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An 14-meter-tall cylindrical tank with a 2-meter radius holds water and is half full. Find the work (in mega-joules) needed to pump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2. Round your answer to two decimal places.)

Respuesta :

Answer:

to two decimal places

= 6.04 mega joules

Step-by-step explanation:

The volume of the half tank

= πr²h

r= 2 m

h= 14/2= 7 m

Volume= 22/7 *2² *7

Volume= 88 m³

work (in mega-joules) needed to pump all of the water to the top of the tank

= Volume*mass density *acceleration*distance

= 88*1000*9.8*7

= 6036800 joules

In mega joules

= 6.036800 mega Joules

to two decimal places

= 6.04 mega joules

asuwafohjames

The work needed to pump all of the water to the top of the tank is 6.03 MJ

What is work?

Work is said to be done whenever a force move a body through a certain distance.

To calculate the work needed to pump the water to the tank, first we need to find the volume of the water in the tank half full.

Formula:

  • V = πr²h/2................ Equation 1

Where:

  • V = Volume of half full water in the tank
  • h = height of the tank
  • r = radius of the base of the tank
  • π = pie

From the question,

Given:

  • r = 2 m
  • h = 14 m
  • π = 3.14

Substitute these values into equation 1

  • V = 3.14(2²)(14)/2
  • V = 87.92 m³.

Finally, to get the work needed to pump all the water to the top of the tank, we use the formula below.

  • W = ρVhg/2................. Equation 2

Where:

  • W = Work needed to pump all the water to the of the tank
  • ρ = Density of the tank
  • h = height of the tank
  • V = Volume of halfull water in the tank
  • g = acceleration due to gravity

From the question.

Given:

  • ρ = 1000 kg/m³
  • h = 14
  • g = 9.8 m/s²
  • V = 87.92 m³

Substitute these values into equation 2

  • W = 1000(14)(9.8)(87.92)/2
  • W = 6031312 J
  • W = 6.03 MJ.

Hence, The work needed to pump all of the water to the top of the tank is 6.03 MJ.

Learn more about work here: https://brainly.com/question/8119756

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