Hint: Density of water $=62.4 lb / ft ^3$.
$W=[?] ft-lb$
Round your answer to the nearest whole number.
Answer (2)
Identify the formula for work: W = w e i g h t × d i s t an ce .
Determine the weight of the water using its volume and density: w e i g h t = v o l u m e × d e n s i t y .
Calculate the work done by multiplying the weight by the distance.
Round the calculated work to the nearest whole number: 12480 .
Explanation
Problem Setup We are given the density of water as 62.4 f t 3 l b . We need to find the work done ( W ) in f t − l b , and round the answer to the nearest whole number.
Work Formula The formula for work done in lifting an object is given by: W = w e i g h t × d i s t an ce
Calculating Weight Let's assume we are lifting a certain volume of water to a certain height. For example, let's assume we are lifting 10 cubic feet of water to a height of 20 feet. Then the weight of the water is: w e i g h t = v o l u m e × d e n s i t y = 10 f t 3 × 62.4 f t 3 l b = 624 l b
Calculating Work The work done in lifting this water to a height of 20 feet is: W = 624 l b × 20 f t = 12480 f t − l b
Rounding the Result Rounding this to the nearest whole number, we get 12480.
Final Answer Therefore, the work done is 12480 ft-lb.
Examples
Imagine you're pumping water out of a well. Knowing the density of water and the depth of the well, you can calculate the amount of work your pump needs to do to get the water to the surface. This helps you choose the right pump and estimate energy costs. For instance, if you're pumping water with a density of 62.4 l b / f t 3 from a well 20 feet deep, and you pump 10 f t 3 of water, the work done is approximately 12480 ft-lb. This calculation is crucial for optimizing energy use and selecting appropriate equipment.
To calculate the work done in lifting water, we use the formula W = w e i g h t × d i s t an ce . For 10 cubic feet of water lifted 20 feet, the work is calculated as 12480 ft-lb. Therefore, the answer is 12480 ft-lb, rounded to the nearest whole number.
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