Total Mechanical Energy: Mass or No Mass?

In summary, the conversation revolves around finding the total mechanical energy in a given system. The initial question asks for the total mechanical energy, but the provided solutions do not use the mass (m) in their calculations. This is because the question is asking for the energy per unit mass, which is a more useful quantity to consider. To calculate this, one simply needs to divide both sides of the equation by the mass. This can be thought of as each kilogram of water carrying 0.887 kJ of mechanical energy, and by considering the volume and mass flow rates, one can determine the energy being generated per second. The conversation concludes by acknowledging the helpfulness of this clarification.
  • #1
TyErd
299
0

Homework Statement



In the diagram I have attached the initial question is to find the total mechanical energy. however in the solutions which I have placed under the diagram, they don't use the mass (m). So total mechanical energy i thought was = mgh + 0.5m[itex]v^{2}[/itex] but they use gh + 0.5[itex]v^{2}[/itex] . no mass. why

i think its something to do with the question asking to be in per unit mass but i don't see why.

Homework Equations


The Attempt at a Solution

 

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  • #2
They ask you for the energy per unit mass that is present, and so they divide both sides of the equation by the mass. It's nothing more complicated than that. It's a more useful quantity to consider in this situation than the amount of energy present, which depends upon how big a "parcel" of water you consider.
 
  • #3
Think of it this way: every kilogram of water that passes by carries with it 0.887 kJ of mechanical energy. You have the volume flow rate (which is the volume of water that flows by in 1 second). You can use that to determine the mass flow rate (the rate at which water flows by in kg/s). Combine that with your energy per unit mass, and suddenly you have the energy per second being generated (EDIT: or at least the energy per second that could be generated if all of that mechanical energy in the water flow could be transferred to some other system with 100% efficiency -- in a real hydro plant the efficiency is sure to be lower).
 
  • #4
in essence,

per unit mass = mass = 1

so mgh = 1gh = gh

same with KE
 
  • #5
thankyou guys. helps alot
 

1. What is total mechanical energy?

Total mechanical energy is the sum of an object's potential and kinetic energy. It represents the total energy that an object possesses due to its position and motion.

2. How is total mechanical energy conserved?

According to the law of conservation of energy, total mechanical energy is conserved in a closed system. This means that the total amount of mechanical energy remains constant, even as it is transferred between potential and kinetic forms.

3. How is total mechanical energy calculated?

Total mechanical energy can be calculated by adding the potential energy and kinetic energy of an object. The formula for total mechanical energy is: E = PE + KE, where E represents total mechanical energy, PE represents potential energy, and KE represents kinetic energy.

4. What factors can affect total mechanical energy?

Total mechanical energy can be affected by factors such as an object's mass, height, and velocity. Changes in these variables can result in changes to an object's potential and kinetic energy, and therefore, its total mechanical energy.

5. Why is total mechanical energy important?

Total mechanical energy is important because it helps us understand and analyze the behavior of objects in motion. It allows us to predict how objects will move and how much energy they will possess at different points in time. Additionally, the conservation of total mechanical energy is a fundamental principle in physics and is used in many real-world applications, such as in the design of roller coasters and other mechanical systems.

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