A 4-wheeled trolley car has a total mass of 3000 kg . Each axle with its two wheels and gears has a total moment of inertia of $32 \mathrm{~kg} . \mathrm{m}^{2}$. Each wheel is of 450 mm radius. The centre distance between two wheels on an axle is 1.4 m . Each axle is driven by a motor with a speed ratio of $1: 3$. Each motor along with its gear has a moment of inertia of $16 \mathrm{~kg} . \mathrm{m}^{2}$ and rotates in the opposite direction to that of the axle. The centre of mass of the car is 1 m above the rails. Calculate the limiting speed of the car when it has to travel around a curve of $250-\mathrm{m}$ radius without the wheels leaving the rails.

Explanation

The total moment of inertia of the car is $I = (32 \times 4 + 16) \times 1.4 = 160.8 kg.m^2$. The total mass of the car is $m = 3000 kg$. The radius of the curve is $r = 250 m$. The limiting speed of the car is given by $v = \sqrt{\frac{2 \times 9.81 \times I \times v^2}{m \times r}}$. Rearranging this equation, we get $v = \sqrt{\frac{2 \times 9.81 \times (32 \times 4 + 16) \times 3.5}{(32 \times 4 + 16) \times 1.4}} = 2.43 m/s$.

Explanation

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