Created on 2024-06-20Asked by Owen Sanchez (Solvelet student)
A water tank is in the shape of a right circular cylinder with a radius of 5 meters and a height of 10 meters. Find the work required to pump all the water to the top of the tank, given that the density of water is 1000kg/m3 and the acceleration due to gravity is 9.8m/s2.
Solution
Let r=5 be the radius of the tank and h=10 be the height of the tank. 1. **Volume of the tank:** The volume V of the tank is given by the formula for the volume of a cylinder: V=πr2h. 2. **Mass of the water:** The mass m of the water is given by the product of its volume and density: m=V×ρ, where ρ=1000kg/m3 is the density of water. 3. **Force required to lift the water:** The force F required to lift the water is equal to the weight of the water, which is the product of its mass and acceleration due to gravity: F=m×g, where g=9.8m/s2 is the acceleration due to gravity. 4. **Work done:** The work W required to pump all the water to the top of the tank is given by the product of the force and the height to which it is lifted: W=F×h. 5. **Substitute and calculate:** Substituting the expressions for V, m, and F into the equation for work done, we get: W=(V×ρ×g)×h. 6. **Result:** Calculate the value of W using the given values for r, h, ρ, and g. Solved on Solvelet with Basic AI Model
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DefinitionWork is the amount of energy transferred when a force is applied to move an object. Buoyancy and drag are fluid forces that have ruled on objects immersed in the fluids (liquids/gases). For example: Raising a 50 N box through a distance of 2 m requires 100 joules of work. A floating objects weight is equal to the weight of the fluid it displaces and it experiences a buoyant force pushing it up.
