Cars move around the “traffic circle” (solved)

Cars move around the “traffic circle” which is in the shape of
an ellipse. If the speed limit is posted at 60 km/h, determine
the minimum acceleration experienced by the passengers.
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Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.

[@martin00114]

Well said!, This is way I enjoy your videos.

[@QuestionSolutions]

Thanks!

[@jhfghrt1918]

Thank you very much!

[@QuestionSolutions]

You are very welcome! :)

[@raheemullah8060]

sir, when we were given the value of a and b then why you take a long method for finding the minimum acceleration...?

[@QuestionSolutions]

In case someone doesn't know how to do it the long way. At the end of the video, I also show the short method :)

[@martin00114]

To find maximum acceleration could we also differentiate by y? and how did you know to differentiate by x to find minimum acceleration?

[@QuestionSolutions]

No, it depends on which curve you want to work with. To get maximum, we need to use the y-distance where as to get the minimum, we need to use the x-distance. It's based on the curve. So the 40m section gives you more acceleration because it's a shorter curve, and vice versa.

[@aimanjamil5454]

how we suppose to get the rho=40^/60? as if we substitute the value of y to the dy/dx and d^2y/dx^2, the answer is undefined.

[@QuestionSolutions]

I am not too sure I understand your question but from what I understand, you're trying to use 60/40? If you want to use the opposite, you need to retake the derivative with respect to x instead of y.

[@aimanjamil5454]

@@QuestionSolutions thanks. I appreciate that

[@engineerinie]

Thank you

[@QuestionSolutions]

You're very welcome!

[@koopakid3102]

Where did the formulas for roh come from, with b^2/a or a^2/b?

[@QuestionSolutions]

The first half of the whole video is basically deriving it. I am unsure what you are asking here, sorry.

[@oximeter_x20a]

why is there no tangential acc.?

[@QuestionSolutions]

It's assumed that the cars are moving at a constant speed of 60km/h since they are following the speed limit. Usually, the question will give a tangential acceleration or say something to hint at it.

[@oximeter_x20a]

@@QuestionSolutions Thank you sir. Your format is really helpful, would u consider teaching mechanical enginerring topics like heat transfer or thermodynamics in the future? When I looked at ur subcribed count i was shock this is a small chanell, its underated. Keep it up sir!

[@QuestionSolutions]

You're very welcome. I will definitely consider the topics you mentioned, I hope to do a lot of topics over time. Your kinds words mean a lot, many thanks :) Best of luck with your studies!

[@Yuzze.official]

why is it sir my answer is -90 ?

[@QuestionSolutions]

I have no idea 😅 It's not possible to say, did you follow the steps I showed?

[@rehanamjad2855]

Brother in question they askedfor minimum acceleration but u answer maximum. Am i right?

[@QuestionSolutions]

No, this is the minimum since we used the larger radius of curvature. Using the smaller one would give you the maximum.

[@rehanamjad2855]

Sorry brother my mistake. You are right

[@QuestionSolutions]

@@rehanamjad2855 No need to apologize, it was a good question. Best wishes with your studies!

[@dartrixs753]

Prhne lg gya ha rehan.

[@rehanamjad2855]

@@dartrixs753 kha bat ha saif