Uniform Circular Motion Problem

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Homework Help Overview

The discussion revolves around a problem related to uniform circular motion, specifically involving a high-speed train (TGV) navigating curves while managing passenger acceleration limits. Participants are tasked with determining the smallest radius of curvature for the track and the necessary speed for a given radius, with a focus on the implications of acceleration due to gravity.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the equations of motion relevant to circular motion, including acceleration and period. There are attempts to calculate the radius and speed based on given parameters, but confusion arises regarding unit consistency and the application of gravitational acceleration.

Discussion Status

Some participants have provided guidance on ensuring unit consistency and the proper use of gravitational acceleration in calculations. There is acknowledgment of confusion regarding the conversion of gravitational acceleration and its application in the problem. While some participants express uncertainty, others indicate progress in understanding the calculations.

Contextual Notes

Participants are navigating the complexities of unit conversions between kilometers, meters, and seconds, as well as the implications of using gravitational acceleration in their calculations. There is a noted lack of consensus on the best approach to handle these conversions.

MFlood7356
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1. The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (in km) (b) At what speed must the train go around a curve with a 1.08 km radius to be at the acceleration limit? (in km/h)

2. a=v2/r and T=2pir/v

3. I have attempted both part a and part b but I have no success in getting the correct answer. Here are m attempts
a) a=0.05g
r=v2/a
r=2162/0.05= 933120

b) r=1.08km a=0.05g
v=sqrtar
v=sqrt0.05x1.08= 0.232
 
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MFlood7356 said:
1. The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (in km) (b) At what speed must the train go around a curve with a 1.08 km radius to be at the acceleration limit? (in km/h)

2. a=v2/r and T=2pir/v

3. I have attempted both part a and part b but I have no success in getting the correct answer. Here are m attempts
a) a=0.05g
r=v2/a
r=2162/0.05= 933120

b) r=1.08km a=0.05g
v=sqrtar
v=sqrt0.05x1.08= 0.232

Your approach is fine, but you need to remember to make sure your units are consistent. Look carefully at them. You can't mix km/h, m, and s like you've done. Also, don't forget that g has a value, you can't just drop it out of your calculation.
 
Well I really was confused about g. I couldn't find out a conversion factor for it anywhere. I don't know how to use it.
 
I would just leave g as 9.81 m/s2, and convert all the other quantities so they are in meters and seconds. Then do the calculations, then convert the final answer back into km/h.

But if you wanted to convert g to km/h2, you don't need to "find" a conversion factor. Just do it dimensionally using the same relations you would use to convert anything else (1 km = 1000 m, 1 hr = 3600 s, etc).
 
Oh okay but I'm still confused on g. Would I multiply 0.05X9.81 to get the correct acceleration?
 
MFlood7356 said:
Oh okay but I'm still confused on g. Would I multiply 0.05X9.81 to get the correct acceleration?

1 G = 9.81 m/s^2

so

0.05 G = ?


yes, u only need to multiply
 
OKay thank you I got the right answer
 

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