A spring with a force constant of 50 N/m is stretched continuously from x_{0}=0 to x_{2}=20 cm. Is more work required to stretch the spring from x_{1}=10 cm to x_{2}=20 cm than from x_{0} to x_{1}? Justify your answer mathematically. I thought the work required is the same because the displacements are equal for both work equations... but I think I'm wrong.
work = 1/2 kx^2 so then the difference would be greater between 20cm and 10cm w= EPEf-EPEi = 0.5(k)400-0.5(k)100 = 150k w0->1 = 0.5(k)(100) - 0.5k(0) = 50k
no, the work is the difference between energies. [tex] EPE_i + W = EPE_f [/tex] [tex] W = EPE_f - EPE_i [/tex] [tex] W = 0.5kx_f^2 - 0.5kx_i^2 [/tex]