In a car race, the first turn of the track is close to the start line. At the be
ID: 1441063 • Letter: I
Question
In a car race, the first turn of the track is close to the start line. At the beginning of the race, a race car accelerates along a straightaway from rest with a constant acceleration a until it reaches the first turn, 100 m away from the starting point. At that point, the car travels with constant speed around the turn. The radius of the turn is 50 m and the turn is banked at an angle of 30 degree . The coefficient of static friction between the car's tires and the road surface Ls fia = 0.8. What is the maximum value of a so that the car can make the turn maintaining a constant radius of 50 in without sliding outward? You can use g = 10 m s-2 for this problem.Explanation / Answer
First we need to find the constant velocity which is required to safely complete the turn on banked road.
Using ,
tan 30 = v2/rg
v= velocity r=radius , g=9.8
solving, we get v= 16.819 m/s
this is the final velocity, now we can use equation of motion,
v2- u2 = 2 a s
here v= 16.819 , u=0 , s=100 m , a=?
So solving above equation we get, a=1.414 m/s2