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 = 18 m, and d = 2 m.) W= ? j
then why even bother answering question?
To find the work required to pump the water out of the spout, we need to calculate the weight of the water and then multiply it by the height it is being lifted.
1. Calculate the volume of the tank: V = a * b * c
V = 4 m * 4 m * 18 m = 288 m^3
2. Calculate the weight of the water: W = density * volume * g
W = 1000 kg/m^3 * 288 m^3 * 9.8 m/s^2
W = 2822400 kg*m^2/s^2
3. Multiply the weight of the water by the height it is being lifted: W = m * g * d
W = 2822400 kg*m^2/s^2 * 2 m
W = 5644800 kg*m^2/s^2
Therefore, the work required to pump the water out of the spout is W = 5644800 joules.
To find the work required to pump the water out of the spout, we need to calculate the gravitational potential energy change of the water.
The formula for calculating the gravitational potential energy change can be written as:
ΔPE = m * g * Δh
Where:
ΔPE: Change in potential energy (work)
m: Mass of the water
g: Acceleration due to gravity (9.8 m/s^2)
Δh: Change in height
To get the mass of water, we will calculate the volume by multiplying the length (a), width (b), and height (c) dimensions of the tank: V = a * b * c
Then, we can find the mass (m) from the volume (V) using the weight density of water: m = V * density
Finally, we calculate the change in height (Δh) by subtracting the initial height (d) from the final height (0).
Now, let's calculate the work required to pump the water out of the spout using the given dimensions and values:
Step 1: Calculate the volume:
V = a * b * c
V = 4m * 4m * 18m
V = 288 m^3
Step 2: Calculate the mass:
m = V * density
m = 288 m^3 * 1000 kg/m^3
m = 288,000 kg
Step 3: Calculate the change in height:
Δh = 0 - d
Δh = -2m
Step 4: Calculate the work:
W = m * g * Δh
W = 288,000 kg * 9.8 m/s^2 * (-2m)
W = -5,657,600 J (rounded to the nearest whole number)
Therefore, the work required to pump the water out of the spout is approximately -5,657,600 Joules (J).
Ihave no idea what a,b,c,d mean, but consider all the water as concentrated at the center of mass of the fluid. The work required to pump it all out is just
work = force * distance
where force is the weight of the water
distance is the height the weight must be raised.
No integration needed!