A highschool student is driving in an empty parking lot They

A highschool student is driving in an empty parking lot. They have the wheel locked at constant angle so that the car follows a circular arc with a radius of curvature of 75m. The speedome- ter increases at a constant rate from 20mph to 30mph in 5 seconds. At the end of the 5 seconds what is the component of the acceleration i) in the front/rear direction and ii) the side/side direction. If the student has a cup of coffee in a cup with 1cm of space at the top and the cup has a radius of 2cm, will the coffee spill? (Assume the base of the cup remains completely horizontal and that the suspension does not allow chassis of the car does not tilt.)

Solution

GIVEN:- Radius of curvature R = 75m, V1 = 20mph = 8.94m/s, V2 = 30mph = 13.41m/s, t = 5s

SOLUTION:-

(i) Component of acceleration in the front/rear direction of the car means linear accleration At = V2-V1/t

i.e. At = (13.41 - 8.94) / 5 = 0.894 m/s2 (ANSWER)

(ii) Side/Side direction means Centrifugal / Centripetal acceleration As = V2^2 / R

i.e. As = 13.41^2 / 75 = 2.4 m/s2 (ANSWER)

(iii) By the banking of road concept, if we apply it to the cup of coffee, we get the below result---

By formula V2^2 / (Rxg) = h / b (where b = 2r = 2x2 = 4cm = 0.04m and h =height of banking)

So 13.41² / (75x9.81) = h / 0.04 i.e. h = 0.009m = 0.97 cm

So by result h = 0.97cm < 1 cm (ANSWER) SO THE COFFEE WILL NOT SPILL (ANSWER)