A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 40

Find the work done on a 40 lb suitcase when it is raised 9 inches.

Find the work done on a 20 kg suitcase when it is raised 30 centimeters.

A particle x feet from the origin has a force of x2 + 2x pounds acting on it. What is the work done in moving the object from the origin a distance of 1 foot?

Find the work done in compressing the spring from x = 1 to x = 2.

Find the work done to compress the spring to x = 3, starting at the equilibrium position, x = 0.

(a) Find the work done in compressing the spring from x = 0 to x = 1 and in compressing the spring from x = 4 to x = 5.

A circular steel plate of radius 20 ft lies flat on the bottom of a lake, at a depth of 150 ft. Find the force on the plate due to the water pressure.

A fish tank is 2 feet long and 1 foot wide, and the depth of the water is 1 foot. What is the force on the bottom of the fish tank?

A child fills a bucket with sand so that the bucket and sand together weigh 10 lbs, lifts it 2 feet up and then walks along the beach, holding the bucket at a constant height of 2 ft above the ground. How much work is done on the bucket after the child has walked 100 ft?

A child fills a bucket with sand so that the bucket and sand together weigh 10 lbs, lifts it 2 feet up and then walks along the beach, holding the bucket at a constant height of 2 ft above the ground. How much work is done on the bucket after the child has walked 100 ft?

How much work is required to lift a 1000-kg satellite from the surface of the earth to an altitude of 2 106 m? The gravitational force is F = GMm/r2, where M is the mass of the earth, m is the mass of the satellite, and r is the distance between them. The radius of the earth is 6.4 106 m, its mass is 6 1024 kg, and in these units the gravitational constant, G, is 6.67 1011.

A worker on a scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to a point 30 ft above the ground by pulling on a rope weighing 0.5 lb/ft. How much work is required?

An anchor weighing 100 lb in water is attached to a chain weighing 3 lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 25 ft.

A 1000-lb weight is being lifted to a height 10 feet off the ground. It is lifted using a rope which weighs 4 lb per foot and which is being pulled up by construction workers standing on a roof 30 feet off the ground. Find the work done to lift the weight.

A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 40 meters above the ground. This takes 10 minutes, during which time 5 kg of water drips out at a steady rate through a hole in the bottom. Find the work needed to raise the bucket to the platform.

A 2000-lb cube of ice must be lifted 100 ft, and it is melting at a rate of 4 lb per minute. If it can be lifted at a rate of one foot every minute, find the work needed to get the block of ice to the desired height.

A cylindrical garbage can of depth 3 ft and radius 1 ft fills with rainwater up to a depth of 2 ft. How much work would be done in pumping the water up to the top edge of the can? (Water weighs 62.4 lb/ft3.)

A rectangular swimming pool 50 ft long, 20 ft wide, and 10 ft deep is filled with water to a depth of 9 ft. Use an integral to find the work required to pump all the water out over the top.

A water tank is in the form of a right circular cylinder with height 20 ft and radius 6 ft. If the tank is half full of water, find the work required to pump all of it over the top rim

Suppose the tank in Problem 19 is full of water. Find the work required to pump all of it to a point 10 ft above the top of the tank.

Water in a cylinder of height 10 ft and radius 4 ft is to be pumped out. Find the work required if (a) The tank is full of water and the water is to pumped over the top of the tank. (b) The tank is full of water and the water must be pumped to a height 5 ft above the top of the tank. (c) The depth of water in the tank is 8 ft and the water must be pumped over the top of the tank.

Water in a cylinder of height 10 ft and radius 4 ft is to be pumped out. Find the work required if (a) The tank is full of water and the water is to pumped over the top of the tank. (b) The tank is full of water and the water must be pumped to a height 5 ft above the top of the tank. (c) The depth of water in the tank is 8 ft and the water must be pumped over the top of the tank.

A cone with height 12 ft and radius 4 ft, pointing downward, is filled with water to a depth of 9 ft. Find the work required to pump all the water out over the top

A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 4 feet, its length is 12 feet, and its top is 10 feet under the ground, find the total amount of work needed to pump the gasoline out of the tank. (Gasoline weighs 42 lb/ft3.

A cylindrical barrel, standing upright on its circular end, contains muddy water. The top of the barrel, which has diameter 1 meter, is open. The height of the barrel is 1.8 meter and it is filled to a depth of 1.5 meter. The density of the water at a depth of h meters below the surface is given by (h) = 1+ kh kg/m3, where k is a positive constant. Find the total work done to pump the muddy water to the top rim of the barrel. (You can leave , k, and g in your answer.

