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

Answer 1

Nora Arzate

Considering

#"the mass of the raft "m=120kg#

#"the density of the raft "d=0.8xx10^3kgm^-3# So

#"the volume of the raft "v=m/d#

#=(120kg)/(0.8xx10^3kgm^-3)=0.15m^3#

Let #wkg# be the weight that should be put on the raft to make it just sink.

We can infer from the condition of flotation that the weight of the raft plus the weight placed on it equals the weight of water that the raft has displaced.

Taking density of water #d_w=1000kgm^-3# we can write

#w+m=vxxd_w#

#=>w+120=0.15m^3xx1000kgm^-3#

#=>w=(150-120)kg=30kg#

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Answer 2

Amelia Adams

To make the raft sink, the weight added should equal the weight of the water displaced by the submerged part of the raft. Use the formula: Weight added = Weight of displaced water = Volume submerged * Density of water * g. The volume submerged equals the submerged depth multiplied by the raft's surface area. The density of water is approximately 1 * 10^3 kg m^-3, and g is the acceleration due to gravity (approximately 9.8 m/s^2). Calculate accordingly.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.