An underground tank is a hemisphere with radius 4 feet (i.e. it is half a sphere,...

An underground tank is a hemisphere with radius 4 feet (i.e. it is half a sphere, and so horizontal cross-sections are circles of varying radius). It is filled to the top with oil weighing 45 lb per cubic foot. The top of the tank is at ground level, and the oil in the tank is pumped to a height of 10 feet above ground level. How much work is done? Set up the integral, but then just use your calculator to evaluate it. The picture is a two-dimensional picture of a vertical cross-section (through the center) of the tank.

Expert Solution

1st we will find work needed to empty a horizontal slice of water and then integrate it to find total work

milcah answered 2 years ago

Rolling Sphere in a Hemisphere Must answer both parts A small sphere, with radius 2.9 cm...

Rolling Sphere in a Hemisphere Must answer both parts A small sphere, with radius 2.9 cm and mass 6.0 kg, rolls without slipping on the inside of a large fixed hemisphere with radius 1.00 m and a vertical axis of symmetry. It starts at the top from rest. What is its kinetic energy of the sphere at the bottom? What fraction of its kinetic energy at the bottom (in percent) is associated with rotation about an axis through its center...

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is...

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is filled to a depth of 140 feet with water. Some of the water will be pumped out and, at the end, the depth of the remaining water must be 40 feet. i) Set up a Riemann sum that approximates the volume of the water that is pumped out of the tank. (use horizontal slicing). You have to draw a diagram and choose a coordinate...

A tank has the shape of a sphere with a radius of 5 m. It is...

A tank has the shape of a sphere with a radius of 5 m. It is filled with water up to 9 m. (i) Let x be the height in meters measured from the bottom of the tank. The weight in Newtons of a thin layer of water between x and x + Δx is approximately P (x) Δx. What is P (x)? P (x) = Express the answer by a formula. Recall that the density of water is ρ...

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform...

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density ρ0, and the “southern” hemisphere a uniform charge density −ρ0. Find the approximate field E(r,θ) for points far from the sphere (r ≫ R). P.S. Please be as neat as possible.

The tank in the form of a right-circular cone of radius 7 feet and height 39...

The tank in the form of a right-circular cone of radius 7 feet and height 39 feet standing on its end, vertex down, is leaking through a circular hole of radius 4 inches. Assume the friction coefficient to be c=0.6 and g=32ft/s^2 . Then the equation governing the height h of the leaking water is dhdt=_______________ If the tank is initially full, it will take _________ seconds to empty.

A conical tank, point down, has a radius of 6 feet and a depth of 9...

A conical tank, point down, has a radius of 6 feet and a depth of 9 feet. Water is filling the tank and thus the volume of water in the tank is changing with time, as is the depth of the water and the radius of the surface of the water. Suppose that at the instant the depth of the water is 4 feet, the depth of the water is changing at an instantaneous rate of0.125 feet per minute. How...

Only half of the volume of an ornamental sphere (radius 0.500m) is submerged when place in...

Only half of the volume of an ornamental sphere (radius 0.500m) is submerged when place in water. a) what is the magnitude of the buoyant force on sphere? b) what is the weight of the sphere? c) what is the density of the sphere? d) what happens when submerged completely when released?

Charges Q1 and Q2 are uniformly distributed in two half of a sphere with radius R....

Charges Q1 and Q2 are uniformly distributed in two half of a sphere with radius R. The two halves rotate around the z-axis with each spinning in opposite directions. The half spheres have angular velocities ω1 and ω2. Using Biot Savart law, find the magnetic field at the center of the sphere.

A system for the storage of thermal energy is to be designed using an underground tank...

A system for the storage of thermal energy is to be designed using an underground tank of water. The tank is buried at a depth of 3 m and is a cube of 1 m on each side. The water in the tank is heated by circulating it through a solar energy collection system. A given heat input to the water may be assumed due to the solar energy flux. Characterize the design problem in terms of the fixed quantities...

A sphere with radius a = 8 cm is in a conductive sphere shell with an...

A sphere with radius a = 8 cm is in a conductive sphere shell with an internal radius of b = 12 cm and an outer radius of c = 18 cm with a load of -200 mC. a) Determine the load distribution in the sphere and sphere shell. b) Calculate the value of the electric field in r = 0 cm, r = 4 cm, r = 8 cm, r = 10 cm, r = 14 cm, r =...

Question