Calculate difference in pressure?

[gibson101]

Calculate the difference in pressure between the top and bottom surfaces of a cube of size 10x10x10 cm at a depth of 20 cm in water. At 100 cm?

I know that P=F/A . and in this case force is referring to buoyant force so F=ρgV. And the density of water is just 1000 kg/m^3. And the area of the cube is just 1000 m^3. But where does the depth of the water come into play?

 

[gibson101]

I did ρgh x A = buoyant force. So (1000)(9.8)(.2) x 100 = 19600. So Pressure equals 19600/100 since P=F/A so P= 1960. But i think this is wrong.

 

[gneill]

I did ρgh x A = buoyant force. So (1000)(9.8)(.2) x 100 = 19600. So Pressure equals 19600/100 since P=F/A so P= 1960. But i think this is wrong.

Your equation is correct for pressure at a given depth. It is not the buoyant force (which will be the difference between the forces exerted by the pressures at the bottom and top surfaces of the cube).

Pressure operates on a surface, not a volume. The volume of a 10x10x10 cube is 1000, but volume is not a surface area. Also, 10cm x 10cm x 10cm is not 1000m³ -- watch your units! cm are not m.

 

[gibson101]

but my answer is correct right? 1960 kg/m^2?

 

[gneill]

but my answer is correct right? 1960 kg/m^2?

No. You're asked to find the difference in pressure between the top and bottom surfaces. Pressure is measured in Pascals (Pa), which is equivalent to N/m².

Use your pressure at a given depth formula to find the two pressures and then their difference.

 

[gibson101]

okay i see. the difference in pressure for both of them is 980 N/m2. Correct?

 

[gneill]

okay i see. the difference in pressure for both of them is 980 N/m2. Correct?

Yes, that looks much better!