Question

A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of `37^@` with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point `1.0 m` above the ground, `1.0 m` horizontally behind the axle of the front wheel, and `35.0` cm in front of the rear axle. Assume that the tires do not skid.

Answer 1

For stoping the cyclist should retard i.e, acceleration should be in the direction up the sloping surface. When the cyclist is one the point of tipping over forward, the normal force on the rear wheel is zero. Parallel to the plane we have `f_(1)-mgsintheta=ma.` Perpendicular to the plane `n_(1)-mgcostheta=0`. Torque about the centre of mass

`f_(1)(1.0m)=n_(1)(1.0m)` or `f_(1)=n_(1)`
From above equation we get `a=-2ms^(-2)`.