A metal soda can of uniform composition has a mass of 0.107 kg and is 13.1 cm ta
ID: 1465479 • Letter: A
Question
A metal soda can of uniform composition has a mass of 0.107 kg and is 13.1 cm tall (see the figure). The can is filled with 1.45 kg of soda. Then small holes are drilled in the top and bottom (with negligible loss of metal) to drain the soda. What is the height h of the center of mass of the can and contents (a) initially and (b) after the can loses all the soda? (c) If x is the height of the remaining soda at any given instant, find x when the center of mass reaches its lowest point. Give your answers in cm.
Explanation / Answer
a )
the hieght of the center of the mass is 13.1 / 2 = 6.55 cm
in this case also the center of amss is 6.55 cm
in inititally
b )
the hieght of the center of the mass is 13.1 / 2 = 6.55 cm
in this case also the center of amss is 6.55 cm
in fianlly also
means in both the cases the center of mass is 6.55 cm
and no matter that how much liquid level will be .
c )
0.107 / 13.1 = 0.16 kg /cm
x = ( 6.55 X 0.107 + ( h / 2 ) ( 0 .16 h) ) / (0.107 +0.16 h )
x = ( 0.642 + 0.08h2 ) / (0.107 +0.16 h )
so by derivating the equation
the center of mass reaches minimum at 2.56 cm