A trough is 3 meters long, 3 meters wide, and 5 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 5 meters, and base, on top, of length 3 kg meters). The trough is full of water (density 1000 ). Find the amount of work in joules required to m3 m empty the trough by pumping the water over the top. (Note: Use g = 9.8 as the acceleration due to gravity.) Зт Зт 5m

A bucket is filled with sand so that the total mass (sand and bucket) is 15 kgs. The bucket is to be lifted to the top of a 30 meter tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.2 kgs of sand each meter it is lifted. Find the work done lifting the bucket to the top of the building. Joules

Suppose you have an ice cream cone full of melted ice cream. The ice cream cone is in the shape of a right circular cone and is 0.5 feet tall with a width (diameter) of 0.25 feet at the top. You decide to drink the melted ice cream using a straw positioned at the top of the cone. How much work is necessary to drink all of the ice cream through the straw? Note that the approximate weight-density of melted ice cream is 64.05 pounds per cubic foot. Round your final answer to 3 decimal places.

A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.) 8 m

3. A container 50 ft by 100 ft by 20 ft deep is half-filled with a liquid (filled to a depth of 10 ft). How much work is done in pumping all the liquid out of the container to a height of 2 ft above the top of the container? (The liquid's density is 60 lb/ft³.) Your answer should include units.

5. (A5-1) A water tank has the shape of an inverted square pyramid with a height of 15 m and a base side length of 21 m. It is currently filled with water to a height of 10 m, which as a density of 1000 kg/m³. Find the amount of work required to empty the tank by pumping all of the water to the top of the tank.

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.

A diver is standing on the diving board. The diver has a mass of 59 kg and has a gravitational potential energy of 832 J standing on the diving board. Determine how high the diver is above the water surface. (Assume the water is at ground level.) O 1.44 m 1.437481643 O 1.44 O 1.4 m