A car of mass travels with a constant speed along a road that first passes through a…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A car of mass m travels with a constant speed v along a road that first passes through a circular dip and immediately over a circular hump, each of radius R. Assume the dip and the hump are semicircular and lie in vertical planes. Neglect air resistance.
(i) Derive expressions for the normal reaction acting on the car at the lowest point of the dip and at the highest point of the hump in terms of m, v, R, and g.
(ii) Using the expressions obtained in part (i), calculate the numerical values of the normal reactions at the lowest and highest points for a car of mass 800kg moving at 18ms−1 over arcs of radius 40m, taking g=9.8ms−2.
(iii) Comment briefly on the practical implications of the difference in these two normal reactions for the comfort of the passengers.