Problem

One end of a seat belt on passenger cars is wound around a ratchet wheel that can be locke...

One end of a seat belt on passenger cars is wound around a ratchet wheel that can be locked when the deceleration of the car exceeds a set value. In the sketch shown, consider a ratchet wheel that can rotate about the fixed point A. The ratchet wheel has cogs and is positioned above a weight. The weight can pivot about point B and is rigidly connected to a pawl that, for a sufficiently large rotation, will lock the motion of the ratchet wheel. Research realistic dimensions for the ratchet wheel, and design a locking mechanism such that the belt’s motion will be stopped for horizontal decelerations greater than 0.5g, where g is the acceleration due to gravity. In your design you may use a spring to limit the motion of the weight.