(a) The trough in Figure 8.79 is full of water. Find the force of the water on a triangular end. (b) Find the work to pump all the water over the top

(a) A reservoir has a dam at one end. The dam is a rectangular wall, 1000 feet long and 50 feet high. Approximate the total force of the water on the dam by a Riemann sum. (b) Write an integral which represents the force, and evaluate it.

What is the total force on the bottom and each side of a full rectangular water tank that has length 20 ft, width 10 ft, and depth 15 ft?

A rectangular dam is 100 ft long and 50 ft high. If the water is 40 ft deep, find the force of the water on the dam.

A lobster tank in a restaurant is 4 ft long by 3 ft wide by 2 ft deep. Find the water force on the bottom and on each of the four sides.

The Three Gorges Dam started operation in China in 2008. With the largest electrical generating capacity in the world, the dam is about 2000 m long and 180 m high, and has created a lake longer than Lake Superior.2 Assume the dam is rectangular in shape. (a) Estimate the water pressure at the base of the dam. (b) Set up and evaluate a definite integral giving the total force of the water on the dam.

On August 12, 2000, the Russian submarine Kursk sank to the bottom of the sea, 350 feet below the surface. Find the following at the depth of the Kursk. (a) The water pressure in pounds per square foot and pounds per square inch. (b) The force on a 5-foot square metal sheet held (i) Horizontally. (ii) Vertically

The ocean liner Titanic lies under 12,500 feet of water at the bottom of the Atlantic Ocean. (a) What is the water pressure at the Titanic? Give your answer in pounds per square foot and pounds per square inch. (b) Set up and calculate an integral giving the total force on a circular porthole (window) of diameter 6 feet standing vertically with its center at the depth of the Titanic.

Set up and calculate a definite integral giving the total force on the dam shown in Figure 8.80, which is about the size of the Aswan Dam in Egypt.

We define the electric potential at a distance r from an electric charge q by q/r. The electric potential of a charge distribution is obtained by adding up the potential from each point. Electric charge is sprayed (with constant density in units of charge/unit area) on to a circular disk of radius a. Consider the axis perpendicular to the disk and through its center. Find the electric potential at the point P on this axis at a distance R from the center. (See Figure 8.81.)

Find the kinetic energy of a rod of mass 10 kg and length 6 m rotating about an axis perpendicular to the rod at its midpoint, with an angular velocity of 2 radians per second. (Imagine a helicopter blade of uniform thickness.)

Find the kinetic energy of a phonograph record of uniform density, mass 50 gm and radius 10 cm rotating at 33 1 3 revolutions per minute.

Find the kinetic energy of a phonograph record of uniform density, mass 50 gm and radius 10 cm rotating at 33 1 3 revolutions per minute.

Two long, thin, uniform rods of lengths l1 and l2 lie on a straight line with a gap between them of length a. Suppose their masses are M1 and M2, respectively, and the constant of the gravitation is G. What is the force of attraction between the rods? (Use the result of Problem 38.)

Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ring through its center. Assume m is at a distance y from the center of the ring

A uniform, thin, circular disk of radius a and mass M lies on a horizontal plane. The point P lies a distance y directly above O, the center of the disk. Calculate the gravitational force on a mass m at the point P. (See Figure 8.82.) Use the fact that the gravitational force exerted on the mass m by a thin horizontal ring of radius r, mass , and center O is toward O and given by F = Gmy (r2 + y2)3/2 , where G is constant.

A 20 meter rope with a mass of 30 kg dangles over the edge of a cliff. Ignoring friction, the work required to pull the rope to the top of the cliff is Work = (30 kg)  9.8 m sec2  (20 m).

A cylindrical tank is 10 meters deep. It takes twice as much work to pump all the oil out through the top of the tank when the tank is full as when the tank is half full.

Lifting a 10 kg rock 2 meters off the ground requires 20 joules of work

Lifting a 10 kg rock 2 meters off the ground requires 20 joules of work

Two cylindrical tanks A and B such that it takes less work to pump the water from tank A to a height of 10

It takes more work to lift a 20 lb weight 10 ft slowly than to lift it the same distance quickly.

Work can be negative or positive.

The force on a rectangular dam is doubled if its length stays the same and its depth is doubled.

To find the force of water on a vertical wall, we always slice the wall horizontally, no matter what the shape of the wall

The force of a liquid on a wall can be negative or positive.

If the average value of the force F(x) is 7 on the interval 1 x 4, then the work done by the force in moving from x = 1 to x = 4 is 21.