A race car accelerates uniformly as it leaves the pit area, going from rest to 3
ID: 1334827 • Letter: A
Question
A race car accelerates uniformly as it leaves the pit area, going from rest to 320 km/h in a semicircular arc (i.e. 1/2 of a circle) with a radius of 192 m. Determine the tangential acceleration of the car when it is halfway through the turn (i.e. 1/4 of a circle), assuming constant tangential acceleration
Determine the radial acceleration of the car at this time (when it has traveled 1/4 of a circle).
If the curve were flat, what would the minimum coefficient of static friction between the tires and the roadbed have to be in order to provide the total acceleration with no slipping or skidding when the car has traveled halfway through the turn?
Explanation / Answer
final speed = 320 km/hr =320x 1000 m / 3600s =88.89 m/s
car goes from 0 to 88.89 m/s in pi R distance.
using , v^2 - u^2 =2ad
88.89^2 - 0 = 2 x a x (pi x 192)
a =6.55 m/s^2 ......................Tangential acc.
when car is halfway the turn
upto then distance d = pi x R/2 = 301.59 m
using v^2 - u^2 = 2ad
v^2 - 0 = 2 x 6.55 x 3101.59
v = 62.86 m/s
radial acc. = v^2 / R = 62.86^2 / 192 = 20.58 m/s^2 .............Ans
to prevend car from skidding ,
radial force = friction
mv^2 /R = u mg
ug = v^2 / R
u x 9.81 = 20.58
u = 2.1