The illustration shows a model of the device used in airplane
carriers to bring the airplane to a stop or to lunch it. The winch
cable used, it’s modeled by two springs with spring constant k ,
anchor points for the spring are distance equal to the width (w) of
the carrier. An airplane of mass M is brought to stop by stretching
the spring from the dashed line to point A.
Determine the force necessary (in terms of k,w,and x) to stop
the airplane at a distance x along the positive x-axis from the
dashed line.
Determine the amount of elastic potential energy (in terms of
k,w,and A) stored in the spring-plane system while stopping the
airplane.
EXTRA CREDIT: 10 pts. Determine the expression for the initial
velocity (v_0) of the airplane as it contacts the cable in terms of
k,w,A,and M.