PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Kinematics and Newtonian dynamics of particles · Lagrangian mechanics
Action and Symmetry, Ch Multipliers, non-holonomic constraints and forces outside the potential
Problem
A cyclist and her bicycle, of combined mass M=78kg, ride at a constant speed v=7.0ms−1 around a circular arc of radius rc=6.0m painted on level, dry tarmac, holding the bicycle exactly upright (no lean) throughout. Model the bicycle and rider together as the single upright rolling disc analysed for steady circular rolling: a body that rolls without slipping and needs a sideways (horizontal, perpendicular to its direction of travel) friction force from the road to supply its centripetal acceleration, this force being exactly the multiplier found for that motion. The road can supply at most a coefficient of static friction μmax=0.70 between tyre and tarmac, and the bicycle's own weight is negligible compared with the rider's.
((a)) Find the sideways friction force the road must supply to keep the bicycle rolling on this circle without slipping, holding it exactly upright.
((b)) Find the minimum coefficient of static friction this requires, and state, with a reason, whether the tarmac can supply it, and whether leaning the bicycle into the turn would change that.