Help In understanding Rate Of Change in mm per sec

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Discussion Overview

The discussion revolves around understanding the rate of change of the left rail's elevation relative to the right rail on a train transition. Participants explore the calculations involved in determining this rate of change, including conversions of speed and the implications of the transition's slope.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents a problem involving a train traveling at 136.794 kph and a transition length of 60 m, where the left rail rises by 25 mm.
  • Another participant notes that the transition suggests a slope, calculating the slope as 25 mm over 60 m, which translates to a rise of 0.416 mm for every meter traveled.
  • Participants discuss the conversion of speed from kilometers per hour to meters per second, with one providing the conversion factor of 1 kph = 0.277777778 m/s.
  • A participant outlines the calculation for the rate of change, breaking it down into steps involving the time taken to cross the transition and the conversion of speed.
  • There is a specific mention of the factor of 3.6 in the calculations, with one participant explaining its origin related to the conversion from kph to m/s.

Areas of Agreement / Disagreement

Participants generally agree on the need to convert units and the implications of the slope, but there is no consensus on the clarity of the calculations or the reasoning behind certain steps, particularly regarding the use of the factor 3.6.

Contextual Notes

Some assumptions about the relationship between speed, distance, and time are present, but the discussion does not resolve how these factors interact fully. The calculations involve multiple steps that may depend on participants' interpretations of the problem.

tomtomtom1
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Hi everyone

Firstly this is not a homework question, i work in transport engineering. ( i do study part time which is why i sometimes post in the homework section)

Now to the problem.

I am trying to understand how to solve this problem, i already know the answer.

A train is traveling on straight & level track at 136.794kph.
It approaches a transition. The transition is 60m long.
Along the transition the Left Rail rises linearly over the length of the transition relative to the right Rail by 25mm.
Calculate the rate of change the left rail raises over the right in mm per sec over the 60m transition at 136.794kph.

i know that the answer is (25mm * 136.794kph) / (3.6 * 60m)

what i need help with is where does the 3.6 some from? and why do you times 25mm by 136.794kph?

can anyone explain

Thanks
 
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The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?
The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?
 
The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?

Yes there is a slope and the slope is 25mm/60m = 1m per 0.416mm which means for every 1m the train travels along the transition the left rail rises by 0.416mm.

The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?

1kph = 0.277777778 m/s so 136.794km/hr in m/s is 136.794*0.277777778 = 37.998m/s.
 
rate of change the left rail raises = 25mm / (time needed to cross 60m)
= 25 mm / (60 m / velocity)
= 25 mm / (60 m / 136.794 km per hour)
Now, 1 km per hour = 1000 m / 3600 sec = 1/3.6 meter per sec
So,
rate of raise = 25 mm / (60 m / ((136.794 / 3.6) meter per sec))
= 25 mm / (3.6 x 60 / 136.794) sec
= (25 mm x 136.794) / (3.6 x 60) sec
 

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