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# Question 3a: 2015 AP Physics 1 free response

Graphing energy versus position for a block accelerated by a spring and stopped by friction.

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• why wouldn't potential energy increase after D=0? At 3D, isn't the spring stretched completely, and ,therefore, storing energy? • I had the same issue you're having, but I realized that the spring and the block are not connected. Since the spring has negligible mass it can be assumed that it stops around the time it hits the equilibrium (x=0) and the block keeps going but decelerates because of friction.
• Wouldn't the kinetic energy from 0 to 3D be curved, because velocity is linear but kinetic energy is proportional to velocity squared, and squared linear is not linear? • Since the block will no longer be in contact with the spring at x=0, the only force acting on the block after this position is the force of friction which is CONSTANT throughout. After this it can be easily deduced why the Kinetic energy vs position graph will be linear:
From 3rd equation of motion,
'v^2-u^2=2as
Or -u^2/2a=s (since final velocity v will ultimately be 0 )
Or -u^2 is directly proportional to distance covered
Or (-m/2)*u^2 is proportional to distance covered', which means that kinetic energy is directly proportional to distance covered. One must remember that this is an energy vs position graph.  