Physics, 16.07.2020 05:01 jfox8741

A bucket begins weighing 15 pounds, including the sand it holds. The bucket is to be lifted to the top of a 35 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.3 pounds of sand each foot it is lifted. Find the work done lifting the bucket to the top of the building.

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Answer from: Chartwig1908

The work done lifting the bucket to the top of the building is 341.25 lbf-ft.

Explanation:

Given that bucket is part of a variable-mass system due to sand losses and such work, measured in $lbf \cdot ft$ is associated to gravitational potential energy by Work-Energy Theorem, the work done by lifting the bucket is represented by the following integral:

$W = \frac{1}{g_{c}} \int\limits^{y_{max}}_{y_{min}} {m(y) \cdot g} \, dy$

Where:

m(y) - Mass of the bucket as a function of height, measured in pounds.

- Gravitational constant, measured in feet per square second. ( $g = 32.174\,\frac{ft}{s^2}$ )

$g_{c}$ - lb-f to lb-m conversion factor, measured in lb-m to lb-f. ( $g_{c} = 32.174\,\frac{lbm}{lbf}$ )

Since leaking is constant, the mass of the bucket can be modelled by using a first-order polynomial (linear function), that is:

$m(y) = m_{o}+\dot m \cdot y$

Where:

$m_{o}$ - Initial mass of the bucket, measured in pounds.

$\dot m$ - Leaking rate, measured in pounds per feet.

- Height of the bucket with respect to bottom, measured in feet.

After replacing the mass and simplifying the integral, the following expression for work is found:

$W = \frac{m_{o}\cdot g}{g_{c}}\int\limits^{y_{max}}_{y_{min}}\, dy + \frac{\dot m \cdot g}{g_{c}}\int\limits^{y_{max}}_{y_{min}} {y} \, dy$

$W = \frac{m_{o}\cdot g}{g_{c}}\cdot (y_{max}-y_{min}) +\frac{\dot m \cdot g}{2\cdot g_{c}}\cdot (y_{max}-y_{min})^{2}$

If $m_{o} = 15\,pd$ , $g = 32.174\,\frac{ft}{s^{2}}$ , $g_{c} = 32.174\,\frac{lbm}{lbf}$ , $\dot m = -0.3\,\frac{pd}{ft}$ and $y_{max} - y_{min} = 35\,ft$ , the work done lifting the bucket to the top of the building is:

$W = \frac{(15\,pd)\cdot \left(32.174\,\frac{ft}{s^{2}} \right)}{32.174\,\frac{lbm}{lbf} }\cdot (35\,ft) + \frac{\left(-0.3\,\frac{pd}{ft} \right)\cdot \left(32.174\,\frac{ft}{s^{2}} \right)}{2\cdot \left(32.174\,\frac{lbm}{lbf} \right)}\cdot (35\,ft)^{2}$

$W = 341.25\,lbf\cdot ft$

The work done lifting the bucket to the top of the building is 341.25 lbf-ft.

Answer from: Quest

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account. she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem. she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem. her desire for the new hairstyle is in conflict with her honesty and integrity.

d. if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it. the amount she has in her account is not the problem. and if i may suggest, she might as well close her checking account, and put the money where it'll work for her. it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now. under no circumstances should he ask for a higher limit.

b. he can ask for the grace period to be extended. but that's no solution, the bank will almost certainly refuse anyway, and there are much better options. he knew the rules of his credit card when he started using it.

c. he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d. he definitely should pay the minimum otherwise they could shut down his card. he should also pay as much more as he possibly can. he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices. what he has to do: pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

Answer from: Quest

answer

procedural programming, object-oriented programming

explanation

procedural programming is a type of computer programming language that specifies a series of well structured steps and procedures within its development period of time. it contains a systematic order of statements, functions and commands to complete a computational task or program. it is centered on creating procedures. while object oriented programming is a programming language that is centered on creating objects rather that actions and data rather than logic.. it has four principles which are inheritance, polymorphism, abstraction and encapsulation

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