An oak barrel with a lid of area 0.20 m2 is filled...

An oak barrel with a lid of area 0.20 m2 is filled with water. A long, thin tube of cross-sectional area 5.0 X 10-5 m2 is inserted into a hole at the center of the lid, and water is poured into the tube. When the water reaches 12 m high, the barrel bursts. What was the weight of the water in the tube? What was the pressure of the water on the lid of the barrel? What was the net force on the lid due to the water pressure?
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    Answers ( 1 )

    1. maélie perez
      maélie perez
      An oak barrel with a lid of area( A = 0.20 m2) is filled with water.
      A long, thin tube of cross-sectional area( a = 5.0 *10-5 m2) is inserted into a hole at thecenter of the lid, and water is poured into the tube.
      When the water reaches ( h = 12 m) high, the barrel bursts.
      Density of water ( ? ) = 1000 kg /m
      3
      The weight of the water in thetube
                                  w = mg
                                      = ( volume * density of water ) *g
                                       = a*h * ? *g
                                    
        = 5.88 N
      At burstscondition
                               Pressurein the lid = Pressure in tube
                                         H *? *g   =    h *? * g
      or , Height of water in thelid   H   =   h
                                                          =  12.0  m
      The pressure of the water on the lid of the barrel
                                    P =   h * ? * g  
                                       
      = 117600 N/ m2
      The net force on the lid dueto the water pressure
                      F = The weight of the water in the tube + The weight of waterin lid
                         = mg + M g
                         = ( m + M ) *g
                         = ( a*h + A * H ) * ? *g
                        
      = 23.53 k N

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