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.

Answers: 1

Show answers

Answers

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

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this. hope that you like the video and that it explains more in detail to you.

that is the link.

Answer from: Quest

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )

Another question on Physics

Physics, 21.06.2019 14:00

Atransverse wave is traveling on a string stretched along the horizontal x-axis. the equation for the vertical displacement y of the string is given by y = (1.8 x 10-3)cos[π(13x - 60t)], where all quantities are in si units. what is the maximum speed of a particle of the string

Answers: 2

Answer

Physics, 22.06.2019 00:00

An inclined plane wrapped around a metal shaft is a a. lever b. screw c. pulley d. wedge

Answers: 2

Answer

Physics, 22.06.2019 04:30

Work out sian speed for the first 30 minutes of her journey. give your answer in km/h.

Answers: 1

Answer

Physics, 22.06.2019 11:00

Aperson walks first at a constant speed of 4.89 m/s along a straight line from point a to point b and then back along the line from b to a at a constant speed of 2.95 m/s. what is the average speed over the entire trip?

Answers: 1

Answer

You know the right answer?

A bucket begins weighing 15 pounds, including the sand it holds. The bucket is to be lifted to the t...

Questions