Find Work: Empty 6ft Hemisphere Tank of Oil (50lb/ft^3)

[idle_09]

Find the work done in emptying a tank containing oil if the tank is hemisphere with a diameter of 6 feet. The tank is full and the density of the oil is 50lb/ft^3. The oil is raised to a point 4 ft about the top of the tank. Thank you for helping. I have no idea how to start.

 

[tiny-tim]

Hi idle_09!

Find the work done in emptying a tank containing oil if the tank is hemisphere with a diameter of 6 feet. The tank is full and the density of the oil is 50lb/ft^3. The oil is raised to a point 4 ft about the top of the tank. Thank you for helping. I have no idea how to start.

(i assume you mean "4 ft above …"?)

work done = change in energy (that's the work-energy theorem) …

so divide the tank into horizontal slices of thickness dz, calculate the mass of each slice, how much energy is needed to raise it to z = 7, and integrate over z.

 

[daytripper]

you'll have to find the size of a slice of the hemisphere as a function of z... just figured I'd throw that hint out there.