Graphing results of performance test and finding area under curve

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Discussion Overview

The discussion revolves around the calculation of the time it takes for a motorcycle to reach 55 miles per hour, focusing on the relationships between engine horsepower, torque, transmission gearing, and sprocket gearing. Participants explore the equations used to model this scenario and the implications of graphing Force Inverse versus Velocity to find the area under the curve, which is proposed to represent time.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents equations involving force, mass, gravity, and velocity to model motorcycle acceleration and seeks validation on their correctness.
  • Another participant questions the meaning of mass/g in the context of the equations, suggesting that it may not be necessary for the calculations.
  • A participant explains that mass/g represents the weight of the motorcycle on the driving wheel, which is relevant for acceleration.
  • Concerns are raised about the applicability of the initial equations after feedback from a teacher, prompting a search for alternative methods to graph in order to find time.
  • There is a suggestion to use 'w' to denote weight instead of 'm' to avoid confusion, as 'm' typically refers to mass.
  • Participants clarify their equations, substituting weight for mass in their calculations and reiterating their approach to graphing Force Inverse versus Velocity.

Areas of Agreement / Disagreement

Participants express uncertainty about the correctness of the equations and the methodology for finding time through graphing. There is no consensus on the validity of the initial approach, and multiple viewpoints regarding the use of weight versus mass are presented.

Contextual Notes

There are unresolved questions regarding the appropriateness of the equations used and the definitions of mass and weight in this context. The discussion reflects a dependence on the participants' interpretations of the physical principles involved.

dirtboi22
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Problem statement, I am calculating the time it takes for my motorcycle to reach 55 miles per hour, through its engine Horsepower, Torque, transmission gearing, and sprocket gearing.(chain driven)

I am using the equations:
F=[mass/g]*[dV/dt]
dt=[mass/g]*[dV/F]
t=∫[mass/g]*[dV/F]

F=[(torque*Drive ratio*gear ratio*primary drive)/(tire radius)]
V=[(RPM*tire radius*2pi)/(Drive ratio*Gear ratio*primary drive*60)]
F'=[mass/g]*[1/F]

Using these equations I plan to graph Force Inverse, F', vs Velocity. With this graph I will find the area under curve from 0 to 55mph. which should be Time?
I am using the rpm range of the engine, 2000-9000, and I am find F,F', and V for all gears of transmission, 1-5.
Does this look correct, equation wise?
I recently met with my Calculus II teacher and he said it did not look correct. Any help would be great, I am a mechanical engineering student and I am very curious. I know this is an in depth question, I am simply asking if my equations look correct and if graphing Force Inverse vs. Velocity will be correct in finding area under curve, time. Thank you, I can add additional info if needed!
 
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What is mass / g supposed to represent? After all, F = m * a
 
SteamKing, Mass/g is mass over gravity, It represents the weight of the entire machine on the the driving wheel, being that the driving wheel is the cause of acceleration? However Maybe this is not needed. This equation is actually the reason I posted this question, I am not sure if F=[m/g]*[dv/dt] is correct or applicable to the problem..
 
I had spoke to one of my school advisers, who actually gave me this equation. It was very short and I honestly felt like they really didn't care. I had used this equation and graphed force inverse vs velocity, and the area under the graph had actually represented a fairly accurate time for the machine to reach 55mph. However I have began to think it is wrong, being that my teacher said it made no sense. If I was looking to find the time it takes for my motorcycle to reach a certain velocity what would I need to graph, so in which the area under the curve equals time?
 
If you are using the weight of the motorcycle, use w to represent the weight, rather than m, which usually stands for the mass. w/g = m.
 
SteamKing said:
If you are using the weight of the motorcycle, use w to represent the weight, rather than m, which usually stands for the mass. w/g = m.
You are most definitely correct! I apologize, with it meaning weight and not mass, do my equations look correct?
 
Just to clarify for everyone, I am using the equations:
F=[weight/g]*[dV/dt]
dt=[weight/g]*[dV/F]
t=∫[weight/g]*[dV/F]
 

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