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
tatiyna
3 years ago
5

A leaky 10-kg bucket is lifted from the ground to a height of 16 m at a constant speed with a rope that weighs 0.7 kg/m. initial

ly the bucket contains 48 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 16-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.)
Physics
1 answer:
IrinaVladis [17]3 years ago
5 0

\displaystyle W =\lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\dfrac{16}{n}}}.

<h3>Explanation</h3>

The mass comes in three parts:

  • the mass of the rope,
  • the mass of the water in the leaky bucket, and
  • the mass of the bucket.

Both the mass of the rope m_\text{rope} and the mass of the water in the bucket m_\text{water} varies with the height x of the bucket. Express the two masses as a function of x:

  • m_\text{rope} = 0.7\;(16 - x),

The water in the bucket behaves like yet another rope of density 48 \;\text{kg}/ 16 \;\text{m}= 3.0\;\text{kg}\cdot\text{m}^{-1}. The mass of the water left in the bucket at height x will be

  • m_\text{water} = 3.0\;(16 - x).

The mass of the bucket is 10\;\text{kg}. Combining the three:

  • m(x)  = m_\text{rope}(x) + m_\text{water}(x) + m_\text{bucket} \\\phantom{m(x)} = 0.7\;(16-x) + 3.0\;(16 - x) + 10\\\phantom{m(x)} = 69.2 - 3.7\;x.

Weight of the bucket at height x:

  • F_\text{weight}(x) = m(x)\cdot g = 9.8\;(69.2 - 3.7\;x) = 678.16 - 36.26\;x.

The bucket moves upward at a constant speed. As a result,

  • F(x) = W(x) = 678.16 - 36.26\;x.

Express the work required as a definite integral:

  • \displaystyle W = \int_{0}^{16}{F(x) \cdot dx} = \int_{0}^{16}{(678.16 - 36.26\;x)\cdot dx}.

Rewrite the definite integral as a Riemann Sum:

  • \displaystyle W = \int_{0}^{16}{(678.16 - 36.26\;x)\cdot dx} \\\phantom{W}= \lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\frac{16-0}{n}}}\\\phantom{W} = \lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\frac{16}{n}}}.
You might be interested in
Communities of organisms coexist in organized, balanced _____?
poizon [28]

Answer: C- ecosystem

An ecosystem is a biological community in which living beings interacts with their non-living environment. An ecosystem consists of abiotic ( non-living factors like water, sunlight, wind and soil) and biotic factors such as plants and animals. Ecosystem allows not only the interaction of abiotic and biotic factors but it favors the interaction between the living species. For example animals are dependent upon plants so as to derive their food. The coexistence of organisms favors the diversity of land forms on earth.

Communities of organisms coexist in organized, balanced ecosystems.


7 0
3 years ago
Read 2 more answers
What are the different ways that the simulation shows you that the equation is balanced, visually? For each balanced reaction, i
Nastasia [14]

Answer:

e

Explanation:

e

3 0
3 years ago
A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in ai
Svetach [21]

Answer:

The  values is  f_b  =14.9 \  beats/s

Explanation:

From the question we are told that

   The  speed of the fire engine is  v =  5\ m/s

    The frequency of the tone is  f =  500 \ Hz

    The speed of sound in air is v_s  =  340 \ m/s

The  beat frequency is mathematically represented as

     f_b  =  f_a  -  f

Where  f_a is the frequency of sound heard by the people in the fire engine and is is mathematically evaluated as

   f_a  =  [\frac{v_s + v }{v_s  -v} ]* f

substituting values

  f_a  =  [\frac{340 + 5 }{340  -5} ]* 500

  f_a  = 514.9 \  Hz

Thus  

      f_b  =514.9 -  500

      f_b  =14.9 \  beats/s

8 0
3 years ago
A diagram of a closed circuit with a power source on the left labeled 6 V. There are 3 resistors in parallel, separate paths, co
AfilCa [17]

Answer:

Current: 1.0 Amperes

The minimum current is flowing through path D

Explanation:

We first find the equivalent resistance to the three resistors in parallel ( which is the total resistance of the circuit) via the equation:

\frac{1}{R_e} =\frac{1}{R_B}+\frac{1}{R_C}+\frac{1}{R_D}\\\frac{1}{R_e} =\frac{1}{10}+\frac{1}{20}+\frac{1}{50}=0.17\\R_e=(1/0.17)\Omega\\R_e=5.88 \Omega

with this info, we can estimate the current going through branch A using Ohm's Law, and the information that the power source is 6 V:

V=I*R\\6V=I*5.88\Omega\\I=\frac{6}{5.88} Amp\\I=1.02A

where the current comes in units of Amperes since all other the quantities are given in the SI system, and we can round this answer to 1.0 Amp following the request to round it to the tenth.

The current will be the lowest through the branch with the largest resistor due to the fact that less current will flow through the path of more resistance.

Than means that the lowest current will be registered through branch D where the 50 \Omega resistor is.

8 0
3 years ago
Read 2 more answers
A charged particle of mass 0.0050 kg is subjected to a 5.0 T magnetic field which acts at a right angle to its motion. If the pa
Irina18 [472]

Answer:

0.01 C

Explanation:

Applying,

F = qvBsinФ................ Equation 1

Where F = Force on the charged particle, q = charge on the particle, v = velocity, B = magnetic field, Ф =  angle

Since the charged particle noves in a circle,

F = mv²/r................. Equation 2

Where m = mass of the particle, v = velocity of the particle, r = radius of the  circle

Substitute equation 2 into equation 1

mv²/r = qvBsinФ

make q the subject of the equation

q = mv/(rBsinФ)............. Equation 3

Given: m = 0.005 kg, v = 2 m/s, r = 0.2 m, B = 5 T, Ф = 90° (Act at right angle)

Substitute these values into equation 3

q = (0.005×2)/(0.2×5×sin90°)

q = 0.01/(1)

q = 0.01 C

5 0
3 years ago
Other questions:
  • On a spring break vacation you decide to visit the grand canyon near flagstaff, arizona. then you head south to visit some frien
    14·1 answer
  • Help !!!! Estimate the number of breaths taken by a person during 44 years?
    15·1 answer
  • What is the usual time ice takes to evaporate above a Bunsen burner?
    13·1 answer
  • What process modifies light waves to vibrate in a single plane
    12·1 answer
  • Property of a moving object equal to its mass times it velocity
    14·1 answer
  • 11. A 3.8 kg object is lifted 12 meters. Approximately how much work is performed during the lifting?
    7·1 answer
  • Which was least likely to have been a component of Earth’s atmosphere before life began?
    15·2 answers
  • A resistor R and a capacitor C are connected in series to a battery of terminal voltage V0. Which of the following equations rel
    7·1 answer
  • Pleaseeee HURRYYY!!!<br> How far will a train moving at 5.7 km/min go in 45 minutes
    10·2 answers
  • In a second order lever system the force ratio is 2.5, the load is at the distance of 0.5m from the fulcrum find distance of eff
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!