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Dynamics of a solid body

Problem 1.289

A locomotive is propelled by a turbine whose axle is parallel to the axes of wheels. The turbine's rotation direction coincides with that of wheels. The moment of inertia of the turbine rotor relative to its own axis is equal to I=240 kg⋅m2I=240 \mathrm{~kg} \cdot \mathrm{m}^{2}. Find the additional force exerted by the gyroscopic forces on the rails when the locomotive moves along a circle of radius R=250 mR=250 \mathrm{~m} with velocity v=v= =50 km=50 \mathrm{~km} per hour. The gauge is equal to l=1.5 m.l=1.5 \mathrm{~m} . The angular velocity of the turbine equals n=1500n=1500 rpm.

Reveal Answer
1.289. Fadd=2πnIv/Rl=1.4kNF_{a d d}=2 \pi n I v / R l=1.4 \mathrm{kN}. The force exerted on the outside rail increases by this value while that exerted on the inside one decreases by the same value.
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