Question

A road heading due east passes over a small hill. You drive a car of mass m at constant speed v over the top of the hill, where the shape of the roadway is well approximated as an arc of a circle with radius R. Sensors have been placed on the road surface there to measure the downward force that cars exert on the surface at various speeds. The table gives values of this force versus speed for your car is shown in the table below. Treat the car as a particle.


Speed (m/s) 6.00 8.00 10.0 12.0 14.0 16.0
Force (N) 8100 7690 7050 6100 5200 4200

Answer 1

The downward force is divided as F = mg - mv^2/R or in linear form F = -m/R*v^2 + mg. The linear approximation gives m = 897 kg and R = 50 m.