text: # Efficiency vs Height: Understanding the Relationship
  
  • Trooper100
  In summary: Try drawing a linear trendline, I don't think efficiency would increase that much in such a small interval.
  
  ## Homework Statement
  
  Hey guys! I am doing a very simple lab, and in need of your expertise!
  
  Haha, I am an intro-physics student, please don't get too complicated with me, my knowledge is very limited.
  
  The QUESTION is: WHAT IS THE RELATIONSHIP BETWEEN EFFICIENCY VS HEIGHT (graphically)...err...our graph is a curve-like line, is that correct? Similar to x^2 graphs...I think.
  
  Thank you to all.
  
  ## Homework Equations
  
  Let subscript g = gravitational potential energy, k = kinetic energy
  
  Efficiency = Edesired/Etotal or Eoutput/Einput
  
  Eg = mass X gravity X height
  Ek = mass X velocity^2
  
  What is your desired energy output? Gravitational pe?
  
  rock.freak667 said:
  What is your desired energy output? Gravitational pe?
  
  Our desired energy output is only Ek.
  
  Our desired energy input is only Eg.
  
  We are trying to find the efficiency vs height relationship.
  
  In our experiment, as we increased the vertical height, but remain a fixed distance, our cart traveled down the slope faster. This makes sense because as you raise height, you also raise angle making the slope steeper, thereby traveling faster.
  
  Our efficiency in percentage also increased, by it did not increase by a steady interval. As we increased the vertical height, efficiency increased but less than the rates before it. It started to increase less and less.
  
  Trooper100 said:
  We are trying to find the efficiency vs height relationship.
  
  In our experiment, as we increased the vertical height, but remain a fixed distance, our cart traveled down the slope faster. This makes sense because as you raise height, you also raise angle making the slope steeper, thereby traveling faster.
  
  Our efficiency in percentage also increased, by it did not increase by a steady interval. As we increased the vertical height, efficiency increased but less than the rates before it. It started to increase less and less.
  
  Could you please post your graph? As I am inclined to think that a graph of η vs. x should be linear.
  
  rock.freak667 said:
  Could you please post your graph? As I am inclined to think that a graph of η vs. x should be linear.
  
  Sure, here it is in a Word Document.
  
  Thanks for any help.
  
  EDIT: I have a feeling that the graph may not be linear. It's hard to find a solid linear relationship in physics (from my experience). Thanks anyway!
  
  Oh yeah, the line in the pictured was generated by Microsoft word. It may not be correct, or it may correct depending on the function (linear, parabolic, curve, etc). I chose polynomial.
  
  #### Attachments
  
  • efficiency vs height graph.doc
  70.5 KB · Views: 185
  Trooper100 said:
  Sure, here it is in a Word Document.
  
  Thanks for any help.
  
  EDIT: I have a feeling that the graph may not be linear. It's hard to find a solid linear relationship in physics (from my experience). Thanks anyway!
  
  Oh yeah, the line in the pictured was generated by Microsoft word. It may not be correct, or it may correct depending on the function (linear, parabolic, curve, etc). I chose polynomial.
  
  Try drawing a linear trendline, I don't think efficiency would increase that much in such a small interval.
  
  Most times they give you an experiment to do, most of the relationships are linear.
  
  ## 1. What is the relationship between efficiency and height?
  
  Efficiency and height have an inverse relationship, meaning that as height increases, efficiency decreases. This is due to the fact that taller structures have a higher potential for energy loss and require more resources to maintain stability.
  
  ## 2. Why does efficiency decrease with height?
  
  Efficiency decreases with height due to several factors, including wind resistance, structural stability, and the need for additional resources such as materials and maintenance. As a structure gets taller, these factors become more significant and can greatly impact overall efficiency.
  
  ## 3. How does the shape of a structure affect its efficiency?
  
  The shape of a structure can greatly impact its efficiency, as certain shapes are better suited for withstanding wind and distributing weight. For example, a pyramid-shaped structure may be more efficient than a rectangular one, as the pyramid's sloping sides can minimize wind resistance and evenly distribute weight.
  
  ## 4. Are there any benefits to building taller structures despite decreased efficiency?
  
  Yes, there are several potential benefits to building taller structures. These may include increased floor space, better views, and the ability to accommodate more people or equipment. Additionally, taller structures can be seen as symbols of innovation and progress.
  
  ## 5. How can we improve efficiency in taller structures?
  
  There are several ways to improve efficiency in taller structures, such as using advanced building materials, incorporating energy-efficient designs, and implementing regular maintenance and upgrades. Additionally, utilizing renewable energy sources and optimizing the building's location and orientation can also help improve efficiency.