Question

A block of wood has a mass of 3.57 kg and a density of 588 kg/m3....

A block of wood has a mass of 3.57 kg and a density of 588 kg/m3. It is to be loaded with lead so that it will float in water with 0.82 of its volume immersed. The density of lead is 1.13 ? 104 kg/m3.

(a) What mass of lead is needed if the lead is on top of the wood?

(b) What mass of lead is needed if the lead is attached below the wood?

Homework Answers

Answer #1

V = volume = 3.57/588 = 6.07*10^-3 m^3

v1 =volume inside water = 0.82*V = 4.97*10^-3 m^3

P = density of water =1000 kg/M^3

a) m1 = V1*P - 3.57 = V1*1000 -3.57 = 4.97 -3.57 = 1.4 kg

b) Let V' = volume of lead below the wood

   m' = mass of lead having volume V'

   m' = 1.13*104 *V'

then    3.57 +m'   = (V' + V1)*1000

            3.57 + 1.13*104 *V'   = V' *1000 + 4.97

                                   V' = 1.4/(10300) =1.359*10-4 m^3

m' = mass of lead= 1.13*104 *V'    = 1.53 kg

                          

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