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Discuss the bending of a cyclist in curves. |
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Answer» Solution :(i) Consider a cyclist negotiating a circular level road(not banked ) of radius r with a speed V about the center O as shown in figure. (ii) Let m be the mass of the system, which includes cycle and cyclist and C be the center of gravity of this system. (III) Let us consider horizontal is along x-axis and vertical is along Z-axis.  (IV) In this rotating frame, the centrifugal force `(mv^2)/ (r )`. acts away from center O and PASSING through the center of gravityC as shown below. (v) As the system is in rotational equilibrium, the net torque must be zero. Thus, `vectau_(" net ") =0` `-mgAB+(mv^2)/(r )BC=0`  (vi) Here, the clock wise moment (mg AB) is taken as negative and the anti clodkwise moment `((mv^2)/(r )BC)` is taken as positive. `mgAB=(mv^2)/(r )BC` (VII) But from `triangleABC, AB=AC sin theta"" & ""BC=AC cos theta`. Therefore, the above equation can be written as, `mg AC sin theta = (mv^2)/(r )AC cos theta` `tan theta = (v^2)/(rg)` `theta = tan^(-1)((v^2)/(rg))` (viii) It shows that while negotiating a circular road of radius r at velocity v, a cyclist has to bend an angle `theta` from vertical, to avoid a fall. |
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