All Problems The Fundamental Equation of Dynamics
Problem 1.116
A train of mass \(m=2000\) tons moves in the latitude \(\varphi\) \(=60^{\circ}\) North. Find: (a) the magnitude and direction of the lateral force that the train exerts on the rails if it moves along a meridian with a velocity \(v\) \(=54 \mathrm{~km}\) per hour; (b) in what direction and with what velocity the train should move for the resultant of the inertial forces acting on the train in the reference frame fixed to the Earth to be equal to zero.
1.116. (a) \(F=2 m v \omega \sin \varphi=3.8 \mathrm{kN},\) on the right rail; (b) along the parallel from the east to the west with the velocity \(v=\) \(=\frac{1}{2} \omega R \cos \varphi \approx 420 \mathrm{~km}\) per hour. Here \(\omega\) is the angular rotation velocity of the Earth about its axis, \(R\) is its radius.