InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A racing car travels on a track (without banking) ABCDEFA ABC is a circular are of radius ` 2 R.CD` and `FA` are strainght paths of length `R` and `DEF` is a circular are of radius `R=100m` The co- efficient of friction on the road is `mu = 0.1` The maximum speed of ther car is `50ms^(-1)` Find the minimum time for completing one round . |
|
Answer» As the track is unbanked the necessary centripetal force is provided by force of friction `(m upsilon^(2))/(r) = F = mu R = mu mg :. upsilon= sqrt(mu r g)` For path ABC : length `= (3)/(4) (2pi2R) = 3 pi R = 3 pi xx 100 = 300 pi m` `upsilon_(1)=sqrt(mu 2 Rg) = sqrt( 0.1 xx 2 xx 100 xx 10) = 14.14 m//s` `:. t_(1) = (300 pi)/(14.14) = 66.6s` For path DEF: length `= (1)/(4) (2pi R) = (pi xx 100)/(2) = 50pi` `upsilon_(2)=sqrt(muRg) = sqrt(0.1 xx 100 xx 10 )= 10 m//s` `t_(2) = (50pi)/(10) = 5 pi sec = 15.7 s` For paths `CD` and `FA` length `=R + R =2 R = 200 m` `t_(3) = (200)/(50) = 4.0 s` `:.` Total time for completing one round `t = t_(1) + t_(2) + t_(3) = 66.6 + 15.7 + 4.0 = 86.3 s`. |
|