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Question Number 19140 by Tinkutara last updated on 05/Aug/17

A racing car travels on a track (without banking) ABCDEFA. ABC is a circular arc of radius 2R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 ms^(−1) . Find the minimum time for completing one round.

$$\mathrm{A}\:\mathrm{racing}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{on}\:\mathrm{a}\:\mathrm{track}\:\left(\mathrm{without}\right. \\ $$$$\left.\mathrm{banking}\right)\:{ABCDEFA}.\:{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circular} \\ $$$$\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{2}{R}.\:{CD}\:\mathrm{and}\:{FA}\:\mathrm{are} \\ $$$$\mathrm{straight}\:\mathrm{paths}\:\mathrm{of}\:\mathrm{length}\:{R}\:\mathrm{and}\:{DEF}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{circular}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:{R}\:=\:\mathrm{100}\:\mathrm{m}.\:\mathrm{The} \\ $$$$\mathrm{co}-\mathrm{efficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{on}\:\mathrm{the}\:\mathrm{road}\:\mathrm{is}\:\mu\:= \\ $$$$\mathrm{0}.\mathrm{1}.\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{is} \\ $$$$\mathrm{50}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{time}\:\mathrm{for} \\ $$$$\mathrm{completing}\:\mathrm{one}\:\mathrm{round}. \\ $$

Commented by Tinkutara last updated on 06/Aug/17

Don′t we neglect such processes in physics?

$$\mathrm{Don}'\mathrm{t}\:\mathrm{we}\:\mathrm{neglect}\:\mathrm{such}\:\mathrm{processes}\:\mathrm{in} \\ $$$$\mathrm{physics}? \\ $$

Commented by Tinkutara last updated on 05/Aug/17

Commented by Tinkutara last updated on 06/Aug/17

I don′t know Sir. I am reading this from a book and it has solution in it. Should I post it?

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{Sir}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{reading}\:\mathrm{this}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{book}\:\mathrm{and}\:\mathrm{it}\:\mathrm{has}\:\mathrm{solution}\:\mathrm{in}\:\mathrm{it}.\:\mathrm{Should} \\ $$$$\mathrm{I}\:\mathrm{post}\:\mathrm{it}? \\ $$

Commented by ajfour last updated on 06/Aug/17

has it to come to stop and can i choose starting point on my own?

$$\mathrm{has}\:\mathrm{it}\:\mathrm{to}\:\mathrm{come}\:\mathrm{to}\:\mathrm{stop}\:\mathrm{and}\:\mathrm{can}\:\mathrm{i} \\ $$$$\mathrm{choose}\:\mathrm{starting}\:\mathrm{point}\:\mathrm{on}\:\mathrm{my}\:\mathrm{own}? \\ $$$$ \\ $$

Commented by ajfour last updated on 06/Aug/17

yes, post it.thanks.

$$\mathrm{yes},\:\mathrm{post}\:\mathrm{it}.\mathrm{thanks}. \\ $$

Commented by Tinkutara last updated on 06/Aug/17

Commented by Tinkutara last updated on 06/Aug/17

Commented by ajfour last updated on 06/Aug/17

this is even wrong, since no time is included to change speed.

$$\mathrm{this}\:\mathrm{is}\:\mathrm{even}\:\mathrm{wrong},\:\mathrm{since}\:\mathrm{no}\:\mathrm{time} \\ $$$$\mathrm{is}\:\mathrm{included}\:\mathrm{to}\:\mathrm{change}\:\mathrm{speed}. \\ $$

Commented by ajfour last updated on 06/Aug/17

not after class X .

$$\mathrm{not}\:\mathrm{after}\:\mathrm{class}\:\mathrm{X}\:. \\ $$

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