Answer :
The work required to compress the spring 4.00 cm from its unstretched length would be 4.75 J, as it is one fourth of the work done to stretch it 8.00 cm.
The concept being asked about in the student's question relates to the work done on a spring and how it relates to the displacement from its equilibrium position, based on Hooke's Law. Given that 19.0 J of work is done to stretch the spring 8.00 cm, to find the work needed to compress the same spring 4.00 cm from its unstretched length, we can use the formula for the elastic potential energy stored in a spring, U = 1/2 kx2.
Since the work required to stretch or compress the spring is proportional to the square of the displacement (x), if the spring is compressed to half the original stretching distance (from 8.00 cm to 4.00 cm), the work done will be one fourth of the original work because (4.00 cm / 8.00 cm)2 = 1/4. Therefore, the work to compress the spring 4.00 cm is 1/4 of 19.0 J, which calculates to 4.75 J.
