Calculate the work (in joules) required to pump all of the water out of the tank. Assume that the tank is full, distances are measured in meters, and the density of water is 1,000 kg/m^3.
Water exits from a small hole at the top of the rectangular box. The dimensions are 8 m, 5 m, and 4 m.
That's supposed to be a rectangular box, where the length is 8 m, the width is 4 m, and the height is 5 m.
Why did the water go see a therapist? Because it had a lot of unresolved issues with pumping! Now, let's calculate the work required to pump all that water out.
The volume of the rectangular box can be calculated by multiplying its length, width, and height:
Volume = 8 m × 4 m × 5 m = 160 m³
Since the tank is full, the volume of water that needs to be pumped out is the same as the volume of the tank:
Volume of water = 160 m³
Given that the density of water is 1,000 kg/m³, we can calculate the mass of water:
Mass = Density × Volume
Mass = 1,000 kg/m³ × 160 m³ = 160,000 kg
Now, the work (W) required to pump the water can be calculated using the formula:
W = force × distance
The force required to lift the water is equal to its weight:
Force = mass × gravity
Force = 160,000 kg × 9.8 m/s² ≈ 1,568,000 N (approximately)
Since the water exits from a small hole at the top, we can assume that the distance the water needs to be lifted is equal to the height of the tank:
Distance = 5 m
Now we can calculate the work required:
W = force × distance
W = 1,568,000 N × 5 m = 7,840,000 J (approximately)
So, the work required to pump all the water out of the tank is approximately 7,840,000 Joules. That's a lot of pumping!
To calculate the work required to pump all of the water out of the tank, we need to determine the volume of the tank first.
The volume of a rectangular box can be found by multiplying its length, width, and height:
Volume = length x width x height
Given:
Length = 8 m
Width = 4 m
Height = 5 m
Volume = 8 m x 4 m x 5 m
Volume = 160 m^3
The next step is to determine the mass of the water in the tank. We can do this by multiplying the volume by the density of water:
Mass = Volume x Density
Given:
Density of water = 1,000 kg/m^3
Volume = 160 m^3
Mass = 160 m^3 x 1,000 kg/m^3
Mass = 160,000 kg
Now, let's calculate the work required to pump all the water out of the tank:
Work = Force x Distance
The force required to lift the water is equal to the weight of the water, which can be found using the formula:
Weight = Mass x Gravity
Given:
Mass = 160,000 kg
Acceleration due to gravity = 9.8 m/s^2 (approximate value)
Weight = 160,000 kg x 9.8 m/s^2
Weight = 1,568,000 N
The distance the water needs to be lifted is equal to the height of the tank, which is 5 m.
Distance = 5 m
Now we can calculate the work required to pump all the water out of the tank:
Work = Force x Distance
Work = 1,568,000 N x 5 m
Work = 7,840,000 J
Therefore, the work required to pump all of the water out of the tank is 7,840,000 joules.
To calculate the work required to pump all of the water out of the tank, you need to find the volume of the tank first. The volume of a rectangular box can be calculated by multiplying its length, width, and height.
Given:
Length (l) = 8 m
Width (w) = 4 m
Height (h) = 5 m
Volume of the tank (V) = l × w × h
V = 8 m × 4 m × 5 m
V = 160 cubic meters
Since the density of water is 1,000 kg/m^3, we can determine the mass of the water using the formula:
Mass (m) = Density (d) × Volume (V)
m = 1,000 kg/m^3 × 160 m^3
m = 160,000 kg
Now, we need to calculate the work required to pump all of the water out of the tank. The work done depends on the force exerted and the distance over which the force is applied.
In this case, the force required to lift the water out of the tank is equal to the weight of the water. The weight of an object can be calculated using the formula:
Weight (W) = Mass (m) × Acceleration due to gravity (g)
Acceleration due to gravity (g) is approximately 9.8 m/s^2.
W = 160,000 kg × 9.8 m/s^2
W = 1,568,000 N
Finally, we can calculate the work (W) required to pump all of the water out of the tank using the formula:
Work (W) = Force (F) × Distance (d)
In this case, the distance is the height of the tank, which is 5 m.
W = 1,568,000 N × 5 m
W = 7,840,000 J
Therefore, the work required to pump all of the water out of the tank is 7,840,000 joules.