A 3220 lb car enters an Scurve at A with a speed of 60 mihr

A 3220 lb car enters an S-curve at A with a speed of 60 mi/hr with brakes applied to reduce the speed to 45 mi/hr at a uniform rate in a distance of 300 ft measured along the curve from A to B. The radius of curvature of the path at B is 600 ft. The road at B lies in a horizontal plan. a) How much time does it take to go from A and B? b) What is the total horizontal force experienced by the tires at point B?

Solution

a) To determine the Time taken for the car to travel along the distance of 300ft

consider the eqn of motion,

v = u +at where v - final velocity, u - initial velocity and t - time

s = ut - 1/2 at² where a - the deceleration of the vehicle

solving for t in the first eqn we get,

a = (v - u) / t replace it with a in the second eqn

s = u t - 1/2 (v-u)/t x t²

s =ut - 1/2 t solve for t we get,

t = 2s / (2u-1) replace with values,

t = 2x300 / (2x60x 1.46 - 1) = 3.44 secs

b) The centripetal acceleration is given by,

F = mv² / r ,

The total horizontal force at B is,

F_total = F_B

F_B = 3220 x 45² / 600 = 10867.5 lbf