- The main span of the Portage Lake lift bridge
^{2}weighs 4,400,000 pounds. How much work is done in raising this main span to a height of 100 feet? - A cylindrical storage tank having radius 20 feet and length 40 feet is filled with a fluid which weighs 50 pounds per cubic foot. This tank is lying on its side on the ground. Find the total force acting on the ends of the tank by the fluid.
- Suppose the tank in Problem 2 is filled to a depth of 8 feet. Find an integral for the work needed to pump the fluid to a height of 50 feet.
- A conical hole is filled with water which has weight 62.5 pounds per cubic feet. If the depth of the hole is 20 feet and the radius of the hole is 10 feet, how much work is needed to pump the water to a height of 10 feet above the ground?
- Suppose the spring constant is 2 pounds per foot. Find the work needed to stretch the spring 3 feet beyond equilibrium.
- A 20 foot chain lies on the ground. It weighs 5 pounds per foot. How much work is done to lift one end of the chain to a height of 20 feet?
- A 200 foot chain dangles from the top of a tall building. How much work is needed to haul it to the top of the building if it weighs 1 pound per foot?
- A dam 500 feet high has a width at depth y equal to 4000 − 2y feet. What is the total force on the dam if it is filled?
^{∗}When the bucket is filled with water it weighs 30 pounds and when empty it weighs 2 pounds and the person on top of a 100 foot building exerts a constant force of 40 pounds. The bucket is full at the bottom but leaks at the rate of .1 cubic feet per second. How much work does the person on the top of the building do in lifting the bucket to the top? Will the bucket be empty when it reaches the top? You can use Newton’s law that force equals mass times acceleration. You can neglect the weight of the rope.- In the situation of the above problem, suppose the person on the top maintains a constant velocity of 1 foot per second and the bucket leaks at the rate of.1 pound per second. How much work does he do and is the bucket empty when it reaches the top?
- A silo is 10 feet in diameter and at a height of 30 feet there is a hemispherical top. The silage weighs 10 pounds per cubic foot. How much work was done in filling it to the very top?
- A cylindrical storage tank having radius 10 feet is filled with water to a depth of 20 feet. If the storage tank stands upright on its circular base, what is the total force the water exerts on the sides of the tank? Hint: The pressure in the water at depth y is 62.5y pounds per square foot.
- A spherical storage tank having radius 10 feet is filled with water. What is the total force the water exerts on the storage tank? Hint: The pressure in the water at depth y is 62.5y consider the area corresponding to a slice at height y. This is a surface of revolution and you know how to deal with these. The area of this slice times the pressure gives the total force acting on it.
- A water barrel which is 11 inches in radius and 34 inches high is filled with water. If it is standing on end, what is the total force acting on the circular sides of the barrel?
- Find the total force acting on the circular sides of the cylinder in Problem 2.
- A cylindrical tank having radius 10 feet is contains water which weight 62.5 pounds per cubic foot. Find the force on one end of this tank if it is filled to a depth of y feet.
- Here is a calculator problem. In the above problem, to what depth may the tank be filled if the total force on an end is not to exceed 40000 pounds?
- The force on a satellite of mass m slugs in pounds is
where k is approximately k = 1.42737408 × 10

^{16}and r is the distance from the center of the earth. Assuming the radius of the earth is 4000 miles, find the work in foot pounds needed to place a satellite weighing 500 pounds on the surface of the earth into an orbit 18,000 miles above the surface of the earth. You should use a calculator on this problem.

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