L = 3.5 m

width of raft, W = 1.75 m

thickness, H = 0.25 m

relative density of the timber = 0.7

water of density = 1019 kg/m³

mass that can be placed without sinking= ?

density of wood

ρ_w = 0.7 x 1000 = 700 kg/m³

volume of the raft = L B H

                              = 3.5 x 1.75 x 0.25 = 1.53125 m³

net force acting on the raft

$F_{net}= Buoyant\ force - weight$

$F_{net}= \rho_f g V - \rho_w g V$

$F_{net}= (1019 - 700)\times 9.8 \times 1.53125$

$F_{net} = 4787 \ N$

where as $F_{net}= m g$

$m\ g= 4787 \ N$

$m\times 9.8= 4787 \ N$

  m = 488.46 Kg

hence, the minimum mass which we can place on the top is equal to 488.46 Kg.