Problem 12.61 An open barge has the dimensions shown in the figure (Figure 1) .
ID: 1378151 • Letter: P
Question
Problem 12.61 An open barge has the dimensions shown in the figure (Figure 1) . Part A If the barge is made out of 4.4-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking? Express your answer using two significant figures. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures. Part B Is there enough room in the barge to hold this amount of coal? (The density of coal is about 1500 kg/m^3 .)Explanation / Answer
first we will calculate the mass of steel by first finding the volume of steel (cut the walls into rectangular prisms and find those volumes.
volume of whole steel is:
Voulme of First wall=0.04*12*40*2 = 38.4 m^3
Volume of Second Wall=0.04*12*22*2 = 21.12 m^3
Volume of Third Wall=0.04*40*22 = 35.2 m^3
Total Volume=38.4+21.2+35.2
=94.8m^3
volume of whole barge---> 22*12*40 = 10560 m^3
Mass=volume*density
mass of steel = 94.72*7800 = 738816 kg
density= 738816/10560
= 69.96 kg/m^3
density of water = 1000 kg/m^3
remain density = 1000 - 69.96 = 930 kg/m^3
mass that can be added = 930*10560
= 9820800 kg
9820800/1500
= 6547.2 m^3--coal that can be carried, which is well less than the volume of the barge