A hollow cube with edge 50.0 cm is filled to 75.0 percent with water. Find the net force exerted on a side of the cube due to the difference between the water and the atmosphere.
2 answers
A hollow cube with edge 50.0 cm is filled to 75.0 percent with water. Find the net force exerted on a side of the cube due to the difference between the water and the atmosphere. (Assume the head space above the water is open to the atmosphere.)
The force above the water is zero. The force below the water is equal to the weight of water above that point. Because the weight is is linear dependent on depth, we can average it.
So from the bottom, up .75*50cm, the average pressure in the water area is densitywater*.75*25cm, and Pascal's principle tells us that at this point, the pressure is transmitted in all directions, so average force=sideareaunderwather*pressure(25cm)*.75
the last .75 is because 25 percent of the side has zero pressure.
net force= (50cm)^2*1g/cm^3*9.8N/kg*.75*25cm * .75
ok, looks like we need to do units in SI, so
net force=(.5m)^2*1E6kg/m^3*9.8N/kg*.75*.25m*.75
you can multiply all that out. Check it, I didn't
So from the bottom, up .75*50cm, the average pressure in the water area is densitywater*.75*25cm, and Pascal's principle tells us that at this point, the pressure is transmitted in all directions, so average force=sideareaunderwather*pressure(25cm)*.75
the last .75 is because 25 percent of the side has zero pressure.
net force= (50cm)^2*1g/cm^3*9.8N/kg*.75*25cm * .75
ok, looks like we need to do units in SI, so
net force=(.5m)^2*1E6kg/m^3*9.8N/kg*.75*.25m*.75
you can multiply all that out. Check it, I didn't
4 answers