A tank is full of water. Find the work (in J) required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1,000 kg/m3 as the density of water. Round your answer to the nearest whole number.)9 m3 mA spherical tank is given. The tank has radius 9 m and spot coming out of the top with height 3 m.
Question
A tank is full of water. Find the work (in J) required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1,000 kg/m3 as the density of water. Round your answer to the nearest whole number.)9 m3 mA spherical tank is given. The tank has radius 9 m and spot coming out of the top with height 3 m.
Solution
The work required to pump water out of a tank can be calculated using the formula for work, which is force times distance.
-
First, we need to calculate the volume of the water in the tank. Since the tank is full and it's a sphere, the volume (V) can be calculated using the formula for the volume of a sphere, which is (4/3)πr³. Given that the radius (r) is 9m, the volume is (4/3)π(9m)³ = 3053.63 cubic meters.
-
Next, we calculate the mass of the water using the formula mass = density * volume. The density of water is given as 1000 kg/m³, so the mass (m) is 1000 kg/m³ * 3053.63 m³ = 3053630 kg.
-
The force required to lift this water is its weight, which is mass times gravity. Using 9.8 m/s² for gravity (g), the weight (W) is 3053630 kg * 9.8 m/s² = 29915574 N (Newtons).
-
The work done (W) in lifting this water to the spout is the force times the distance. The distance (d) is the height of the spout, which is 3m. So, the work is 29915574 N * 3m = 89746722 J (Joules).
So, the work required to pump the water out of the spout is approximately 89746722 J, or 89746722 Joules when rounded to the nearest whole number.
Similar Questions
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water.)4 m4 m6 m3 mA water tank shaped like a triangular prism is given. The base of the prism is at the top and a spout is located at the top of the tank. The dimensions of the tank are 6 meters long, 4 meters wide, and 4 meters deep. The spout is 3 meters long.W = J
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 6 m, and d = 1 m.)W =
A hemispherical tank, 10 ft in diameter is full of liquid (density: 40 lb/ft3). Find the work required to pump the water out of the top of the tank.
A water pump is pumping up water from a well which is 120 m deep.How much work must be done by the pump to raise 2 kg of water?(g=9.8 m s^-2)
The diameter of a solid metal sphere is 18cm. If it is dropped in a completely filled cubical water tank with a side of 20 cm, then what quantity of water will be left in the tank? (Assume density of metal of sphere and density of water to be the sam
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.