A car moves at constant speed on a straight but hilly road

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A car moves at constant speed on a straight but hilly road. One section has a crest and a dip, each of radius 250 m250\,\text{m}. (1) As the car passes over the crest, the normal force on the car is half its 16 kN16\,\text{kN} weight. What is the normal force on the car as it passes through the bottom of the dip? (2) What is the greatest speed at which the car can move without leaving the road at the top of the hill? (3) Moving at the speed found in part (b), what is the normal force on the car as it moves through the bottom of the dip? Take g=10 m s−2g=10\,\text{m s}^{-2}.

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