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# (Solved): A 24N bucket attached to a rope of negligible weight is used to draw water from a well 25m deep. A ...

A

`24N`

bucket attached to a rope of negligible weight is used to draw water from a well

`25m`

deep. At the outset, at the bottom of the well, the bucket is filled with

`180N`

of water. A winch raises the bucket at a constant speed of

`50c(m)/(s)`

, but the water escapes through a hole at a rate of

`0.6(N)/(s)`

. (i) What is the weight of water contained in the bucket, once it reaches a height of

`x`

meters measured from the bottom of the well? weight

`=`

`N`

FORMATTING: Express the answer as a formula. (ii) for

`\Delta x`

small, the amount of work done by the winch to raise the bucket from heights

`x`

to

`x+\Delta x`

(measured from the bottom) is approximately

`P(x)\Delta x`

. What is

`P(x)`

?

`P(x)=`

`Q`

FORMATTING: Give a formula for your answer. (iii) What is, in Joules, the amount of work required to raise the bucket to the surface? FORMATTING: If you round your anwer, ensure that the round-off error is less thatn

`1%`

of the value. Answer: JoulesA 24 N bucket attached to a rope of negligible weight is used to draw water from a well 25 m deep. At the outset, at the bottom of the well, the bucket is ﬁlled with 180 N of water. A winch raises the bucket at a constant speed of 50 cm/s, but the water escapes through a hole at a rate of 0.6 N/s. (i) What is the weight of water contained in the bucket, once it reaches a height of x meters measured from the bottom of the well? weight = 180-((.1200000000e-1)*x) Preview Change entry mode N FORMATTING: Express the answer as a formula. (ii) for \Delta x small, the amount of work done by the winch to raise the bucket from heights x to x+\Delta x (measured from the bottom) is approximately P(x)\Delta x . What is P(x) ? P(x)= 204-((.1200000000e-1)*x) Preview Change entry mode FORMATTING: Give a formula for your answer. (iii) What is, in Joules, the amount of work required to raise the bucket to the surface? FORMATTING: If you round your anwer, ensure that the round-off error is less thatn 1% of the value. Answer: Number Joules

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