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
Yuliya22 [10]
3 years ago
12

The cable is being used to lift a 2lb leaky bucket that is initially filled with 30 lb of water. When the bucket reaches the top

of the building, it only has 5 lb of water left in it. If the cable was being pulled up at a constant rate of speed, how much work is done?
Mathematics
1 answer:
GenaCL600 [577]3 years ago
7 0

Answer:

The answer to the question is

W = 25 × (Building height) - 30× ( total time taken) +  (Building height)²

which is of the form W = Y² + 25·Y - 30·t where Y = Building height and t = total time from the start to the top of the building

Step-by-step explanation:

Firstly let us take the height as = Y

consider the work done in lifting the bucket,

W_{cable} = \int\limits^Y_0 {{2x, dx = (2·Y²/2) = Y² ft·lb

Next to consider the work done in lifting the water alone we have

The weight at the top of the building  = 5 lb

Weight at the start of the lift = 30 lb

The work done in lifting the bucket from level x to level x - dx is the product of the weight dx

Therefore the total work in lifting the bucket is

\int\limits^Y_0 {{Weight at level x, dx

The position is time dependent thus x = Y - Vt ft

\int\limits^Y_0 {{Y-t*V} \, dx

The water weight after t seconds is 30 - tl lb, where l = leak rate

where t1l = 25 lb total time =  

Therefore dx = -Vdt

Substituting we have vt = Y and lt = 25 lb substituting t at

  \int\limits^b_0 {} \, {{30-t*l} \, (-Vdt)

= [30·t -t²·L·V]ᵇ₀ = -30·b +b²× l×v = b(-30 + blv) but bv = Y and bl = 25

Therefore we have → 25Y- 30b

or W = 25 × (Building height) - 30× ( total time taken) +  (Building height)²

which is of the form W = Y² + 25·Y - 30·t

To solve a specific case, let height of the building be 5 ft and the cable weighs 1.5 lb/ft  pull rope speed = 1 ft/s

bucket leak rate = 25 lb in 5 seconds = 5 lb/s

To calculate the work done in lifting the cable we have

considering a small length of cable dx located at x below the top has a weight of 1.5 dx, the required work to completely pull the total length of the cable to the top is dW = 1.5 x dx, that is

W_{cable} =   \int\limits^ 5_0 {\frac{1}{2} x} \, dx = [x²/4]⁵₀ = 25/4 ft·lb

For the bucket without water we have

W_{bucket} = 5 × 2 = 10 ft·lb

Next we calculate the work done  is given by considering a displacement dx of the water from level x = weight of the water at x × dx that is the total work done  is given by

W_{water} = \int\limits^5_0 {Weight of water at level x} \, dx  as the level of the water at a particular time is dependent on time we have 30 - 5·t lb and the distance to the top of the building = 5 -t substituting, we have

\int\limits^0_5 {30 - 5t \, (-dt) = [-30·t + 5·t²/2]⁵₀ = 87.5 ft·lb

Therefore the answer is

Total work done =  W_{cable} + W_{bucket} + W_{water} = 25/4 ft·lb + 10 ft·lb + 87.5 ft·lb = 103.75 ft·lb

You might be interested in
The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, find th
damaskus [11]

Answer:

A two-digit number can be written as:

a*10 + b*1

Where a and b are single-digit numbers, and a ≠ 0.

We know that:

"The sum of a two-digit number and the number obtained by interchanging the digits is 132."

then:

a*10 + b*1 + (b*10 + a*1) = 132

And we also know that the digits differ by 2.

then:

a = b + 2

or

a =  b - 2

So let's solve this:

We start with the equation:

a*10 + b*1 + (b*10 + a*1) = 132

(a*10 + a) + (b*10 + b) = 132

a*11 + b*11 = 132

(a + b)*11 = 132

(a + b) = 132/11 = 12

Then:

a + b = 12

And remember that:

a = b + 2

or

a = b - 2

Then if we select the first one, we get:

a + b = 12

(b + 2) + b = 12

2*b + 2 = 12

2*b = 12 -2 = 10

b = 10/2 = 5

b = 5

then a = b + 2= 5 + 2 = 7

The number is 75.

And if we selected:

a = b - 2, we would get the number 57.

Both are valid solutions because we are changing the order of the digits, so is the same:

75 + 57

than

57 + 75.

6 0
3 years ago
The slope, m, of a linear equation can be found using the formula m = , where the x- and y-values come from two ordered pairs, a
tino4ka555 [31]
The answer is y2 = m(x2 – x1) + y1 i believe.
5 0
3 years ago
Read 2 more answers
Simplify.....<br> 4p + 2p
aleksley [76]

Answer:

6p

Step-by-step explanation:

You just add 4 and 2 together and then put p at the end because they are like terms.

6 0
3 years ago
Read 2 more answers
290 is 10 times as much as?
katrin2010 [14]
I'm pretty sure it's 29 . . . A way to remember is that when you multiply a number by ten, add a zero. For example, 34 x 10 is 340. Just add the zero!
3 0
3 years ago
Find the value of x in each case.
Tatiana [17]

Answer:

• First pic

{ \tt{4x + 65 \degree + x = 180 \degree}} \\  \dashrightarrow \: { \sf{ \{angles \: on \: straight \: line \}}} \\  \\ { \tt{5x + 65 \degree = 180 \degree}} \\  \\ { \tt{5x = 180 \degree - 65 \degree}} \\  \\ { \tt{x =  (\frac{115}{5} ) \degree}} \\  \\  \dashrightarrow \: { \boxed{ \tt{ \:  \: x = 23 \degree \:  \: }}}

• Second pic:

{ \tt{(180 \degree - 124 \degree) + 2x = 6x}} \\  \dashrightarrow \: { \sf{ \{interior \: angle \: sum equivexterior \: angle \} }} \\  \\  { \tt{56 \degree = 6x - 2x}} \\  \\ { \tt{4x = 56 \degree}} \\  \\ { \tt{x = ( \frac{56}{4} ) \degree}} \\  \\  \dashrightarrow \: { \boxed{ \tt{x = 14 \degree}}}

8 0
2 years ago
Read 2 more answers
Other questions:
  • Write an integer to describe a gain of 25 yards
    5·2 answers
  • If the area of a rhombus is 100 square inches and one of the diagonals is 25 inches long, what is the length of the other diagon
    5·1 answer
  • By visual inspections, determine the best fitting regression model for the scatterplot
    15·2 answers
  • Need help again, I hate this lol
    15·2 answers
  • Angles PTQ and STR are vertical angles and congruent.
    8·1 answer
  • What is the greatest common factor of 27 and 45?​
    8·2 answers
  • An egg carton holds 12 eggs. A breakfast buffet uses 96 eggs by
    11·1 answer
  • Arrange the systems of equations that have a single solution in increasing order of the x-values in their solutions. 2x + y = 10
    5·2 answers
  • Pls help no links pls
    12·2 answers
  • Is this a proportional or nonproportional linear relationship?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!