Help : isolated system-conservation of mechnaical energy

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In summary, the conversation is about a physics problem involving a windmill and pumping water from a well into a tank. The windmill has a diameter of 2.3m and an efficiency of 27.5%. The energy generated by the windmill is used to pump water from a 32.5m deep well to a tank 2.30m above the ground. The conversation includes calculations of kinetic energy and potential energy to find the rate at which water can be pumped into the tank.
  • #1
cgt32
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can canyone here help me with this physics problem:
Air moving at 11.0 m/s in a steady winds encounters a windmill of diameter 2.3m and having an efficiency of 27.5 %. The energy generated by the windmill is used to pump water from a well 32.5m deep into a tank 2.30m above the ground. At what rate in liters per minute can water be pumped into the tank?

This is what I have so far:
Ekin = 1/2mv^2
Density for air is: 1.29 kg/m^3
The time for this energy to form is 1 sec.
m = ( a * v * A ) ... where A is air density and v is velocity, a in this case is area of the windmill, which is pi(diameter/2)^2

Thus
Ekin = 1/2 (a * v * A)

So :
Ekin * 25% = energy generated by the windmill

After that, I'm lost. But I think it has to do something with potential energy.
 
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  • #2
Originally posted by cgt32

This is what I have so far:
Ekin = 1/2mv^2
Density for air is: 1.29 kg/m^3
The time for this energy to form is 1 sec.
m = ( a * v * A ) ... where A is air density and v is velocity, a in this case is area of the windmill, which is pi(diameter/2)^2

Thus
Ekin = 1/2 (a * v * A)
That should be v^3
Originally posted by cgt32

So :
Ekin * 25% = energy generated by the windmill

After that, I'm lost. But I think it has to do something with potential energy.
The energy needed to raise mass m a height h is mgh where g is acceleration of gravity (9.8 m/sec/sec). This should give you enough info to do the problem.
 

FAQ: Help : isolated system-conservation of mechnaical energy

What is an isolated system?

An isolated system is a physical system that does not interact with its surroundings, meaning that there is no exchange of matter or energy between the system and its surroundings. This allows for the conservation of mechanical energy within the system.

What is conservation of mechanical energy?

The law of conservation of mechanical energy states that in an isolated system, the total amount of mechanical energy (the sum of kinetic and potential energy) remains constant over time. This means that energy cannot be created or destroyed, but can only be converted from one form to another.

Why is conservation of mechanical energy important?

Conservation of mechanical energy is important because it is a fundamental law of physics that helps us understand and predict the behavior of isolated systems. It also allows us to make calculations and solve problems involving mechanical energy.

What are some examples of isolated systems?

Some examples of isolated systems include a swinging pendulum, a roller coaster car at the top of a hill, and a planet orbiting around the sun. These systems do not exchange energy with their surroundings and therefore, the total mechanical energy remains constant.

What factors can affect the conservation of mechanical energy in an isolated system?

The main factors that can affect the conservation of mechanical energy in an isolated system are external forces, such as friction and air resistance, and the conversion of energy from one form to another within the system. These factors can cause a decrease in the total mechanical energy of the system over time.

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