Two identical spheres, Sphere 1 and Sphere 2, each of mass \(m\), slide horizontally across a frictionless floor toward a fixed vertical wall with the same initial speed \(v_0\). Sphere 1 collides elastically with the wall, rebounding in the opposite direction with speed \(v_0\) during a contact time interval of duration \(2\Delta t_0\). Sphere 2 collides inelastically with the wall, coming completely to rest and sticking to the wall during a contact time interval of duration \(\Delta t_0\). Which of the following correctly compares the magnitude of the average force \(\bar{F}_1\) exerted by the wall on Sphere 1 to the magnitude of the average force \(\bar{F}_2\) exerted by the wall on Sphere 2, and provides the correct physical justification?