4.Two particles with mass m, and m2 are floating in space connected by amassless spring with spring constant k and relaxed length (. Do not neglect gravity in thisproblem!(a) Show that the total force on m, is given by the gradient of a potential energy function:F1(r1) = -V,Vi(r12).(1)where r12 = T12|, r12 = r1 - r2. Find Vi(r12).(b) Write the conserved energy for this system.(c) Now take m = m2 = m. The particles are initially a distance l apart, and eachhas an initial velocty to away from the other. Find the minimum value of zo such that theparticles never come back, if we neglect the spring. (This is the 'escape velocity' of theparticles.)(d) Now suppose that the particles are initially moving apart with the escape velocityyou found in part (c), but now don't neglect the spring. Set up an equation that determinesthe maximum separation of the two masses rmax in the subsequent motion. This will be acubic equation; do not attempt to solve it. (There is an analytic solution, but it is a mess.)

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