A leaky 10-kg bucket is lifted from the ground to a height of 14 m at a constant speed with a...
Question:
A leaky {eq}10-\mathrm{kg} {/eq} bucket is lifted from the ground to a height of {eq}14 \, \mathrm{m} {/eq} at a constant speed with a rope that weighs {eq}0.7 \, \mathrm{kg/m} {/eq}. Initially the bucket contains {eq}42 \, \mathrm{kg} {/eq} of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the {eq}14-\mathrm{m} {/eq} level. Find the work done. (Use {eq}9.8 \, \mathrm{m/s^2} {/eq} for {eq}g {/eq}.)
A) Show how to approximate the required work by a Riemann sum. (Let {eq}x {/eq} be the height in meters above the ground.)
B) Express the work as an integral.
C) Evaluate the integral. (Round your answer to the nearest integer.)
Riemann Sum
Riemann sum formula:
{eq}\int_{a}^{b}f(x)dx = \lim_{x\rightarrow \infty} \sum_{i=1}^{n}f(x_{i})(\frac{b-a}{n}) {/eq}
Weight = Force = Mass(m) x Gravity(g)
Work amount depends on the size of the force on the object and the distance it moves.
Answer and Explanation: 1
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View this answerA) Initial mass of the bucket is {eq}m = 10 + 42 = 52 kg {/eq}
If uniformly looses 42 kg of water over a distance of 14 m, so bucket looses per m is...
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Understand different types of graphs, including force vs. time and force vs. distance, and see examples. Discover what the area under the force-time graph refers to.
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