Dynamics | Part IA, 2004

A lecturer driving his car of mass m1m_{1} along the flat at speed U1U_{1} accidentally collides with a stationary vehicle of mass m2m_{2}. As both vehicles are old and very solidly built, neither suffers damage in the collision: they simply bounce elastically off each other in a straight line. Determine how both vehicles are moving after the collision if neither driver applied their brakes. State any assumptions made and consider all possible values of the mass ratio R=m1/m2R=m_{1} / m_{2}. You may neglect friction and other such losses.

An undergraduate drives into a rigid rock wall at speed VV. The undergraduate's car of mass MM is modern and has a crumple zone of length LL at its front. As this zone crumples upon impact, it exerts a net force F=(Ly)1/2F=(L-y)^{-1 / 2} on the car, where yy is the amount the zone has crumpled. Determine the value of yy at the point the car stops moving forwards as a function of VV, where V<2L14/M12V<2 L^{\frac{1}{4}} / M^{\frac{1}{2}}.

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