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Answer :
Answer: [tex]10,000\ lb.ft[/tex]
Step-by-step explanation:
Given
Initial weight of the bucket is [tex]145\ lb[/tex]
It is lifted at constant rate and rate of sand escaping is [tex]0.5\ lb/ft[/tex]
At any height weight of the sand is [tex]w(h)=145-0.5h[/tex]
Work done is given by the product of applied force and displacement or the area under weight-displacement graph
from the figure area is given by
[tex]\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft[/tex]
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Final answer:
To calculate the work done in lifting the sand, subtract the weight lost from the original weight and then multiply it by the distance lifted. In this case, the work done is 8400 ft-lbs.
Explanation:
To calculate the work done in lifting the sand, we need to find the change in weight of the sand as it is lifted. The bucket originally weighs 145 lbs and loses sand at a rate of 0.5 lbs/ft. So, for every 1 ft the sand is lifted, the weight decreases by 0.5 lbs.
Therefore, the weight of the sand after being lifted 80 ft is 145 lbs - (0.5 lbs/ft * 80 ft) = 145 lbs - 40 lbs = 105 lbs.
The work done in lifting the sand is given by the formula:
Work = Force x Distance
In this case, the force is the weight of the sand, which is 105 lbs, and the distance is 80 ft.
So, the work done in lifting the sand 80 ft is 105 lbs x 80 ft = 8400 ft-lbs.
