At a construction site, there is a pile of sand in the shape of a cone. The cone has a height of 5 m and a base radius of 8 m. Suppose that the density of the sand is 1400 kg/m3. In order to assemble this pile, energy must be expended to lift each bit of sand (working against gravity) to its final height in the pile. It is known that the energy, E required to lift a mass m (in kg) to a height h (in m) is given by E = mgh (where g can be taken to be 10 m/s2). How much energy is required in total to assemble the pile?

A water fountain uses 125 Watts of power each hour. It is run 24 hours each day for 7 days. If electricity costs 10 cents per Kilowatt-hour, how much does it cost to keep the fountain working for those 7 days? Put your answer in $##.## form, but without the money symbol ($).

Under normal conditions the human heart converts about 12.7 J of chemical energy per second into 1.27 W of mechanical power as it pumps blood throughout the body HINT (a) Determine the number of Calories required to power the heart for one day, given that 1 Calorie equals 4186 J. Cal (b) Metabolizing 1 kg of fat can release about 9000 Calories of energy. What mass of metabolized fat (in kg) would power the heart for one day? kg Need Help? Watch it Read It

A 35-kW freight elevator with a total mass of 1950 kilograms rises to a height of 25 metres in 32 seconds. What is the efficiency of the elevator? 45% 43% Option 2 Option 4 46% 44% Option 1 Option 3

If a particle is moving, it has kinetic energy. Kinetic energy is the energy of motion, and it depends on the speed and mass of the particle. It is given by the formula Ek = 1/2*mv2, where  Ek  is the kinetic energy, m is the mass, and v is the speed of the particle. The formula for kinetic energy has some important features to keep in mind. Kinetic energy, and every other type of energy as well, is a scalar quantity, given by only a single number. Energy does not have a "direction", unlike a vector quantity. (This is in contrast to the vector quantity momentum, which you might have already studied.) Kinetic energy, in particular, is always a positive number. (Note the speed v is the magnitude of the vector velocity, and therefore is positive. But even if it were a negative number, squaring it would always lead to a positive result.) Kinetic energy depends on the square of the speed. (This is in contrast to the magnitude of momentum, mv, a quantity you may have already studied, which…

In recent years, there has been a large push for an increase in the use of renewable resources to produce the energy we need to power our vehicles. One of the newer fuels that has become more widely available is E85, a mixture of 85% ethanol and 15% gasoline. Despite being more environmentally friendly, one of the potential drawbacks of E85 fuel is that it produces less energy than conventional gasoline. Assume a car gets 27.5 mi gal using gasoline at $3.50/gal and 21.5 mi gal using E85 at $2.85/gal. How much will it cost to drive 700. miles using conventional gasoline fuel? How much will it cost to drive 700. miles using E85 fuel?

When the Glen Canyon hydroelectric power plant in Arizona is running at capacity, 690 m3 of water flows through the dam each second. The water is released 220 m below the top of the reservoir. If the generators that the dam employs are 90% efficient, what is the maximum possible electric power output?

A heavy box is pulled by a rope on a horizontal surface. (a) Assume that there is no frictional force between the box and the surface. If the tension force in the rope is 240 N and the box moves by the distance of 5.6 m in 2.9 s, what is the power output of the work done by the tension force?  (b) Assume that the surface is rough and there is frictional force between the box and the surface. If the box moves at the constant speed of 0.31 m/s when the tension force is 240 N, what is the power output of the work done by the tension force?

A heavy rope, 50 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 140 ft high. (a) How much work W is done in pulling the rope to the top of the building? W = ft-lb (b) How much work W is done in pulling half the rope to the top of the building? W = ft-lb

A tank has the shape of an inverted right circular cone with height 9m and radius 18m. It is filled with 5m of hot chocolate. Assume that the density of the hot chocolate is 1450kg/m^3 and g=9.8m/s^2.Find the work required to empty the tank by pumping the hot chocolate over the top of the tank.Work =  Joules.