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.
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
To find the net force exerted on a side of the cube due to the difference between the water and the atmosphere, we need to calculate the pressure difference between the water and the atmosphere.
First, let's find the volume of water in the cube. Since the cube is hollow, the water fills only 75.0 percent of the total volume.
Volume of the cube = (side length)^3 = (50.0 cm)^3 = 125,000 cm^3
Volume of water = 75.0 percent of total volume = (75.0/100) * 125,000 cm^3 = 93,750 cm^3
Next, we need to find the mass of water in the cube. Since the density of water is 1 g/cm^3, the mass of water will be the same as its volume.
Mass of water = 93,750 cm^3
Now, we can calculate the weight of the water using the formula:
Weight = mass * gravity
Assuming the acceleration due to gravity is 9.8 m/s^2:
Weight of water = 93,750 g * 9.8 m/s^2
Next, we need to find the force exerted by the water on the side of the cube. Since the cube has 6 sides of equal area, the force exerted by the water on one side is:
Force = Weight of water / 6
Now, let's find the pressure exerted by the water on one side of the cube:
Area of one side = (side length)^2 = (50.0 cm)^2 = 2500 cm^2
Pressure = Force / Area of one side
Now we can calculate the pressure difference between the water and the atmosphere. The pressure difference is equal to the pressure exerted by water minus the pressure exerted by the atmosphere:
Pressure difference = Pressure (water) - Pressure (atmosphere)
The pressure exerted by the atmosphere is typically considered to be around 101,325 Pa (Pascal), which is equivalent to 101,325 N/m^2.
Finally, to calculate the net force exerted on a side of the cube, we multiply the pressure difference by the area of one side:
Net force = Pressure difference * Area of one side
By following these steps, we can find the net force exerted on a side of the cube due to the difference between the water and the atmosphere.