Question

A barge floating in fresh water (Q = 1000 kg/m) is shaped like a hollow rectangular prism with base area A = 750 m² and height H=2.0 m. When empty the bottom of the barge is located Ho=0.55 m below the surface of the water. When fully loaded with coal the bottom of the barge is located H=1.05 m below the surface. 

Part (a) Select the correct free-body diagram for the barge when it is empty.

Part (b) Write an equation for the buoyant force on the empty barge in terms of the known data 

Part (c) Determine the mass of the barge in kilograms. 

Part (d) Which freebody diagram represents the barge when it is loaded with coal? 

Part (e) Find the mass of the coal in terms of the given data. 

Part (f) Find the mass of the coal in kilograms. 

Part (g) How far would the barge be submerged (in meters) if m2 150000 kg of coal had been placed in the empty barge?

Answer 1

a.

Here in the question,buoyant force acts in upper direction and balances the weight as its shown floating in water when its not fully filled.

Hence the correct Free-body diagram should be option D,as depicted below.

F F N Fabarge FG.barge Fo.barge fo Fa.barge FObarge FGbarge

b.

Buoyent freP k m vis vumofoa dpleces -AossX50 m 3. 412 5m =Pua LODO218)N =7.042 XID N Hehre, upthust

c.

Sine,Upthrst4ov2 X 4042 Xj muma M4.01 2 XIO 0412 X

d. When It is filled with coal , the block will have more weight so component of weight downward will be greater.

Hence, third FBD is correct as shown below.

FB FO barge Fbarge FG.barge FB Fo barge Fobarge FGbarge