1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gemiola [76]
3 years ago
12

A bucket that weighs 4lband a rope of negligible weight are used todraw water from a well that is 80ftdeep. The bucket is filled

with 40lbof waterand is pulled up at a rate of 2ft/s, but water leaks out of a hole in the bucketat a rate of 0.2lb/s. Find the work done in pulling the bucket to the top ofthe well.
Mathematics
1 answer:
liq [111]3 years ago
8 0

Answer:

Workdone = 3200 lb.ft

Step-by-step explanation:

We are told that the bucket is filled with 40 lb of water but water leaks out of a hole in the bucket at a rate of 0.2lb/s

Thus,

Weight of water at any given time (t) would be;

w(t) = 40 - 0.2t - - - - (1)

We are told the bucket is pulled up at a rate of 2ft/s.

Thus, height at time (t); y = 0 + 2t = 2t

Since y = 2t,

Then,t = y/2

Put y/2 for t in eq 1

Thus; w(y) = 40 - 0.2(y/2)

w(y) = 40 - 0.1y

Now, at y = 80 ft, we have;

w(80) = 40 - 0.1(80)

w(80) = 40 - 8 = 32 lb

Since 32 lbs are left, it means there is always water in the bucket.

Thus, work done is;

W = 80,0[∫(Total weight).dy]

W = 80,0[∫[(weight of rope) + (weight of bucket) + (weight of water)]dy]

W = 80,0[∫[0 + 4 + 40 - 0.1y]dy]

Integrating, we have;

W = [44y - y²/20] at boundary of 80 and 0

So,

W = [44(80) - 80²/20] - [0 - 0²/20]

W = 3200 lb.ft

You might be interested in
Natalia paid $38.95 for three medium-sized pizzas and a salad. if Natalia paid $11.98 for the salad, which equation can be used
kondaur [170]

Answer:

A

Step-by-step explanation:

$38.95 for 3 m size pizzas and a salad

38.95 = 3m + 11.98

5 0
2 years ago
Read 2 more answers
A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final leng
Andrej [43]

Answer:

The Poisson's ratio for the material is 0.0134.

Step-by-step explanation:

The Poisson's ratio (\nu), no unit, is the ratio of transversal strain (\epsilon_{t}), in inches, to axial strain (\epsilon_{a}), in inches:

\nu = -\frac{\epsilon_{t}}{\epsilon_{a}} (1)

\epsilon_{a} = l_{a,f}-l_{a,o} (2)

\epsilon_{t} = l_{t,f}-l_{t,o} (3)

Where:

l_{a,o} - Initial axial length, in inches.

l_{a,f} - Final axial length, in inches.

l_{t,o} - Initial transversal length, in inches.

l_{t,f} - Final transversal length, in inches.

If we know that l_{a,o} = 61.2\,in, l_{a,f} = 61.235\,in, l_{t,o} = 2.7\,in and l_{t,f} = 2.69953\,in, then the Poisson's ratio is:

\epsilon_{a} = 61.235\,in - 61.2\,in

\epsilon_{a} = 0.035\,in

\epsilon_{t} = 2.69953\,in - 2.7\,in

\epsilon_{t} = -4.7\times 10^{-4}\,in

\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}

\nu = 0.0134

The Poisson's ratio for the material is 0.0134.

7 0
3 years ago
(HELP ASAP!!)
7nadin3 [17]

Answer:

1500

Step-by-step explanation:

24 month means 2 years ( N )

rate 15 pcpa ( R )

amount is 5000 ( P )

so by formula

interest = P×N×R/100

so ( I ) = 5000×2×15/100

so( I ) = 50×2×15 ....... ( here 100 ( 2 zero ) and 5000.( 2 zero ) got canceled

so ( I ) = 50×2×15

so ( I ) = 100×15

so ( I ) = 1500

MARK AS BRAINLIST IF IT IS USEFUL

3 0
3 years ago
I need to know the distance and if your could please tell me the formula for future problems thank you!! ASAP
Ksivusya [100]

Distances in 2- and 3-dimensions (and even higher dimensions) can be found using the Pythagorean theorem. The straight-line distance can be considered to be the hypotenuse of a right triangle whose sides are the horizontal and vertical differences between the coordinates.

Here, you have A = (0, 0) and B = (3, 6). The horizontal distance between the points is ...

... 3 - 0 = 3 . . . . the difference of x-coordinates

The vertical distance between the points is ...

... 6 - 0 = 6 . . . . the difference of y-coordinates

Then the straight-line distance (d) between the points is found from the Pythagorean theorem, which tells you ...

... d² = 3² + 6²

... d = √(9 + 36) = √45 ≈ 6.7 . . . units

8 0
3 years ago
Giant spider crabs prefer an elevation of around -800 feet, and Atlantic wolffish prefer an elevation of around -300 feet.
Zepler [3.9K]
Giant spider crabs tend to be farther from the surface of the ocean than Atlantic wolffish
8 0
2 years ago
Other questions:
  • Ren built a birdhouse with a volume of 224 in.3 Find the height of the birdhouse. A square pyramid. The square base has side len
    15·2 answers
  • The price of a train ticket from Los Angeles to Flint is normally $134.00. However, children under the age of 16 receive a 40% d
    15·1 answer
  • Brainliest answer<br><br> 590- 67
    5·2 answers
  • A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x
    14·1 answer
  • What is 399713 rounded to the place value of the underlined digit
    15·1 answer
  • If x is a whole number and 437 = (21 + x)(21 - x), then x =
    8·1 answer
  • Please help me with this question
    11·1 answer
  • Please help due very soon!!!!
    7·2 answers
  • Select the correct answer from the drop-down menu. A box contains 20 lightbulbs, of which 5 are defective. If 4 lightbulbs are p
    15·2 answers
  • Find f(-2) if f(x) = -3x + 5
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!