Efficiency vs Height: Understanding the Relationship

[Trooper100]

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

 

[rock.freak667]

What is your desired energy output? Gravitational pe?

 

[Trooper100]

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.

PLEASE help if you can. thank you thank you.

 

[rock.freak667]

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.

 

[Trooper100]

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.

 

[rock.freak667]

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.