For a train traveling at 160 km /h around a horizontal curve of radius 1.9 km, calculate...

For a train traveling at 160 km /h around a horizontal curve of radius 1.9 km, calculate the elevation angle β of the track so that passengers will feel only a force normal to their seats and the rails will exert no side thrust against the wheels, as indicated in part (a) of the figure. An experimental train rounds this same curve at a speed of 260 km /h with cars which are automatically tilted an angle Θ with respect to the rails, as shown in part (b) of the figure. This angle reduces the side thrust F felt by the passengers. Determine the tilt angle _ required to limit F to 30 percent of the side thrust they would feel if both Θ and β were zero.