Questions: How much work is required to empty the full tank shown below by pumping water up and over the top edge? Hint: Density of water = 62.4 lb / ft^3. W=[?] ft-lb Round your answer to the nearest whole number

How much work is required to empty the full tank shown below by pumping water up and over the top edge? Hint: Density of water = 62.4 lb / ft^3. W=[?] ft-lb Round your answer to the nearest whole number
Transcript text: How much work is required to empty the full tank shown below by pumping water up and over the top edge? Hint: Density of water $=62.4 \mathrm{lb} / \mathrm{ft}^{3}$. \[ \mathrm{W}=[?] \mathrm{ft}-\mathrm{lb} \] Round your answer to the nearest whole number
failed

Solution

failed
failed

Solution Steps

Step 1: Find the cross-sectional area

The triangular cross-section has a base of 2 ft and a height of 2 ft. Therefore, its area is: A = (1/2) * base * height = (1/2) * 2 ft * 2 ft = 2 ft²

Step 2: Set up the integral for work

The work required to lift a slice of water at depth 'y' with thickness 'dy' over the top edge is given by: dW = (density of water) * (cross-sectional area) * (distance lifted) * (thickness) * g dW = 62.4 lb/ft³ * 2 ft² * y * dy * 32.2 ft/s² (Here, g is implicit since we're given lb, not slugs). Since we're taking slices horizontally, y represents the distance the slice has to be lifted. The length of the tank is 6 ft. This gives us: dW = 62.4 lb/ft³ * 2 ft² * y dy * 6 ft dW = 748.8y dy ft-lb

Step 3: Integrate to find the total work

Integrating the above expression from y = 0 to y = 2 (the depth of the tank) gives the total work: W = ∫(from 0 to 2) 748.8y dy W = 748.8 [y²/2](from 0 to 2) W = 748.8 * (4/2 - 0/2) W = 748.8 * 2 W = 1497.6 ft-lb

Final Answer The final answer is $\boxed{1498}$

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
An X-ray has a wavelength of 1.87 Å. Calculate the energy (in J) of one photon of this radiation. (10^10 Å=1 m). Round your answer to 3 significant figures.
failedAnswered
C. Paschal Mystery 2. extraordinary ministers of Holy Communion 1. People who take Holy Communion to those who are sick or unable to come to Mass
failedAnswered
relationship between the time (in hours) spent sailing, (x), and the distance (in miles) that the Parker family traveled from shore, (y). (y=6 x) (k=b) This table shows the proportional relationship between the number of hours Josiah worked, (x), and the number of dollars he earned, (y). (x) 2 4 6 10 (y) 30 60 90 150 (k=)
failedAnswered
Question 6 of 15 (1 point) Question Attempts: 1 of Unlimited 1 2 3 4 5 6 7 8 9 10 In Salma's bucket there are 9 brown worms and 6 red worms. Salma is going to choose 7 worms at random from the bucket to use for fishing. What is the probability that she will choose 5 brown worms and 2 red worms? Round your answer to three decimal places. Check
failedAnswered
The social status of school principal is associated with a(n) that encompasses relationships with other statuses such as students, parents, teachers, and school staff.